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Does not execute original native C++ matching.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 104, "source_commit": "948ce1510df750f4c18b96bdaef436a86f8bf834", "certificate_file": "pr104-odd21-finite-controller-early-upper.json", "certificate_sha256": "e93030415b91ba323b0030c9bc327196f6cfdb72c3b5382f4d9c9d923d8eb468", "peer_review_file": "pr104-odd21-finite-controller-peer-review.json", "peer_review_sha256": "035e9ebb1dd5f6620f6527f14462f893badfdc61e5f86a3ae9548c70e416100f", "proof_file": "early-odd21-finite-uppers.md", "family_kind": "own-odd21-finite-controller-with-retained-native-producer-contract", "program_fingerprint": "5bcf00402bbfb768bd2fc0935f32ad329ee0780a3dfe5827bb010831d7909c4d", "program_fingerprint_scope": "Exact own selected complex input and own producer source; original C++ matching/scalar/frame engine not rerun and remains explicit correctness premise.", "invoice_fingerprint": "b52a9f7b11a813d9d503b3694f00a66d31201ace6d442147e932e8b6fcce6e53", "invoice_fingerprint_scope": "Complete own finite G/E/C0/C1 and stock certificate reproduced by untouched arithmetic producer, with same allnumerical/contract fields and transparent source-digest inventory difference.", "params_fingerprint": "0ca8ca83b194edd6ecef65226d61156347d0903f960c628f193f44e91b4f560c", "effective_kappa": "1/100000", "kappa_record": "194869/2500000000", "native_coordinate_rank": 576, "uniform_rank_H": null, "upper": { "input_bits": "2^(2^281475047079400177656)", "exact_log2log2_integer": "281475047079400177656", "source": "data/operation-audit/pr104-odd21-finite-controller-early-upper.json", "scope": "Conditional sufficient upper at weaker earlysaving1e-5, own odd21 interface. Original C++ native correctness and unquantified originalrecord sameXAG hybrid are extra retained premises.", "exact_individual_crossing": false }, "record_tail_quantified": false, "lower": null, "scope": [ "Own original C++ scalar/frame/matching producer, absolute phase, normalized-wrapper, whole-job and owned/spectator correctness; not freshly replayed here.", "Own exact common21-odd grid, completed Gaussian-dyadic endpoint/new-child odd divisibility, C1=1 and all-size/common-label realization.", "Gaussian/fine-prime/finite-section/boundary/recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility requires an extra same-XAG realization contract; no numerical original-tail bound." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "early_odd21_finite_uppers.py" ] ], "offline_verification_commands": [ [ "early_odd21_finite_uppers.py" ] ], "offline_verification_scope": "Fresh fixed21 circuit/own finite/outer/whole-tail checks, binding own source arithmetic replay. Does not execute original C++ native engines.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 115, "source_commit": "cf60442983c153a3a0f5272ea4713f99eba13c86", "certificate_file": "pr115-odd21-partial-gauge-finite-early-upper.json", "certificate_sha256": "3a315ca4f88c2cff2b8eef038efe23376f4838d283543836ed2f656757e44a66", "peer_review_file": "pr115-odd21-partial-gauge-finite-controller-peer-review.json", "peer_review_sha256": "d795a73c4c395ba1a28ae49239bec1cbcf3faf12fb75b1e4b9e15b8f9bd754cd", "proof_file": "pr115-odd21-finite-upper.md", "family_kind": "own-partial-gauge-odd21-finite-controller-with-retained-native-producer-contract", "program_fingerprint": "05e3b07a16910775a5fb96c6e4bd4aa87173d370e75cb14cf535f70a4462189e", "program_fingerprint_scope": "Exact own partial-gauge source/native input and fixedodd21 contract; unchanged own arithmetic freshly replayed, original CPP native matching not rerun.", "invoice_fingerprint": "4c042930e44ba9be7b2765807ddf2786eeb00697e6084e82448b9298534b5f71", "invoice_fingerprint_scope": "Whole own partial-gauge G/E/C0/C1 and40000degree stock regenerate through unchanged actual own arithmetic producer; source-digest inventory difference disclosed.", "params_fingerprint": "cd31f08f82ff7f72be7a8d79fa134fcd2752cede4bd1022a53872b8edd7f7490", "effective_kappa": "1/100000", "kappa_record": "7237/78125000", "native_coordinate_rank": 576, "uniform_rank_H": null, "upper": { "input_bits": "2^(2^281475047079400177656)", "exact_log2log2_integer": "281475047079400177656", "source": "data/operation-audit/pr115-odd21-partial-gauge-finite-early-upper.json", "scope": "Conditional own partial-gauge sufficient upper at weak saving1e-5, with full40000Qstopped stock and fixedodd21 interfaces; no meaningful lower/quantifiedoriginaltail.", "exact_individual_crossing": false }, "record_tail_quantified": false, "lower": null, "scope": [ "Own original C++ scalar/frame/matching producer, absolute phase, normalized-wrapper, whole-job and owned/spectator correctness; not freshly replayed here.", "Own exact common21-odd grid, completed Gaussian-dyadic endpoint/new-child odd divisibility, C1=1 and all-size/common-label realization.", "Gaussian/fine-prime/finite-section/boundary/recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires an own same-XAG realization contract; numerical original-record tail remains unquantified." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "pr115_odd21_finite_upper.py" ] ], "offline_verification_commands": [ [ "pr115_odd21_finite_upper.py" ] ], "offline_verification_scope": "Fixed21 circuit, own partial-gauge finite profile/moment/ordinaryBIT/outer/whole-tail checks; original CPP native matching not executed.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 130, "source_commit": "6a9970a530119174507904e23592fd59ede19a5d", "certificate_file": "pr130-odd21-finite-controller-early-upper.json", "certificate_sha256": "615adb8c2b821e8a616713edb5a552ae249e48d68f2b92f97f0d80b43afe4e5d", "peer_review_file": "pr130-odd21-finite-controller-peer-review.json", "peer_review_sha256": "a35ec547e48b8a7233ea15fad345b609593e9cc9535d4493c13ddb113f6a03e6", "proof_file": "early-odd21-finite-uppers.md", "family_kind": "own-odd21-finite-controller-with-retained-native-producer-contract", "program_fingerprint": "afecf8ce2d8eb259074e61cd0c386b464ca2f57c61b00979eac808fa26e0b770", "program_fingerprint_scope": "Exact own selected complex input and own producer source; original C++ matching/scalar/frame engine not rerun and remains explicit correctness premise.", "invoice_fingerprint": "aed306af23c82d89d57ffa72aa55a57bbc63f96c4386fe782c7c35733329ba3e", "invoice_fingerprint_scope": "Complete own finite G/E/C0/C1 and stock certificate reproduced by untouched arithmetic producer, with same allnumerical/contract fields and transparent source-digest inventory difference.", "params_fingerprint": "f98306f2954c47717776d2e10b9810306e85b5977c839958d7c7612ca492317e", "effective_kappa": "1/100000", "kappa_record": "3146011/10000000000", "native_coordinate_rank": 70, "uniform_rank_H": null, "upper": { "input_bits": "2^(2^281475047079400177656)", "exact_log2log2_integer": "281475047079400177656", "source": "data/operation-audit/pr130-odd21-finite-controller-early-upper.json", "scope": "Conditional sufficient upper at weaker earlysaving1e-5, own odd21 interface. Original C++ native correctness and unquantified originalrecord sameXAG hybrid are extra retained premises.", "exact_individual_crossing": false }, "record_tail_quantified": false, "lower": null, "scope": [ "Own original C++ scalar/frame/matching producer, absolute phase, normalized-wrapper, whole-job and owned/spectator correctness; not freshly replayed here.", "Own exact common21-odd grid, completed Gaussian-dyadic endpoint/new-child odd divisibility, C1=1 and all-size/common-label realization.", "Gaussian/fine-prime/finite-section/boundary/recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility requires an extra same-XAG realization contract; no numerical original-tail bound." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "early_odd21_finite_uppers.py" ] ], "offline_verification_commands": [ [ "early_odd21_finite_uppers.py" ] ], "offline_verification_scope": "Fresh fixed21 circuit/own finite/outer/whole-tail checks, binding own source arithmetic replay. Does not execute original C++ native engines.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 144, "source_commit": "c8b22bc5c10dba497ac25804e27d9647d818e2ff", "certificate_file": "pr144-finite-controller-early-upper.json", "certificate_sha256": "c79094fc8983bd3e4850a111d777146752e4e07652d589a72a327fd130803eb7", "peer_review_file": "pr144-finite-controller-peer-review.json", "peer_review_sha256": "b67aaa956386019fc40d9bb61c78a6efa86af7927505e1d2c3b12774c8089bcf", "proof_file": "pr144-finite-controller-upper.md", "family_kind": "own-rank72-paired-cube-finite-controller", "program_fingerprint": "11894aa8fd4d5e258ec534726eba5fc9c9fa7b826f993e229425c31ee2ad2440", "program_fingerprint_scope": "Exact own selected complex specification and own source producer, freshly rebuilt and checked atPR144; no native algorithm equality inferred fromkappa.", "invoice_fingerprint": "686edf015b6d036f2ae48be2dc5109ccf3ff669932346458e90c6528463147bf", "invoice_fingerprint_scope": "Own complete finite bridge code/input is byteidentical to namedlemma and allW/s/G/E/C0/rowstock recomputed fresh; native/analytic implementation interfaces remain explicit.", "params_fingerprint": "c4f076f5fdaaf62bece90108710a64143d9cb82e2481686df7ba241873a6a6a5", "effective_kappa": "1/5000", "kappa_record": "4609169/10000000000", "native_coordinate_rank": 72, "uniform_rank_H": null, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr144-finite-controller-early-upper.json", "scope": "Own conditional sufficient upper at weaker earlyexponent1/5000; originalrecord compatibility needs extra sameXAG contract with unquantifiedtail.", "exact_individual_crossing": false }, "record_tail_quantified": false, "lower": null, "scope": "['Own native/full-group/arbitrary-column scalar and absolute-phase identities, sharing and complete spectator/owned restoration.', 'Own source unequal-child batching, once-only padding, fixed odd-grid and completed-child semantic C1=1 interfaces.', 'Parameterized Gaussian/fine-prime/finite-section/boundary/recovery analytic branch.', 'Exact fixed small-rational and odd-grid fixed-divisor conversion conditions, including endpoint divisibility and stored-width guards.', 'Unchanged optimized-GMP finite-native correctness/halting and model contracts.', 'Original-record asymptotic compatibility requires an extra retained same-XAG realization contract; no numerical original-tail bound is supplied.'] Supplemental75-guard replay corrects the earlier extracted-function argument-order evidence; every guard passes and the cutoff is unchanged.", "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "pr144_finite_controller_upper.py" ], [ "pr144_source_guard_supplement.py" ] ], "offline_verification_commands": [ [ "pr144_finite_controller_upper.py" ], [ "pr144_source_guard_supplement.py" ] ], "offline_verification_scope": "Recomputes own finite interface/outer rows and verifies allownsource andfreshproducerreceipt hashes; original31.8s nativeproducer replay is separately supplied.", "source_peer_review_file": "pr144-source-guard-supplement-peer-review.json", "source_peer_review_sha256": "2fb3402d2c7d7e8f23546d0679696406e51c942f76cbb826431bc717c2add454", "source_guard_supplement": { "file": "pr144-source-guard-supplement.json", "sha256": "2252e7d47c308609ada731e64f2b9c7114773f099c12bdf736960d84cdf84888", "scope": "Correctly ordered75-source-guard replay supplements the earlier extracted-function adapter argument-order defect. All guards pass and complete native/finite values and cutoff remain unchanged. Original untouched full producer also passed." }, "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 147, "source_commit": "29383a28d96b9880edbe59ed930f1da1dd6fdfa6", "certificate_file": "pr147-finite-full-cover-range.json", "certificate_sha256": "faafc1f40e403815f5709c67c0f8401b1abf169974c5181fb6b299d82b396642", "peer_review_file": "pr147-finite-full-cover-range-peer-review.json", "peer_review_sha256": "b49eea3b5b3bc6f12873a2a76549820ce894d02bd02396d9c4bf361c47133a49", "source_peer_review_file": "pr147-finite-full-cover-source-peer-review.json", "source_peer_review_sha256": "aa0cba459675c43765712a2a69f1b15dfc8d6b6372688f44d00b9799579e42f6", "proof_file": "finite-full-cover-literal-lowers.md", "family_kind": "finite-literal-complete-cover-source-core", "effective_kappa": "1/5000", "kappa_record": "4646633/10000000000", "native_coordinate_rank": 72, "uniform_rank_H": null, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr147-finite-full-cover-range.json", "scope": "Existence of the bound counted literal early Gaussian schedule above its verified domain; this is not an upper for every switching policy.", "exact_individual_crossing": false }, "lower": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 85, "input_bits": "2^85", "plot_triple_log": { "exact_log2_integer": 85, "expression": "log2(log2(85))" }, "scope": "Declared explicit EARLY Gaussian unreduced complete finite-cover literal enhancement family: every active native word retains every group vertex and full field coordinate with paid ADD lowering and no pruning/aggregation/bypass; if no native word is used the output branch is exactly the same optimized GMP reference. All switching policies are included. The optional original-record/min-total hybrid and every other implementation are excluded; the early effective exponent is1/5000.", "source": "data/operation-audit/pr147-finite-full-cover-lower.json", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source_explanation": "Own PR147 mandatory complete O(72,2) cover and actual producer binary additions, compared with the independently closed same-reference compact upper." }, "lower_certificate_file": "pr147-finite-full-cover-lower.json", "lower_certificate_sha256": "4b615474237d991c223e95127f295a30793c5d8c2147b5a4cc9075ee19fd49ac", "record_tail_quantified": false, "necessary_lower_quantifier": "all_valid_literal_family_public_policies", "sufficient_upper_policy": "the_bound_counted_early_schedule_above_its_verified_domain", "upper_not_for_all_switching_policies": true, "source_base_upper_certificate": "pr147-finite-gate-refined-upper.json", "source_base_upper_certificate_sha256": "ff002893d9f467bf1d310a24c6b8a17a7a68a859d9a271f8766a60985ff1cae2", "baseline_upper_refinement_file": "optimized-gmp-degree8-compact-upper.json", "baseline_upper_refinement_sha256": "2bad0e4989947e2ef601613c1ad49ba54088c83a4827fd2feacb9f5b69c24956", "baseline_refinement_scope": "Necessary lower calculation only; reference algorithm and old sufficient upper certificate are unchanged.", "scope": [ "Original scalar/frame identities, completed-core sharing, ambient O(72,2) realization, uniform recursion, analytic precision/recovery and fixed-tape contracts remain original source assumptions. No full native replay or Lean proof is claimed.", "Declared explicit EARLY Gaussian unreduced complete finite-cover literal enhancement family: every active native word retains every group vertex and full field coordinate with paid ADD lowering and no pruning/aggregation/bypass; if no native word is used the output branch is exactly the same optimized GMP reference. All switching policies are included. The optional original-record/min-total hybrid and every other implementation are excluded; the early effective exponent is1/5000.", "Fixed real ADD word width at least two and the stipulated unreduced truncated addition subnetworks; full word and every physical coordinate remain present.", "Declared explicit EARLY Gaussian unreduced complete finite-cover literal enhancement family: every active native word retains every group vertex and full field coordinate with paid ADD lowering and no pruning/aggregation/bypass; if no native word is used the output branch is exactly the same optimized GMP reference. All switching policies are included. The optional original-record/min-total hybrid and every other implementation are excluded; the early effective exponent is1/5000.", "The explicit full-cover early circuit only. Its full source elementary charge is retained without dividing byW; corrected/refined rows fund the same full producer and complete field coefficient volume. Original-record/min-total hybrid branch is not in this lower family." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "finite_full_cover_literal_lowers.py" ], "reproduction_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "finite_full_cover_literal_lowers.py" ] ], "offline_verification_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "finite_full_cover_literal_lowers.py" ] ], "offline_verification_scope": "Fresh source/control/opcode/native component checks, same-reference degree8 induction and own literal-family lower/upper compatibility. No expensive original universal native/phase pipeline is asserted by these jobs.", "record_certificate_file": null, "record_P": null, "unquantified_original_record_tail": true, "original_record_hybrid_included": false, "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "conditional_finite_source_upper_only", "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr147-finite-gate-refined-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": "Corrected own PR147 finite-controller weaker branch with fully paid stopped-child reserve. Optional record preservation additionally retains original same-XAG realization; no quantified original tail, meaningful lower or actual crossing. The current numerical upper additionally uses the independently checked integral gate refinement." }, "meaningful_lower_bound": null } }, { "pr": 149, "source_commit": "6aed8701e3e3102898c66b5dcfc28d3cfc264edc", "certificate_file": "pr149-finite-controller-early-upper.json", "certificate_sha256": "558bbed9ea5bbbf1ded6b4b139c473f23dd847495e891a8138693cf6f17a7149", "peer_review_file": "pr149-finite-controller-peer-review.json", "peer_review_sha256": "1481a231a4db82ff62995ca69d13b5e527332655176b2de8dcaab5f18377d2c7", "proof_file": "pr149-finite-controller-upper.md", "family_kind": "own-integrated-paired-cube-finite-controller", "program_fingerprint": "f896f429f82fd3009bcef463388e6f8c141e2923c9790d30d05c343c907c3830", "program_fingerprint_scope": "Own38source bindings and freshly unchanged selected scalar/frame/physical producer, correctly ordered source guard replay; no equal-kappa algorithm inference.", "invoice_fingerprint": "555558e3bfd03bb227e384763dee225f2563f769ca42e7d302ad1606f469d1e4", "params_fingerprint": "c4f076f5fdaaf62bece90108710a64143d9cb82e2481686df7ba241873a6a6a5", "effective_kappa": "1/5000", "kappa_record": "4609169/10000000000", "native_coordinate_rank": 72, "uniform_rank_H": null, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr149-finite-controller-early-upper.json", "scope": "Conditional own integrated paired-cube upper at weaker saving1/5000, full70000Q stopped stock; no lower or original-record numerical tail.", "exact_individual_crossing": false }, "record_tail_quantified": false, "lower": null, "scope": [ "Own native/full-group/arbitrary-column scalar and absolute-phase identities, sharing and complete spectator/owned restoration.", "Own source unequal-child batching, once-only padding, fixed odd-grid and completed-child semantic C1=1 interfaces.", "Parameterized Gaussian/fine-prime/finite-section/boundary/recovery analytic branch.", "Exact fixed small-rational and odd-grid fixed-divisor conversion conditions, including endpoint divisibility and stored-width guards.", "Unchanged optimized-GMP finite-native correctness/halting and model contracts.", "Optional original-record asymptotic preservation requires own original-record same-XAG realization; original-record numerical tail remains unquantified." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "pr149_finite_controller_upper.py" ] ], "offline_verification_commands": [ [ "pr149_finite_controller_upper.py" ] ], "offline_verification_scope": "Own selected record/input/constants/profile/moment/finite stock/outer/full-tail checks; binds fresh unchanged original Python native producer. 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Gzip container serialization is disclosed separately; complete mathematical payloads must agree.", "invoice_fingerprint": "cb229f879514cdaded0954e4d63f2fd6110f777d6cb18a3aaa5ae3f29f1d0a67", "invoice_fingerprint_scope": "Fresh unchanged own complete40,320wholeowner/72call and independentraw/invoice replay; no priorinvoice substitution.", "params_fingerprint": "356d7da44955ce90bca36dcab90a6e54b98b9d5810d3f33d8862481e7c3be35b", "effective_kappa": "1/5000", "kappa_record": "182243220215421/125000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "operator_phase_proved": false, "fresh_source_finite_phase_replay_completed": true, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr523-punctured-gaussian-early-upper.json", "scope": "Conditional own punctured112 directGaussian eventualupper in same XAG/unlimitedoptimizedGMP model; fresh finite sourcephase/owner/invoice replay does not discharge allsize/analytic contracts.", "exact_individual_crossing": false }, "record_certificate_file": "pr523-punctured-gaussian-record-upper.json", "record_certificate_sha256": "5a3828497995b7aa9f202dec348d381fb339ecf398e73b50528483652d72bc90", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "record_tail_scope": "New counted directGaussian realization of same selected punctured112 core, not literal historical dual-supplier replay.", "lower": null, "scope": [ "Own exact required-entry/output all-column native phase realizations, complete row covers/common-label mutable-basis interfaces, owned erasure and all-size compiler semantics. Fresh14-stage replay checks finite native/frame/phase/owner/invoice/outer source implementations; universal analytic/physical interfaces remain hypotheses.", "Concrete normalized Gaussian/finite-LDU/narrow-gap/cyclic-border/fine-prime/exact-recovery and fixed repaired optimized-GMP correctness/halting contracts.", "New direct Gaussian/Fermat circuit realization of the exact selected punctured112 source core. Original optional493ordinaryBIT construction is not consumed or asserted freshly replayed." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "pr523_punctured_gaussian_upper.py" ] ], "offline_verification_commands": [ [ "pr523_punctured_gaussian_upper.py" ] ], "offline_verification_scope": "Deterministic513-check source/receipt/native/physical/invoice/moment/finitework/reducedledger/allcostgate replay. Optional unchanged fullsource reconstruction took861.5s; retained allsize/analytic interfaces remain conditional.", "broader_discovery_reproduction": [ "replay_pr523_full_source.py" ], "broader_discovery_scope": "Optional fullnative/phase/owner/invoice source reconstruction; writes a new timing-bearing execution receipt and regenerated containers, not the deterministic numeric-cost certificate.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 533, "source_commit": "6ad231bea07da57e94dbe4062bd045941db3287e", "certificate_file": "pr533-legacy-kernel92-literal-cover-range.json", "certificate_sha256": "ea42caea6db243b2ddb14dd4f18309fa9551b19733658ba2b261f907ff32120d", "peer_review_file": "pr533-legacy-kernel92-literal-cover-range-peer-review.json", "peer_review_sha256": "78b4c5ae8864adbe9547ef68c5b1ed2ce5bcffba553340330f56adf871ea67e3", "source_peer_review_file": "pr533-legacy-kernel92-literal-cover-range-source-peer-review.json", "source_peer_review_sha256": "717a1e558c9f1b2a3e34315d2cc68a233eecddf6caad35499b643ca63f83bfa0", "proof_file": "legacy-kernel92-literal-cover-ranges.md", "family_kind": "finite-literal-complete-cover-source-core", "effective_kappa": "1/5000", "kappa_record": "381051987698311/250000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr533-legacy-kernel92-literal-cover-range.json", "scope": "Existence of the same own counted literal early Gaussian schedule throughout its verified domain; no upper for every switching policy.", "exact_individual_crossing": false }, "lower": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public switching policies for this own source-selected literal complete O(73,2) cover enhancement: keep one actual selected public real ADD at every cover vertex with guarded width>=2 and the stipulated ADD lowering; no pruning, CSE, compression, aggregation or native bypass. A branch without such a native invocation is the identical fixed GMP reference. This added inactive rule is a comparison-family definition, not an original source fact. No other implementation or original BIT composition is covered.", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source": "data/operation-audit/pr533-open-legacy-literal-cover-lower.json" }, "lower_certificate_file": "pr533-open-legacy-literal-cover-lower.json", "lower_certificate_sha256": "0a76ee76d1538ab3332d62f1af4db838c6341d81c775faab39ed33be1c11c8b8", "source_base_upper_certificate": "pr533-legacy-kernel92-finite-early-upper.json", "source_base_upper_certificate_sha256": "42ad9073d49cc57fd74a9c56958c6af032b7683444c31acf0d907dc33b460327", "native_certificate_file": "pr533-legacy-kernel92-finite-native.json", "native_certificate_sha256": "d8a298aa1e887861c4de1b520c3535f940aac3750895e6ef02ab619036f376ea", "record_certificate_file": "pr533-legacy-kernel92-finite-record-upper.json", "record_certificate_sha256": "d0ef0f84bfc106eec775936be28f8df4dba74c278c381679ab15856dc3a88fef", "record_P": "230584301497830147503423480", "record_tail_input_bits": "2^(2^230584301497830147503423480)", "record_tail_quantified": true, "record_tail_policy": "the_bound_counted_same_core_record_schedule_above_its_separately_verified_domain", "necessary_lower_quantifier": "all_valid_literal_family_public_policies", "sufficient_upper_policy": "the_bound_counted_early_schedule_above_its_verified_domain", "upper_not_for_all_switching_policies": true, "baseline_upper_refinement_file": "optimized-gmp-degree8-compact-upper.json", "baseline_upper_refinement_sha256": "2bad0e4989947e2ef601613c1ad49ba54088c83a4827fd2feacb9f5b69c24956", "baseline_refinement_scope": "Sharper bound on the same fixed reference supports the necessary prefix. The separately closed own lower and813-check sufficient certificates remain unchanged.", "scope": [ "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "Own selected native all-input Gaussian/helper endpoints, exact physical entry/output frames and absolute phases, normalized residual wrappers and identity spectators remain substantive universal interfaces. Actual finite local phase/source checks strengthen the evidence but do not prove arbitrary all-size operator identities.", "Own common-label/mutable-basis owned restore, normalized completed-child semantic height, all-size compiler/occupied-row/stock/tape and analytic recovery remain conditional. The bounded73-axis binary-affine/even-quadratic-Z4 finite-phase grammar is required for the charged universal compiler tariff.", "Actual own constructor/kernel controls, native scalar/frame/wrapper and every finite local phase edge/endpoint, complete owner emitter plus seven mutations and fresh invoice with no retained prior allowance were executed. Original full global CLI, unchanged global data-phase replay and original BIT runtime are not claimed.", "This newly counted direct Gaussian/Fermat circuit uses the exact own selected source body and literal complete finite cover. No source equivalence, previous upper threshold, prior invoice or fabricated BIT saving is consumed. The fixed fallback density tax, per-coefficient40e fallback and full u^(1000000Q) stopped reserve remain paid in all seven operation rows.", "All valid public switching policies for this own source-selected literal complete O(73,2) cover enhancement: keep one actual selected public real ADD at every cover vertex with guarded width>=2 and the stipulated ADD lowering; no pruning, CSE, compression, aggregation or native bypass. A branch without such a native invocation is the identical fixed GMP reference. This added inactive rule is a comparison-family definition, not an original source fact. No other implementation or original BIT composition is covered.", "All valid public switching policies for this own source-selected literal complete O(73,2) cover enhancement: keep one actual selected public real ADD at every cover vertex with guarded width>=2 and the stipulated ADD lowering; no pruning, CSE, compression, aggregation or native bypass. A branch without such a native invocation is the identical fixed GMP reference. This added inactive rule is a comparison-family definition, not an original source fact. No other implementation or original BIT composition is covered.", "Exact same own literal selected programme and full-cover body; complete new group invoice pays it. Both early and record domains separately imply a nonempty native H row above the full1e6Q stopped base. Lower forall policies and constructive upper exists schedule remain distinct." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "legacy_kernel92_literal_cover_ranges.py" ], "reproduction_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "open_legacy_literal_cover_lowers.py" ], [ "legacy_kernel92_gaussian_bounds.py" ], [ "legacy_kernel92_literal_cover_ranges.py" ] ], "offline_verification_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "open_legacy_literal_cover_lowers.py" ], [ "legacy_kernel92_gaussian_bounds.py" ], [ "legacy_kernel92_literal_cover_ranges.py" ] ], "optional_original_source_recovery_commands": [ [ "replay_legacy_kernel92_completed_subset.py" ], [ "legacy_kernel92_536_source_inputs_v2.py" ] ], "offline_verification_scope": "Fresh source-byte/count/reference/whole-cost/compatibility checks; complete d-axis top native presence and globally paid word-width checked separately. Default checks authenticate the completed source/native/phase/owner evidence without claiming an expensive phase pipeline rerun or universal operator proof.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 534, "source_commit": "3e148183cbf124fcaba4d3c2d609133ff2edd518", "certificate_file": "pr534-legacy-expected-finite-early-upper.json", "certificate_sha256": "cb75690b04afff2897a366ba5d48356a608ba5d1b76112f97e3fc0c257dc8712", "peer_review_file": "pr534-legacy-expected-finite-peer-review.json", "peer_review_sha256": "692908312888fb7538f6e740dd72e5f80e8a1f7c7518976f3de4b0b09974bbfb", "source_peer_review_file": "pr534-legacy-expected-finite-source-peer-review.json", "source_peer_review_sha256": "dac6eb6009de611ad3c4a9b363b94d6a09188b4b59ed7c16fbb48c3d8966d2d4", "proof_file": "legacy-expected-controller-534-bounds.md", "family_kind": "own-pre-SPEC-EXPECTED-complete-controller-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr534-legacy-expected-finite-record-upper.json", "record_certificate_sha256": "8176e3c7d66c75031b89e0d8b69a967773ae7a2a46eff40decc27b129ad82537", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "1526158885117467/1000000000000000000", "native_certificate_file": "pr534-legacy-expected-finite-native.json", "native_certificate_sha256": "82f59822ca2707f53999e4ad91169c76d0d3ea30f6078ab717622a6e5e1ec489", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "source_selection_by_literal_own_verifier": true, "complete_generated_template_matches_own_commitment": true, "retained_previous_invoice": null, "original_global_verifier_full_PASS_claimed": false, "original_phase_engines_freshly_replayed": false, "scalar_only_census_not_operator_proof": true, "scope": [ "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "Own534 completed native all-input Gaussian/helper endpoints, exact required entry/output frames and absolute phases, normalised residual wrappers and identity on spectators are substantive retained interfaces. Scalar-only specialization and finite frame checks do not prove these operator identities.", "The own all-size compiler, common-label/mutable-basis owned realisation, normalized completed-child height, restored-row/tape and analytic recovery contracts remain conditional exactly as qualified in the own README. The source bounded73-axis binary-affine/even-quadratic-Z4 finite phase grammar is required for the charged universal compiler tariff.", "The fresh original source preparation, complete owner/controller audit with seven mutations and no-prior-invoice full recount were actually executed. No full original global verifier, all-edge phase engine or predecessor cold replay is claimed.", "This is a newly counted direct Gaussian/Fermat XAG realization of the own selected complete complex construction. The original optional BIT supplier is neither consumed nor assigned an invented saving.", "The preserved finite fallback density tax is not adjustable. Full stopped-child reserve u^(1000000*Q), per-coordinate40e direct tensor fallback and all seven actual operation rows are included by the independently closed finite component." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "legacy_expected_controller_534_inputs.py" ], [ "legacy_expected_controller_534_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 536, "source_commit": "71a7ed7a95776810fede6f583885b7faf5d5ff2a", "certificate_file": "pr536-legacy-kernel92-literal-cover-range.json", "certificate_sha256": "4638adc2d2db02423a52b5f19f1bbf2c290f31f174bf839b1fe2ce877b8581d0", "peer_review_file": "pr536-legacy-kernel92-literal-cover-range-peer-review.json", "peer_review_sha256": "e489269f8aef75949e4944e9a5e68aa59000dacab3c5c05862fdecf8da179df5", "source_peer_review_file": "pr536-legacy-kernel92-literal-cover-range-source-peer-review.json", "source_peer_review_sha256": "9828f509c3884a8f09ea6d999e27f9fc352e49b1e8b414556f662e6d0427aeda", "proof_file": "legacy-kernel92-literal-cover-ranges.md", "family_kind": "finite-literal-complete-cover-source-core", "effective_kappa": "1/5000", "kappa_record": "382581895225733/250000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr536-legacy-kernel92-literal-cover-range.json", "scope": "Existence of the same own counted literal early Gaussian schedule throughout its verified domain; no upper for every switching policy.", "exact_individual_crossing": false }, "lower": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public switching policies of this exact own source-selected literal complete O(73,2) cover enhancement; at least one actual selected public-main unit real ADD per vertex survives at guarded width>=2. No pruning, CSE, aggregation, compression, cover quotienting or native bypass removes it. A branch without such a native invocation returns the identical fixed GMP reference. This inactive rule is an added comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source": "data/operation-audit/pr536-open-legacy-v2-literal-cover-lower.json" }, "lower_certificate_file": "pr536-open-legacy-v2-literal-cover-lower.json", "lower_certificate_sha256": "38c51dc94383e64a0157405f4e55fd3eb25f6bbe2174d52734faec91fe10e4bd", "source_base_upper_certificate": "pr536-legacy-kernel92-finite-early-upper.json", "source_base_upper_certificate_sha256": "5af122c5b83edf61de9a13128bfce3092ce8cae80df4a26ca26fc663ae91bc61", "native_certificate_file": "pr536-legacy-kernel92-finite-native.json", "native_certificate_sha256": "15df3103690997ff1f03818bf4e97a5796e516493d2d916af858fda0b57914e4", "record_certificate_file": "pr536-legacy-kernel92-finite-record-upper.json", "record_certificate_sha256": "01a35e5b7a07620d23038f21939c180a738b5bdcbf90ae0f4c05fbdd8f66ee61", "record_P": "230584301497830147503423480", "record_tail_input_bits": "2^(2^230584301497830147503423480)", "record_tail_quantified": true, "record_tail_policy": "the_bound_counted_same_core_record_schedule_above_its_separately_verified_domain", "necessary_lower_quantifier": "all_valid_literal_family_public_policies", "sufficient_upper_policy": "the_bound_counted_early_schedule_above_its_verified_domain", "upper_not_for_all_switching_policies": true, "baseline_upper_refinement_file": "optimized-gmp-degree8-compact-upper.json", "baseline_upper_refinement_sha256": "2bad0e4989947e2ef601613c1ad49ba54088c83a4827fd2feacb9f5b69c24956", "baseline_refinement_scope": "Sharper bound on the same fixed reference supports the necessary prefix. The separately closed own lower and813-check sufficient certificates remain unchanged.", "scope": [ "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "Own selected native all-input Gaussian/helper endpoints, exact physical entry/output frames and absolute phases, normalized residual wrappers and identity spectators remain substantive universal interfaces. Actual finite local phase/source checks strengthen the evidence but do not prove arbitrary all-size operator identities.", "Own common-label/mutable-basis owned restore, normalized completed-child semantic height, all-size compiler/occupied-row/stock/tape and analytic recovery remain conditional. The bounded73-axis binary-affine/even-quadratic-Z4 finite-phase grammar is required for the charged universal compiler tariff.", "Actual own constructor/kernel controls, native scalar/frame/wrapper and every finite local phase edge/endpoint, complete owner emitter plus seven mutations and fresh invoice with no retained prior allowance were executed. Original full global CLI, unchanged global data-phase replay and original BIT runtime are not claimed.", "This newly counted direct Gaussian/Fermat circuit uses the exact own selected source body and literal complete finite cover. No source equivalence, previous upper threshold, prior invoice or fabricated BIT saving is consumed. The fixed fallback density tax, per-coefficient40e fallback and full u^(1000000Q) stopped reserve remain paid in all seven operation rows.", "All valid public switching policies of this exact own source-selected literal complete O(73,2) cover enhancement; at least one actual selected public-main unit real ADD per vertex survives at guarded width>=2. No pruning, CSE, aggregation, compression, cover quotienting or native bypass removes it. A branch without such a native invocation returns the identical fixed GMP reference. This inactive rule is an added comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "All valid public switching policies of this exact own source-selected literal complete O(73,2) cover enhancement; at least one actual selected public-main unit real ADD per vertex survives at guarded width>=2. No pruning, CSE, aggregation, compression, cover quotienting or native bypass removes it. A branch without such a native invocation returns the identical fixed GMP reference. This inactive rule is an added comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "Exact same own literal selected programme and full-cover body; complete new group invoice pays it. Both early and record domains separately imply a nonempty native H row above the full1e6Q stopped base. Lower forall policies and constructive upper exists schedule remain distinct." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "legacy_kernel92_literal_cover_ranges.py" ], "reproduction_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "open_legacy_literal_cover_lowers_v2.py" ], [ "legacy_kernel92_gaussian_bounds.py" ], [ "legacy_kernel92_literal_cover_ranges.py" ] ], "offline_verification_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "open_legacy_literal_cover_lowers_v2.py" ], [ "legacy_kernel92_gaussian_bounds.py" ], [ "legacy_kernel92_literal_cover_ranges.py" ] ], "optional_original_source_recovery_commands": [ [ "replay_legacy_kernel92_completed_subset.py" ], [ "legacy_kernel92_536_source_inputs_v2.py" ] ], "offline_verification_scope": "Fresh source-byte/count/reference/whole-cost/compatibility checks; complete d-axis top native presence and globally paid word-width checked separately. Default checks authenticate the completed source/native/phase/owner evidence without claiming an expensive phase pipeline rerun or universal operator proof.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 537, "source_commit": "39958faec4fd7e7958ca81f6cffcf70ce74c5e89", "certificate_file": "pr537-open-legacy-v2-literal-cover-lower.json", "certificate_sha256": "e7021b15fda270d8a2bc76ea87b37a2a7aac7d1016dcf41bf539feb77d93a8d0", "lower_certificate_file": "pr537-open-legacy-v2-literal-cover-lower.json", "lower_certificate_sha256": "e7021b15fda270d8a2bc76ea87b37a2a7aac7d1016dcf41bf539feb77d93a8d0", "peer_review_file": "pr537-open-legacy-v2-literal-cover-peer-review.json", "peer_review_sha256": "53f5666ef041b0842b1c25c0546783007559c35be5bad589d5f9b9aafc7c912a", "source_peer_review_file": "pr537-open-legacy-v2-literal-cover-source-peer-review.json", "source_peer_review_sha256": "01d3bc85313f705685b5195b3e59d734765649c439d3c787a159bd81c3ab49f6", "proof_file": "open-legacy-literal-cover-lowers-v2.md", "family_kind": "finite-literal-complete-cover-source-core", "upper": null, "lower": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public switching policies of this exact own source-selected literal complete O(73,2) cover enhancement; at least one actual selected public-main unit real ADD per vertex survives at guarded width>=2. No pruning, CSE, aggregation, compression, cover quotienting or native bypass removes it. A branch without such a native invocation returns the identical fixed GMP reference. This inactive rule is an added comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source": "data/operation-audit/pr537-open-legacy-v2-literal-cover-lower.json" }, "effective_kappa": "1538356846647141/1000000000000000000", "kappa_record": "1538356846647141/1000000000000000000", "kappa_is_source_provenance_only": true, "asymptotic_record_exponent_reproved": false, "native_coordinate_rank": 73, "uniform_rank_H": null, "record_tail_quantified": false, "necessary_lower_quantifier": "all_valid_literal_family_public_policies", "sufficient_upper_policy": null, "upper_not_for_all_switching_policies": true, "baseline_upper_refinement_file": "optimized-gmp-degree8-compact-upper.json", "baseline_upper_refinement_sha256": "2bad0e4989947e2ef601613c1ad49ba54088c83a4827fd2feacb9f5b69c24956", "baseline_refinement_scope": "Sharper upper on the same fixed reference used only to prove this necessary literal-family prefix; no reference algorithm or sufficient upper changed.", "scope": [ "Own native arbitrary-input full operator/required phase, dirty helpers, full columns/spectators, owned restoration and compiler/all-size correctness remain explicit hypotheses; finite scalar/byte checks do not discharge them.", "Narrow literal source-selected complete-cover family only; no superior alternative implementation, original BIT saving, sufficient upper, actual first crossing, formal or human proof is claimed.", "All valid public switching policies of this exact own source-selected literal complete O(73,2) cover enhancement; at least one actual selected public-main unit real ADD per vertex survives at guarded width>=2. No pruning, CSE, aggregation, compression, cover quotienting or native bypass removes it. A branch without such a native invocation returns the identical fixed GMP reference. This inactive rule is an added comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "Lower only. No upper, record saving, exact crossing, original full phase/owner replay or universal implementation bound is inferred." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "open_legacy_literal_cover_lowers_v2.py" ], "reproduction_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "open_legacy_literal_cover_lowers_v2.py" ] ], "offline_verification_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "open_legacy_literal_cover_lowers_v2.py" ] ], "offline_verification_scope": "Reauthenticate consumed own immutable source, API authority, selector, exact selected words and full-cover path; check exact group/reference arithmetic. The six bounded PR537 constructor/transport/emitter jobs are bound to their durable receipt, not claimed rerun by the lower-only checker. No phase, owner, invoice or full original CLI pass is claimed.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 538, "source_commit": "a1460516226555dd375d9adb82a8e1dcbfe1ca79", "certificate_file": "pr538-legacy-kernel92-literal-cover-range.json", "certificate_sha256": "fa690e22ea954ebd8ee6676dcc7d47dc41687306acf42ad2391bb067902141e3", "peer_review_file": "pr538-legacy-kernel92-literal-cover-range-peer-review.json", "peer_review_sha256": "99023385743bfc26ddedd111833d1041e125d8559bac1cc21f47e58aa45d7495", "source_peer_review_file": "pr538-legacy-kernel92-literal-cover-range-source-peer-review.json", "source_peer_review_sha256": "bb51df46a87c88a9824a838a794052b9ee8ff8b532f81692ea03a0db1eb7c12f", "proof_file": "legacy-kernel92-literal-cover-ranges.md", "family_kind": "finite-literal-complete-cover-source-core", "effective_kappa": "1/5000", "kappa_record": "382581895225733/250000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr538-legacy-kernel92-literal-cover-range.json", "scope": "Existence of the same own counted literal early Gaussian schedule throughout its verified domain; no upper for every switching policy.", "exact_individual_crossing": false }, "lower": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public switching policies for this own source-selected literal complete O(73,2) cover enhancement: keep one actual selected public real ADD at every cover vertex with guarded width>=2 and the stipulated ADD lowering; no pruning, CSE, compression, aggregation or native bypass. A branch without such a native invocation is the identical fixed GMP reference. This added inactive rule is a comparison-family definition, not an original source fact. No other implementation or original BIT composition is covered.", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source": "data/operation-audit/pr538-open-legacy-literal-cover-lower.json" }, "lower_certificate_file": "pr538-open-legacy-literal-cover-lower.json", "lower_certificate_sha256": "ab1c37c4d305ff0f52527675c903888520b4ab03326e9a6607126e1dbda7e9f5", "source_base_upper_certificate": "pr538-legacy-kernel92-finite-early-upper.json", "source_base_upper_certificate_sha256": "6409d5426fa6da530de1cb4b749fb595940157af97547ea45e189025e709a1ff", "native_certificate_file": "pr538-legacy-kernel92-finite-native.json", "native_certificate_sha256": "1736cb8d0083f22e7655d53fc5ada1137f1ac54a4adbd1beac1c466ab673423c", "record_certificate_file": "pr538-legacy-kernel92-finite-record-upper.json", "record_certificate_sha256": "cc54b37a8a4796e2e43791ea5b1df90ae25fd492a2c99a02d61114100ea05af3", "record_P": "230584301497830147503423480", "record_tail_input_bits": "2^(2^230584301497830147503423480)", "record_tail_quantified": true, "record_tail_policy": "the_bound_counted_same_core_record_schedule_above_its_separately_verified_domain", "necessary_lower_quantifier": "all_valid_literal_family_public_policies", "sufficient_upper_policy": "the_bound_counted_early_schedule_above_its_verified_domain", "upper_not_for_all_switching_policies": true, "baseline_upper_refinement_file": "optimized-gmp-degree8-compact-upper.json", "baseline_upper_refinement_sha256": "2bad0e4989947e2ef601613c1ad49ba54088c83a4827fd2feacb9f5b69c24956", "baseline_refinement_scope": "Sharper bound on the same fixed reference supports the necessary prefix. The separately closed own lower and813-check sufficient certificates remain unchanged.", "scope": [ "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "Own selected native all-input Gaussian/helper endpoints, exact physical entry/output frames and absolute phases, normalized residual wrappers and identity spectators remain substantive universal interfaces. Actual finite local phase/source checks strengthen the evidence but do not prove arbitrary all-size operator identities.", "Own common-label/mutable-basis owned restore, normalized completed-child semantic height, all-size compiler/occupied-row/stock/tape and analytic recovery remain conditional. The bounded73-axis binary-affine/even-quadratic-Z4 finite-phase grammar is required for the charged universal compiler tariff.", "Actual own constructor/kernel controls, native scalar/frame/wrapper and every finite local phase edge/endpoint, complete owner emitter plus seven mutations and fresh invoice with no retained prior allowance were executed. Original full global CLI, unchanged global data-phase replay and original BIT runtime are not claimed.", "This newly counted direct Gaussian/Fermat circuit uses the exact own selected source body and literal complete finite cover. No source equivalence, previous upper threshold, prior invoice or fabricated BIT saving is consumed. The fixed fallback density tax, per-coefficient40e fallback and full u^(1000000Q) stopped reserve remain paid in all seven operation rows.", "All valid public switching policies for this own source-selected literal complete O(73,2) cover enhancement: keep one actual selected public real ADD at every cover vertex with guarded width>=2 and the stipulated ADD lowering; no pruning, CSE, compression, aggregation or native bypass. A branch without such a native invocation is the identical fixed GMP reference. This added inactive rule is a comparison-family definition, not an original source fact. No other implementation or original BIT composition is covered.", "All valid public switching policies for this own source-selected literal complete O(73,2) cover enhancement: keep one actual selected public real ADD at every cover vertex with guarded width>=2 and the stipulated ADD lowering; no pruning, CSE, compression, aggregation or native bypass. A branch without such a native invocation is the identical fixed GMP reference. This added inactive rule is a comparison-family definition, not an original source fact. No other implementation or original BIT composition is covered.", "Exact same own literal selected programme and full-cover body; complete new group invoice pays it. Both early and record domains separately imply a nonempty native H row above the full1e6Q stopped base. Lower forall policies and constructive upper exists schedule remain distinct." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "legacy_kernel92_literal_cover_ranges.py" ], "reproduction_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "open_legacy_literal_cover_lowers.py" ], [ "legacy_kernel92_gaussian_bounds.py" ], [ "legacy_kernel92_literal_cover_ranges.py" ] ], "offline_verification_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "open_legacy_literal_cover_lowers.py" ], [ "legacy_kernel92_gaussian_bounds.py" ], [ "legacy_kernel92_literal_cover_ranges.py" ] ], "optional_original_source_recovery_commands": [ [ "replay_legacy_kernel92_completed_subset.py" ], [ "legacy_kernel92_536_source_inputs_v2.py" ] ], "offline_verification_scope": "Fresh source-byte/count/reference/whole-cost/compatibility checks; complete d-axis top native presence and globally paid word-width checked separately. Default checks authenticate the completed source/native/phase/owner evidence without claiming an expensive phase pipeline rerun or universal operator proof.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 543, "source_commit": "2065fe4f72a914d907f1046603f5a36f17018535", "certificate_file": "pr543-paired-selected-complex-early-upper.json", "certificate_sha256": "471705f1347176cb6b8950e0757002ac4b63670dface7785493d5638ae299ba0", "peer_review_file": "pr543-paired-selected-complex-peer-review.json", "peer_review_sha256": "b806c58bbae7b0edfb0b4951e214b86ca8890357dfa87f0aea6919e30d1192ae", "source_peer_review_file": "pr543-paired-selected-complex-source-peer-review.json", "source_peer_review_sha256": "b0c69f1cfc134aca982a8e79a15a5777e3e07cd7836c2d76b1cb826aead9baf5", "proof_file": "paired-selected-complex-gaussian-bounds.md", "family_kind": "own-paired-selected-complete-complex-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr543-paired-selected-complex-record-upper.json", "record_certificate_sha256": "39f03281f6d340445ba2bda61ab4f1299ce9e844f062ba82707ac8bdad8f0ed4", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "793733736881443/500000000000000000", "native_certificate_file": "pr543-paired-selected-complex-native.json", "native_certificate_sha256": "8208acf0095789b2fd6cab4e7e30ffc692295f1e51277b910132f4add935a31a", "native_coordinate_rank": 73, "record_tail_quantified": true, "selected_complete_complex_supplier_pr": 535, "selected_complete_complex_supplier_head": "8b758a103915179322766bed5798f9b6e7198011", "complete_selected_source_payloads": 52, "source_equivalent_numeric_realization": true, "ordinary_BIT_supplier_consumed": false, "changed_own_BIT_circuit_priced": false, "changed_own_BIT_benefit_attributed": false, "original_global_verifier_full_PASS_claimed": false, "scope": [ "Own arbitrary-column local/frame/phase identities, absolute phases, all distinct live owners, full spectator/dirty-helper restoration.", "Own all-size unequal-child normalized Lemma A, common-label/mutable-basis compiler, once-only padding, and restored-row stock interfaces.", "Own precision/tape semantic completed-child guard C0=2^210000; completed exact Gaussian children have semantic norm one under their endpoint contract.", "Parameterized direct Gaussian/fine-prime/finite-section/boundary/recovery analytic interfaces; no finite-field BIT-routing wrapper.", "Same fixed XAG lowering and repaired unlimited optimized-GMP correctness/halting contracts as the prior source-specific certificates.", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "This NEW direct Gaussian/Fermat XAG realization executes the complete complex supplier explicitly named primary by the own paired construction. The changed own BIT circuit is wholly UNUSED: no claim is made to price it or to attribute the resulting runtime to its optimization.", "Both actually cited535 source heads have the exact complete52item MANIFEST of the separately closed535 native/physical/invoice component. Every actual selected source payload is rechecked; this is full serialized source identity, not equality of kappa, a histogram or an old upper.", "Required normalized Gaussian/native absolute-phase, entry/output frames, arbitrary-input helper/spectator restore, common-label/owned all-size compiler/row/tape and analytic contracts remain substantive explicit premises. No fresh original BIT/native-phase/global verifier run is claimed.", "All inherited fallback density tax, per-coefficient40e direct fallback, full u^(1000000Q) stopped reserve, concrete-scale Schur and all actual seven operation rows are retained. The optional BIT argument/saving is absent from this reduced branch." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "paired_selected_complex_source_chronology.py" ], [ "paired_selected_complex_gaussian_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 545, "source_commit": "376426f3b2b26ab430d10baf16bbd9ff42990a7c", "certificate_file": "pr545-paired-selected-complex-early-upper.json", "certificate_sha256": "1344ae5dc60a2aae9c9676e1deb3feb9ae8dbfdd3d3c057f500cb73ff45a2834", "peer_review_file": "pr545-paired-selected-complex-peer-review.json", "peer_review_sha256": "392e2f01def8b9c8630b14191e65c647e3f2befa1259f72978b45045e05d3ce5", "source_peer_review_file": "pr545-paired-selected-complex-source-peer-review.json", "source_peer_review_sha256": "61dac7a68d072f23622503fddaf49aa193d629f6a71bd42b8b1a45d4319b5232", "proof_file": "paired-selected-complex-gaussian-bounds.md", "family_kind": "own-paired-selected-complete-complex-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr545-paired-selected-complex-record-upper.json", "record_certificate_sha256": "d2df994dded0b75e04c265073fafcd4ec09339bbc6d4e20a1a7299a35e2fc650", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "793733736881443/500000000000000000", "native_certificate_file": "pr545-paired-selected-complex-native.json", "native_certificate_sha256": "de63c9303814e4608cd1bb31cb86c8d49e70c55d19cab758322144eeacfa6559", "native_coordinate_rank": 73, "record_tail_quantified": true, "selected_complete_complex_supplier_pr": 535, "selected_complete_complex_supplier_head": "25f9b7c2310d40c9efdfbe368a40ba6e74d3b0a2", "complete_selected_source_payloads": 52, "source_equivalent_numeric_realization": true, "ordinary_BIT_supplier_consumed": false, "changed_own_BIT_circuit_priced": false, "changed_own_BIT_benefit_attributed": false, "original_global_verifier_full_PASS_claimed": false, "scope": [ "Own arbitrary-column local/frame/phase identities, absolute phases, all distinct live owners, full spectator/dirty-helper restoration.", "Own all-size unequal-child normalized Lemma A, common-label/mutable-basis compiler, once-only padding, and restored-row stock interfaces.", "Own precision/tape semantic completed-child guard C0=2^210000; completed exact Gaussian children have semantic norm one under their endpoint contract.", "Parameterized direct Gaussian/fine-prime/finite-section/boundary/recovery analytic interfaces; no finite-field BIT-routing wrapper.", "Same fixed XAG lowering and repaired unlimited optimized-GMP correctness/halting contracts as the prior source-specific certificates.", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "This NEW direct Gaussian/Fermat XAG realization executes the complete complex supplier explicitly named primary by the own paired construction. The changed own BIT circuit is wholly UNUSED: no claim is made to price it or to attribute the resulting runtime to its optimization.", "Both actually cited535 source heads have the exact complete52item MANIFEST of the separately closed535 native/physical/invoice component. Every actual selected source payload is rechecked; this is full serialized source identity, not equality of kappa, a histogram or an old upper.", "Required normalized Gaussian/native absolute-phase, entry/output frames, arbitrary-input helper/spectator restore, common-label/owned all-size compiler/row/tape and analytic contracts remain substantive explicit premises. No fresh original BIT/native-phase/global verifier run is claimed.", "All inherited fallback density tax, per-coefficient40e direct fallback, full u^(1000000Q) stopped reserve, concrete-scale Schur and all actual seven operation rows are retained. The optional BIT argument/saving is absent from this reduced branch." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "paired_selected_complex_source_chronology.py" ], [ "paired_selected_complex_gaussian_bounds.py" ] ], "source_selected_kappa_correction": true, "frozen_metadata_kappa": "1584931111785787/1000000000000000000", "actual_own_selected_kappa": "793733736881443/500000000000000000", "source_kappa_correction_primary_receipt": "paired-complex-selection-source/545/chronology.json", "source_revision_included_at_merge": "2026-10-12T15:45:41Z", "source_revision_merge_commit": "1a580eafa09fb09a6a3c65d5ab1aab492cec3571", "source_revision_committed_at": "2026-10-12T03:31:30Z", "source_selected_kappa_correction_basis": "Own EXPECTED.kappa.pr535 and literal verifier select the complete primary composition. The frozen parser instead quoted own EXPECTED.pr535, explicitly the cited535 baseline. Both values are preserved; actual ownhead is eighth of43 merge parents.", "source_selected_kappa_correction_note": "The quoted historical baseline remains visible. This new cost realization uses the actual own selected composition target at its authenticated merge date, without backdating or adjudicating a new accepted exponent record.", "new_accepted_exponent_record_claimed": false, "source_kappa_correction_primary_sha256": "d50291d6e8aabba64479c3bee1070c560330ce614aafc364b08c8f07e18e9c02", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null, "kappa_fraction": "1584931111785787/1000000000000000000", "kappa_decimal": "0.001584931111785787", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews." } }, { "pr": 550, "source_commit": "c7337040822978f1611ce9d9d44e7bb96d887e23", "certificate_file": "pr550-trace-rank5-v4-literal-cover-lower.json", "certificate_sha256": "081b1b62ca887696f16173a303ffe2958be3e726bc26b6f1890ab25b78d6b3fc", "lower_certificate_file": "pr550-trace-rank5-v4-literal-cover-lower.json", "lower_certificate_sha256": "081b1b62ca887696f16173a303ffe2958be3e726bc26b6f1890ab25b78d6b3fc", "peer_review_file": "pr550-trace-rank5-v4-literal-cover-peer-review.json", "peer_review_sha256": "a038892b0f5a1066eab0112d767caeda7c3a9e09fc495b75955621a65e6db0af", "source_peer_review_file": "pr550-trace-rank5-v4-literal-cover-source-peer-review.json", "source_peer_review_sha256": "a4dca05eed30f9edfe66cfb133d5a40aab9d15c36ca849029223567f36085de6", "proof_file": "trace-rank5-literal-cover-lowers-v4.md", "family_kind": "finite-literal-complete-cover-source-core", "upper": null, "lower": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public policies of this own source-selected literal complete O(73,2) native body, with a surviving actual distinct public-main unit ADD at each vertex at guarded width>=2. No pruning/CSE/aggregation/cover quotient/compression/native bypass. Any branch without such a body returns identical fixed GMP; this inactive rule is an explicit additional comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source": "data/operation-audit/pr550-trace-rank5-v4-literal-cover-lower.json" }, "effective_kappa": "397761416533549/250000000000000000", "kappa_record": "397761416533549/250000000000000000", "kappa_is_source_provenance_only": true, "asymptotic_record_exponent_reproved": false, "native_coordinate_rank": 73, "uniform_rank_H": null, "record_tail_quantified": false, "necessary_lower_quantifier": "all_valid_literal_family_public_policies", "sufficient_upper_policy": null, "upper_not_for_all_switching_policies": true, "baseline_upper_refinement_file": "optimized-gmp-degree8-compact-upper.json", "baseline_upper_refinement_sha256": "2bad0e4989947e2ef601613c1ad49ba54088c83a4827fd2feacb9f5b69c24956", "baseline_refinement_scope": "Sharper upper on the same fixed reference used only to prove this necessary literal-family prefix; no reference algorithm or sufficient upper changed.", "scope": [ "Universal Gaussian/helper entry/output/required phase/identity-spectator, owned/all-size and fixed-reference correctness remain substantive hypotheses. Bounded actual source/native scalar-frame jobs do not prove universal phase/operator or original record correctness.", "All valid public policies of this own source-selected literal complete O(73,2) native body, with a surviving actual distinct public-main unit ADD at each vertex at guarded width>=2. No pruning/CSE/aggregation/cover quotient/compression/native bypass. Any branch without such a body returns identical fixed GMP; this inactive rule is an explicit additional comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "Lower only, V-only. No upper, actual crossing, original full phase/owner/invoice/CLI pass, human/formal proof or hardware claim.", "All valid public policies of this own source-selected literal complete O(73,2) native body, with a surviving actual distinct public-main unit ADD at each vertex at guarded width>=2. No pruning/CSE/aggregation/cover quotient/compression/native bypass. Any branch without such a body returns identical fixed GMP; this inactive rule is an explicit additional comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "Lower only. 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The five unchanged bounded constructor/scalar-transport/emitter jobs are bound through their twice-reproduced durable recovery receipt; this lower-only checker does not rerun them or claim phase, owner, invoice or full original CLI verification.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 554, "source_commit": "c1c252e2838918f3de866b228f5a3f21cb9f4b2d", "certificate_file": "pr554-trace-rank5-v4-literal-cover-lower.json", "certificate_sha256": "e1a8bd3bf7d301518c32658a18e01414f5734010b86eec1d30aba2fdb6c6dced", "lower_certificate_file": "pr554-trace-rank5-v4-literal-cover-lower.json", "lower_certificate_sha256": "e1a8bd3bf7d301518c32658a18e01414f5734010b86eec1d30aba2fdb6c6dced", "peer_review_file": "pr554-trace-rank5-v4-literal-cover-peer-review.json", "peer_review_sha256": "b1013134a9a58a0663a375ce20d2343378c57e7603e5353163da7d0ea8ff5976", "source_peer_review_file": "pr554-trace-rank5-v4-literal-cover-source-peer-review.json", "source_peer_review_sha256": "3998f21f01f16b1b2efa44b96f05135a2f10afbb8b07ba10b53a47a1610f264c", "proof_file": "trace-rank5-literal-cover-lowers-v4.md", "family_kind": "finite-literal-complete-cover-source-core", "upper": null, "lower": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public policies of this own source-selected literal complete O(73,2) native body, with a surviving actual distinct public-main unit ADD at each vertex at guarded width>=2. No pruning/CSE/aggregation/cover quotient/compression/native bypass. Any branch without such a body returns identical fixed GMP; this inactive rule is an explicit additional comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source": "data/operation-audit/pr554-trace-rank5-v4-literal-cover-lower.json" }, "effective_kappa": "318241989417709/200000000000000000", "kappa_record": "318241989417709/200000000000000000", "kappa_is_source_provenance_only": true, "asymptotic_record_exponent_reproved": false, "native_coordinate_rank": 73, "uniform_rank_H": null, "record_tail_quantified": false, "necessary_lower_quantifier": "all_valid_literal_family_public_policies", "sufficient_upper_policy": null, "upper_not_for_all_switching_policies": true, "baseline_upper_refinement_file": "optimized-gmp-degree8-compact-upper.json", "baseline_upper_refinement_sha256": "2bad0e4989947e2ef601613c1ad49ba54088c83a4827fd2feacb9f5b69c24956", "baseline_refinement_scope": "Sharper upper on the same fixed reference used only to prove this necessary literal-family prefix; no reference algorithm or sufficient upper changed.", "scope": [ "Universal Gaussian/helper entry/output/required phase/identity-spectator, owned/all-size and fixed-reference correctness remain substantive hypotheses. Bounded actual source/native scalar-frame jobs do not prove universal phase/operator or original record correctness.", "All valid public policies of this own source-selected literal complete O(73,2) native body, with a surviving actual distinct public-main unit ADD at each vertex at guarded width>=2. No pruning/CSE/aggregation/cover quotient/compression/native bypass. Any branch without such a body returns identical fixed GMP; this inactive rule is an explicit additional comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "Lower only, V-only. No upper, actual crossing, original full phase/owner/invoice/CLI pass, human/formal proof or hardware claim.", "All valid public policies of this own source-selected literal complete O(73,2) native body, with a surviving actual distinct public-main unit ADD at each vertex at guarded width>=2. No pruning/CSE/aggregation/cover quotient/compression/native bypass. Any branch without such a body returns identical fixed GMP; this inactive rule is an explicit additional comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "Lower only. No upper, record saving, exact crossing, original full phase/owner/invoice/CLI pass or universal implementation bound is inferred." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "trace_rank5_literal_cover_lowers_v4.py" ], "reproduction_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "trace_rank5_literal_cover_lowers_v4.py" ] ], "offline_verification_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "trace_rank5_literal_cover_lowers_v4.py" ] ], "offline_verification_scope": "Reauthenticate each consumed own immutable source/API authority, literal selector, exact selected words and full-cover path, then check exact group/reference arithmetic. The five unchanged bounded constructor/scalar-transport/emitter jobs are bound through their twice-reproduced durable recovery receipt; this lower-only checker does not rerun them or claim phase, owner, invoice or full original CLI verification.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 561, "source_commit": "210dfa4896e77a8fb5e22ca5a970b0fb0ac984a6", "certificate_file": "pr561-open-multicold-v3-literal-cover-lower.json", "certificate_sha256": "0839f33aca3e8829e0b6dfa89aa6d3d047d9b9e8fe4c0705d89dcc0d7e1027b4", "lower_certificate_file": "pr561-open-multicold-v3-literal-cover-lower.json", "lower_certificate_sha256": "0839f33aca3e8829e0b6dfa89aa6d3d047d9b9e8fe4c0705d89dcc0d7e1027b4", "peer_review_file": "pr561-open-multicold-v3-literal-cover-peer-review.json", "peer_review_sha256": "3fab83a8def76295ad5e17cb1615d6b059f4724ae8d6eebeafd80cce5638a373", "source_peer_review_file": "pr561-open-multicold-v3-literal-cover-source-peer-review.json", "source_peer_review_sha256": "931ac83769d03ea59b88cd89bf420cd1dd958cae20b4eb44aa13af2f5b12a8c7", "proof_file": "open-multicold-literal-cover-lowers-v3.md", "family_kind": "finite-literal-complete-cover-source-core", "upper": null, "lower": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public policies of this own selected literal complete O(73,2) source body. 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A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. 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This lower proves compulsory cost of the prescribed literal body, not correctness or original record validity of unexecuted providers.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Only V is used; no coordinate-volume factor, stock upper used as lower, selected activation threshold, sufficient upper, exact crossing, human/formal proof or hardware claim.", "All valid public policies of this own selected literal complete O(73,2) source body. 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No constructor, full phase, owner, invoice or original CLI pass is claimed by these lower-only jobs.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 568, "source_commit": "71c99ac935a33bb7b59a1b4a7af8725a939b0b90", "certificate_file": "pr568-open-multicold-v3-literal-cover-lower.json", "certificate_sha256": "df4e14ae45186b3d5e6186e1504180472df341e954eb36bf1e6df12497ddff3c", "lower_certificate_file": "pr568-open-multicold-v3-literal-cover-lower.json", "lower_certificate_sha256": "df4e14ae45186b3d5e6186e1504180472df341e954eb36bf1e6df12497ddff3c", "peer_review_file": "pr568-open-multicold-v3-literal-cover-peer-review.json", "peer_review_sha256": "f92a7cedacac49b7b71e74a74e728b3b0e1284eca8f9e87d78870f8e1e50f931", "source_peer_review_file": "pr568-open-multicold-v3-literal-cover-source-peer-review.json", "source_peer_review_sha256": "98710983762724e4091088c303f17b7e890bce81aa7d7b2b5eb96a059b606f76", "proof_file": "open-multicold-literal-cover-lowers-v3.md", "family_kind": "finite-literal-complete-cover-source-core", "upper": null, "lower": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public policies of this own selected literal complete O(73,2) source body. 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A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source": "data/operation-audit/pr575-open-multicold-v3-literal-cover-lower.json" }, "effective_kappa": "1600770286423653/1000000000000000000", "kappa_record": "1600770286423653/1000000000000000000", "kappa_is_source_provenance_only": true, "asymptotic_record_exponent_reproved": false, "native_coordinate_rank": 73, "uniform_rank_H": null, "record_tail_quantified": false, "necessary_lower_quantifier": "all_valid_literal_family_public_policies", "sufficient_upper_policy": null, "upper_not_for_all_switching_policies": true, "selected_provider": "width7_eight", "actual_selected_provider_calls": 63, "other_changed_providers_claimed_validated": false, "baseline_upper_refinement_file": "optimized-gmp-degree8-compact-upper.json", "baseline_upper_refinement_sha256": "2bad0e4989947e2ef601613c1ad49ba54088c83a4827fd2feacb9f5b69c24956", "baseline_refinement_scope": "Sharper upper on the same fixed reference proves only this necessary prefix; no reference algorithm, source record or sufficient upper changes.", "scope": [ "Own universal Gaussian/helper required entry/output/absolute-phase/identity-spectator and owned/all-size correctness remain substantive hypotheses. This lower proves compulsory cost of the prescribed literal body, not correctness or original record validity of unexecuted providers.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Only V is used; no coordinate-volume factor, stock upper used as lower, selected activation threshold, sufficient upper, exact crossing, human/formal proof or hardware claim.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Lower only; one positively used exact own-source provider suffices for compulsory work in the complete prescribed kernel. Other changed providers are not substituted or claimed validated. No upper or actual crossing." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "open_multicold_literal_cover_lowers_v3.py" ], "reproduction_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "open_multicold_literal_cover_lowers_v3.py" ] ], "offline_verification_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "open_multicold_literal_cover_lowers_v3.py" ] ], "offline_verification_scope": "Reauthenticate exact own immutable MANIFEST/API/PLAN, selected actual canonical/programme/orientation and descriptor commitments, selected main complete-cover source chain, group count and same-reference strict tariff inequality. No constructor, full phase, owner, invoice or original CLI pass is claimed by these lower-only jobs.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 576, "source_commit": "f4e9f7e85e9211cf6ba6c5789da2aa0902d9121e", "certificate_file": "pr576-exact-mixed-finite-early-upper.json", "certificate_sha256": "8fb606ace514e8a7515d4e826c790f486d84663b7b54992e5ca1b59643468945", "peer_review_file": "pr576-exact-mixed-finite-peer-review.json", "peer_review_sha256": "70dc65787cf6c3d6b14cd21bfc429be9b1ceef309e12322cfc23e2ddca0ae3e6", "source_peer_review_file": "pr576-exact-mixed-finite-source-peer-review.json", "source_peer_review_sha256": "91f14803c1dff9656602dc82d5dfd6694c8d50d010d30c329b037f979eb45b84", "proof_file": "selected-provider-v3-whole-upper.md", "family_kind": "rank73-own-exact-recovered-mixed-direct-Gaussian-no-BIT", "native_certificate_file": "pr576-exact-mixed-finite-native.json", "native_certificate_sha256": "279bf2528b27e0b67aaba0a93e44de998f1143b268cb8444f4bd866f43f4f179", "program_fingerprint": "d38855a934d85a5a83d97c0ce1ff3e8a2fede0a8b5711f0817e1b0569d5ff657", "program_fingerprint_scope": "Actual own selected full/orientation hashes are checked. Optional canonical absence remains explicit; scalar specialization does not prove operator or phase endpoints.", "invoice_fingerprint": "a3ebe4d62e2543177d1d79334864ee862ca29ffb0a4ec4285c1e76448aca785a", "invoice_fingerprint_scope": "Fresh own complete PLAN/OWNERS, whole helper widths, chronological windows, charts, stock and full no-prior invoice; source-equivalent numeric parent provenance is disclosed.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "160109005167629/100000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "canonical_catalogue_absent_for": [], "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_scope": "New direct Gaussian realization of the same own selected source core; no literal historical dual-supplier replay is claimed.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr576-exact-mixed-finite-early-upper.json", "scope": "Conditional sufficient eventual bound for every positive XOR tariff against the same repaired unlimited optimized-GMP reference, retaining the stated own typed native/frame/phase/all-size and analytic interfaces.", "exact_individual_crossing": false }, "record_certificate_file": "pr576-exact-mixed-finite-record-upper.json", "record_certificate_sha256": "3303cca507953ab433b59cbd37d44ca71057a80e9e158e86563650624acff319", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "selected_provider_v3_whole_bounds.py" ], "reproduction_commands": [ [ "selected_provider_dispatch_v3.py", "--execute" ], [ "selected_provider_v3_whole_bounds.py" ] ], "source_discovery_scope": "Two own original mixed-provider specifications are bound to exact recovered raw canonical/program digests and both orientations. Full native scalar/GF2 and owner/invoice replays are separate from the retained absolute phase/operator/all-size premises.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 577, "source_commit": "086bd33ff5c1ce46f3ff23298b8dc756a54414db", "certificate_file": "pr577-open-multicold-v3-literal-cover-lower.json", "certificate_sha256": "80a32675d9a849526029e485225ba4ebb44994ad23a96a533ffb562d663e9fce", "lower_certificate_file": "pr577-open-multicold-v3-literal-cover-lower.json", "lower_certificate_sha256": "80a32675d9a849526029e485225ba4ebb44994ad23a96a533ffb562d663e9fce", "peer_review_file": "pr577-open-multicold-v3-literal-cover-peer-review.json", "peer_review_sha256": "52e711d0fbd59390b98befed623439efd5b077fc12be558d7b7f0256696df9f2", "source_peer_review_file": "pr577-open-multicold-v3-literal-cover-source-peer-review.json", "source_peer_review_sha256": "6b4d016b9b7281232d3156810ac0e195cf2423481dfacd4505a9cbe0816ab65e", "proof_file": "open-multicold-literal-cover-lowers-v3.md", "family_kind": "finite-literal-complete-cover-source-core", "upper": null, "lower": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source": "data/operation-audit/pr577-open-multicold-v3-literal-cover-lower.json" }, "effective_kappa": "400212132038723/250000000000000000", "kappa_record": "400212132038723/250000000000000000", "kappa_is_source_provenance_only": true, "asymptotic_record_exponent_reproved": false, "native_coordinate_rank": 73, "uniform_rank_H": null, "record_tail_quantified": false, "necessary_lower_quantifier": "all_valid_literal_family_public_policies", "sufficient_upper_policy": null, "upper_not_for_all_switching_policies": true, "selected_provider": "prefix_width7_eight", "actual_selected_provider_calls": 58, "other_changed_providers_claimed_validated": false, "baseline_upper_refinement_file": "optimized-gmp-degree8-compact-upper.json", "baseline_upper_refinement_sha256": "2bad0e4989947e2ef601613c1ad49ba54088c83a4827fd2feacb9f5b69c24956", "baseline_refinement_scope": "Sharper upper on the same fixed reference proves only this necessary prefix; no reference algorithm, source record or sufficient upper changes.", "scope": [ "Own universal Gaussian/helper required entry/output/absolute-phase/identity-spectator and owned/all-size correctness remain substantive hypotheses. This lower proves compulsory cost of the prescribed literal body, not correctness or original record validity of unexecuted providers.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Only V is used; no coordinate-volume factor, stock upper used as lower, selected activation threshold, sufficient upper, exact crossing, human/formal proof or hardware claim.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Lower only; one positively used exact own-source provider suffices for compulsory work in the complete prescribed kernel. Other changed providers are not substituted or claimed validated. No upper or actual crossing." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "open_multicold_literal_cover_lowers_v3.py" ], "reproduction_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "open_multicold_literal_cover_lowers_v3.py" ] ], "offline_verification_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "open_multicold_literal_cover_lowers_v3.py" ] ], "offline_verification_scope": "Reauthenticate exact own immutable MANIFEST/API/PLAN, selected actual canonical/programme/orientation and descriptor commitments, selected main complete-cover source chain, group count and same-reference strict tariff inequality. No constructor, full phase, owner, invoice or original CLI pass is claimed by these lower-only jobs.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 578, "source_commit": "2aacc1f2edae76fc963699be5cfaf31bcf3ef56b", "certificate_file": "pr578-exact-mixed-finite-early-upper.json", "certificate_sha256": "89a5315dab6dd8140b2a327a0ca8837c169d394582fc392abcf49342f83bc564", "peer_review_file": "pr578-exact-mixed-finite-peer-review.json", "peer_review_sha256": "bd1ed0001ad4db96af5442586caf981a68fff7beed099715ea66909a920aa553", "source_peer_review_file": "pr578-exact-mixed-finite-source-peer-review.json", "source_peer_review_sha256": "7e6cb05d71c899672075874f9fdb3ba774c5a8962e5851eb517e76fb76f08444", "proof_file": "selected-provider-v3-whole-upper.md", "family_kind": "rank73-own-exact-recovered-mixed-direct-Gaussian-no-BIT", "native_certificate_file": "pr578-exact-mixed-finite-native.json", "native_certificate_sha256": "3ddefed3cb8ee8a11777cefda3dbe1e63397a6ff7d630e4a179f00d11b8e19e0", "program_fingerprint": "d38855a934d85a5a83d97c0ce1ff3e8a2fede0a8b5711f0817e1b0569d5ff657", "program_fingerprint_scope": "Actual own selected full/orientation hashes are checked. Optional canonical absence remains explicit; scalar specialization does not prove operator or phase endpoints.", "invoice_fingerprint": "a3ebe4d62e2543177d1d79334864ee862ca29ffb0a4ec4285c1e76448aca785a", "invoice_fingerprint_scope": "Fresh own complete PLAN/OWNERS, whole helper widths, chronological windows, charts, stock and full no-prior invoice; source-equivalent numeric parent provenance is disclosed.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "1601159251759369/1000000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "canonical_catalogue_absent_for": [], "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_scope": "New direct Gaussian realization of the same own selected source core; no literal historical dual-supplier replay is claimed.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr578-exact-mixed-finite-early-upper.json", "scope": "Conditional sufficient eventual bound for every positive XOR tariff against the same repaired unlimited optimized-GMP reference, retaining the stated own typed native/frame/phase/all-size and analytic interfaces.", "exact_individual_crossing": false }, "record_certificate_file": "pr578-exact-mixed-finite-record-upper.json", "record_certificate_sha256": "baa5892675bfae13b11a2517667afb8a19d2439588ac89af159b734e173ca028", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "selected_provider_v3_whole_bounds.py" ], "reproduction_commands": [ [ "selected_provider_dispatch_v3.py", "--execute" ], [ "selected_provider_v3_whole_bounds.py" ] ], "source_discovery_scope": "Two own original mixed-provider specifications are bound to exact recovered raw canonical/program digests and both orientations. Full native scalar/GF2 and owner/invoice replays are separate from the retained absolute phase/operator/all-size premises.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 579, "source_commit": "970d38a3862ee35064a827b671d196744ee2a928", "certificate_file": "pr579-open-multicold-v3-literal-cover-lower.json", "certificate_sha256": "7b415b50210dd3e65e1021f14f2d7100c648393f4d296b139b583662c27943d8", "lower_certificate_file": "pr579-open-multicold-v3-literal-cover-lower.json", "lower_certificate_sha256": "7b415b50210dd3e65e1021f14f2d7100c648393f4d296b139b583662c27943d8", "peer_review_file": "pr579-open-multicold-v3-literal-cover-peer-review.json", "peer_review_sha256": "3290aeaffb9725dd6c51131075ee39a3166dead9ce12545d2d82b321f8b56761", "source_peer_review_file": "pr579-open-multicold-v3-literal-cover-source-peer-review.json", "source_peer_review_sha256": "8e48d2a0cf37220338697b3f4944ff7c1f9249af9b951ec0aecf380c724e08a6", "proof_file": "open-multicold-literal-cover-lowers-v3.md", "family_kind": "finite-literal-complete-cover-source-core", "upper": null, "lower": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source": "data/operation-audit/pr579-open-multicold-v3-literal-cover-lower.json" }, "effective_kappa": "64050406799533/40000000000000000", "kappa_record": "64050406799533/40000000000000000", "kappa_is_source_provenance_only": true, "asymptotic_record_exponent_reproved": false, "native_coordinate_rank": 73, "uniform_rank_H": null, "record_tail_quantified": false, "necessary_lower_quantifier": "all_valid_literal_family_public_policies", "sufficient_upper_policy": null, "upper_not_for_all_switching_policies": true, "selected_provider": "prefixk_eight", "actual_selected_provider_calls": 48, "other_changed_providers_claimed_validated": false, "baseline_upper_refinement_file": "optimized-gmp-degree8-compact-upper.json", "baseline_upper_refinement_sha256": "2bad0e4989947e2ef601613c1ad49ba54088c83a4827fd2feacb9f5b69c24956", "baseline_refinement_scope": "Sharper upper on the same fixed reference proves only this necessary prefix; no reference algorithm, source record or sufficient upper changes.", "scope": [ "Own universal Gaussian/helper required entry/output/absolute-phase/identity-spectator and owned/all-size correctness remain substantive hypotheses. This lower proves compulsory cost of the prescribed literal body, not correctness or original record validity of unexecuted providers.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Only V is used; no coordinate-volume factor, stock upper used as lower, selected activation threshold, sufficient upper, exact crossing, human/formal proof or hardware claim.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Lower only; one positively used exact own-source provider suffices for compulsory work in the complete prescribed kernel. Other changed providers are not substituted or claimed validated. No upper or actual crossing." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "open_multicold_literal_cover_lowers_v3.py" ], "reproduction_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "open_multicold_literal_cover_lowers_v3.py" ] ], "offline_verification_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "open_multicold_literal_cover_lowers_v3.py" ] ], "offline_verification_scope": "Reauthenticate exact own immutable MANIFEST/API/PLAN, selected actual canonical/programme/orientation and descriptor commitments, selected main complete-cover source chain, group count and same-reference strict tariff inequality. No constructor, full phase, owner, invoice or original CLI pass is claimed by these lower-only jobs.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 582, "source_commit": "747ec97129eb85b1e57bf73c934400fe08a8c6cd", "certificate_file": "pr582-early-frame-finite-early-upper.json", "certificate_sha256": "3e10361b3659179fb81c97914b5bd7e8d42fed2d3778ceb8a87141508d7c7b38", "peer_review_file": "pr582-early-frame-finite-peer-review.json", "peer_review_sha256": "6f3c857414864362626bcd5611a72a08390b5e3c15e675ffdf2616b00599b2f7", "source_peer_review_file": "pr582-early-frame-finite-source-peer-review.json", "source_peer_review_sha256": "d392f0318d348eb0c22954e99bee03fa53c90ff9d04f342f9945f5207e6268d7", "proof_file": "selected-provider-v22-whole-upper.md", "family_kind": "own-selected-early-frame-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr582-early-frame-finite-record-upper.json", "record_certificate_sha256": "1348db3eb3446518ecbcbc47fc825f787ac088e30e475a4bb72c754465961c86", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "800743477696243/500000000000000000", "native_certificate_file": "pr582-early-frame-finite-native.json", "native_certificate_sha256": "d35aa7d482767392ec03a7e5317f70237cbe70b8c794151d4da55c2577952773", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "historical_parent_byte_identity_claimed": false, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": false, "source_report_counter_mismatch": false, "descriptive_entering_counter": { "source_declared_entering_helper_roles": 16404, "actual_nonzero_start_frame_roles": 16404, "width_below_9_roles": 16404, "source_declared_meter_style": "actual_initial_nonzero_frames", "source_declared_counter_matches_actual": true, "used_by_new_cost_stock_or_precision": false }, "source_caveats": [ "The early own SPEC does not declare a canonical semantic digest. Its actual canonical catalogue is explicitly derived from the exact own selected RAW endpoint and unchanged native engines, with both complete own orientation programs checked.", "The original complete582/584 phase/global CLI is not claimed rerun. Required operator/absolute-phase/owned/all-size/analytic interfaces remain conditional." ], "scope": "Own explicitly selected finite source core, exact RAW and complete program commitments, full own PLAN/OWNERS and fresh complete physical invoice; newly counted direct Gaussian realization with retained operator, phase, owned, all-size and analytic contracts. No earlier invoice or cutoff transfer.", "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "prepare_selected_provider_v22.py" ], [ "selected_provider_dispatch_v22.py", "--execute" ], [ "prepare_selected_provider_v22_whole_costs.py" ], [ "selected_provider_v22_whole_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 583, "source_commit": "89be768f0157f5a3d8e4db69cf1748768605eac9", "certificate_file": "pr583-open-multicold-v3-literal-cover-lower.json", "certificate_sha256": "621524eb0dc2d7ef9aab96373da2323f8cb3e4d3ae044cd23c6c00498606bb71", "lower_certificate_file": "pr583-open-multicold-v3-literal-cover-lower.json", "lower_certificate_sha256": "621524eb0dc2d7ef9aab96373da2323f8cb3e4d3ae044cd23c6c00498606bb71", "peer_review_file": "pr583-open-multicold-v3-literal-cover-peer-review.json", "peer_review_sha256": "004d408e738e38bd74fb8cfd159d163f55ec1ce7bc90e35cbb504cf2438e0eba", "source_peer_review_file": "pr583-open-multicold-v3-literal-cover-source-peer-review.json", "source_peer_review_sha256": "70495a777ae95dd79df2e998cce8701b7d34833529a02d6cc61ea072a241b244", "proof_file": "open-multicold-literal-cover-lowers-v3.md", "family_kind": "finite-literal-complete-cover-source-core", "upper": null, "lower": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source": "data/operation-audit/pr583-open-multicold-v3-literal-cover-lower.json" }, "effective_kappa": "800830761063899/500000000000000000", "kappa_record": "800830761063899/500000000000000000", "kappa_is_source_provenance_only": true, "asymptotic_record_exponent_reproved": false, "native_coordinate_rank": 73, "uniform_rank_H": null, "record_tail_quantified": false, "necessary_lower_quantifier": "all_valid_literal_family_public_policies", "sufficient_upper_policy": null, "upper_not_for_all_switching_policies": true, "selected_provider": "prefix_eight", "actual_selected_provider_calls": 24, "other_changed_providers_claimed_validated": false, "baseline_upper_refinement_file": "optimized-gmp-degree8-compact-upper.json", "baseline_upper_refinement_sha256": "2bad0e4989947e2ef601613c1ad49ba54088c83a4827fd2feacb9f5b69c24956", "baseline_refinement_scope": "Sharper upper on the same fixed reference proves only this necessary prefix; no reference algorithm, source record or sufficient upper changes.", "scope": [ "Own universal Gaussian/helper required entry/output/absolute-phase/identity-spectator and owned/all-size correctness remain substantive hypotheses. This lower proves compulsory cost of the prescribed literal body, not correctness or original record validity of unexecuted providers.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Only V is used; no coordinate-volume factor, stock upper used as lower, selected activation threshold, sufficient upper, exact crossing, human/formal proof or hardware claim.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Lower only; one positively used exact own-source provider suffices for compulsory work in the complete prescribed kernel. Other changed providers are not substituted or claimed validated. No upper or actual crossing." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "open_multicold_literal_cover_lowers_v3.py" ], "reproduction_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "open_multicold_literal_cover_lowers_v3.py" ] ], "offline_verification_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "open_multicold_literal_cover_lowers_v3.py" ] ], "offline_verification_scope": "Reauthenticate exact own immutable MANIFEST/API/PLAN, selected actual canonical/programme/orientation and descriptor commitments, selected main complete-cover source chain, group count and same-reference strict tariff inequality. No constructor, full phase, owner, invoice or original CLI pass is claimed by these lower-only jobs.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 584, "source_commit": "e580557d85eb8b8a100361926252d120eb447a44", "certificate_file": "pr584-early-frame-finite-early-upper.json", "certificate_sha256": "cabeadee90bcadaf35097efb1084b3cd3ddd5dbafd9bc13d1df4693c00b6a214", "peer_review_file": "pr584-early-frame-finite-peer-review.json", "peer_review_sha256": "7cb34c952c1a7dbe1caf0626584ae4cdd093f3c6a38ebdb2ee6d5e6b65ee64ea", "source_peer_review_file": "pr584-early-frame-finite-source-peer-review.json", "source_peer_review_sha256": "fb117a28a40e2bf784ae905ce3fdf0f1270fd3b699c033789ef4ab7a1c662512", "proof_file": "selected-provider-v22-whole-upper.md", "family_kind": "own-selected-early-frame-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr584-early-frame-finite-record-upper.json", "record_certificate_sha256": "71d4d4eef7c349c624070d01f54b9033422af514e91a1ebd65ff480142546ad2", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "1602080856660739/1000000000000000000", "native_certificate_file": "pr584-early-frame-finite-native.json", "native_certificate_sha256": "aba9aa112d4f5b8641dc64df6b26b523a6d791081654b09e209fe4234293ae45", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "historical_parent_byte_identity_claimed": false, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": false, "source_report_counter_mismatch": false, "descriptive_entering_counter": { "source_declared_entering_helper_roles": 16404, "actual_nonzero_start_frame_roles": 16404, "width_below_9_roles": 16404, "source_declared_meter_style": "actual_initial_nonzero_frames", "source_declared_counter_matches_actual": true, "used_by_new_cost_stock_or_precision": false }, "source_caveats": [ "The early own SPEC does not declare a canonical semantic digest. Its actual canonical catalogue is explicitly derived from the exact own selected RAW endpoint and unchanged native engines, with both complete own orientation programs checked.", "The original complete582/584 phase/global CLI is not claimed rerun. Required operator/absolute-phase/owned/all-size/analytic interfaces remain conditional." ], "scope": "Own explicitly selected finite source core, exact RAW and complete program commitments, full own PLAN/OWNERS and fresh complete physical invoice; newly counted direct Gaussian realization with retained operator, phase, owned, all-size and analytic contracts. No earlier invoice or cutoff transfer.", "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "prepare_selected_provider_v22.py" ], [ "selected_provider_dispatch_v22.py", "--execute" ], [ "prepare_selected_provider_v22_whole_costs.py" ], [ "selected_provider_v22_whole_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 586, "source_commit": "4846fee5b06af770e9b3a10c36200f673d656725", "certificate_file": "pr586-cold14-typed-finite-early-upper.json", "certificate_sha256": "cc1d191ce50f3065cfb567dc3240e32ceef056682eb5894aba31cce4b5ad4957", "peer_review_file": "pr586-cold14-typed-finite-peer-review.json", "peer_review_sha256": "b7d52925f4b62d0fb2db8f1e9da7fe75a07090c6696d0005f3260b4849c52c44", "source_peer_review_file": "pr586-cold14-typed-finite-source-peer-review.json", "source_peer_review_sha256": "1a0e114167c63d82ddb9db2c01ee58aa44fe03a13cd60c6ffb7c7fc8b2b6ef91", "proof_file": "selected-provider-v12-whole-upper.md", "family_kind": "rank73-exact-own-selected-typed-cold14-early-Gaussian-no-BIT", "native_certificate_file": "pr586-cold14-typed-finite-native.json", "native_certificate_sha256": "64f0acdff05c62b234877c94d95527e8bfa32716abb2d325c5912b753e476656", "program_fingerprint": "9d71ae0e06a2b53b8b529fd49632eb80b5f81f43e090f1244be8d3c61f5a81c3", "program_fingerprint_scope": "Actual complete selected programme/canonical byteobjects and both orientation commitments are exact. Full operator-valued required-boundary and absolute-phase contract remains explicit.", "invoice_fingerprint": "7ff3f4f2d182da15902fa5feb2746292ae1f12a7c07217e7fab14f1907eb263f", "invoice_fingerprint_scope": "Fresh complete own PLAN/OWNERS/calls/windows/charts/profile and no-prior full invoice, with disclosed new numeric parent provenance.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "1602080856660739/1000000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_quantified": true, "record_tail_scope": "Own original record exponent is separately quantified by this new direct Gaussian circuit.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr586-cold14-typed-finite-early-upper.json", "scope": "Conditional sufficient eventual bound for the explicitly weaker early exponent1/5000, all positive XOR tariffs, same repaired unlimited optimized-GMP reference; retained native/frame/phase/all-size/analytic interfaces.", "exact_individual_crossing": false }, "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "recover_cold14_chain_native_bytes.py" ], [ "prepare_selected_provider_v12.py" ], [ "selected_provider_dispatch_v12.py", "--execute" ], [ "cold14_descriptive_counter_audit.py" ], [ "selected_provider_v12_whole_bounds.py" ] ], "offline_verification_commands": [ [ "cold14_descriptive_counter_audit.py" ], [ "selected_provider_v12_whole_bounds.py" ] ], "offline_verification_scope": "Fast complete numerical envelope replay from bound source censuses. Actual typed native byte and complete physical invoice replays are explicit separate reproduction jobs, with their closed source/receipt bytes bound; complete operator/phase endpoints remain stated premises.", "source_discovery_scope": "The actual own author-head MANIFEST and literal verifier select each own SPEC/PLAN/OWNERS. Exact actual typed-constructor intermediate byteobjects match every selected canonical/program/orientation commitment. Actual own selected programme/orientation commitments and newly fetched exact physical inputs are checked; no equal-kappa/profile inference or cutoff transfer.", "descriptive_entering_counter": { "source_declared_entering_helper_roles": 16404, "actual_nonzero_start_frame_roles": 16404, "width_below_9_roles": 16404, "source_declared_meter_style": "actual_initial_nonzero_frames", "source_declared_counter_matches_actual": true, "used_by_new_cost_stock_or_precision": false }, "original_global_verifier_full_PASS_claimed": false, "source_caveats": [], "record_certificate_file": "pr586-cold14-typed-finite-record-upper.json", "record_certificate_sha256": "37cc2dcbcecfd54b654a43b995cd6a4050adb4bf08ad2885d44135ea537c2aa0", "record_P": "230584301497830147503423480", "record_tail_input_bits": "2^(2^230584301497830147503423480)", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 588, "source_commit": "6d0e53b66c29abd17981881a09eaff41ac862d85", "certificate_file": "pr588-mixed-finite-controller-early-upper.json", "certificate_sha256": "11cfab50be1ec275616b9fc31af20b8befc0d8584d1fbb6c59ddf0288db6c6b9", "peer_review_file": "pr588-mixed-finite-controller-peer-review.json", "peer_review_sha256": "fd1afa89543f281ac7e364b1baf6ab9a0986cfe2de6429a37556b27228efc321", "source_peer_review_file": "pr588-mixed-finite-controller-source-peer-review.json", "source_peer_review_sha256": "1cc877075f75ae1e4b5805357a21ea850a131964219be9cfe00e3c40fa285c05", "proof_file": "early-mixed-finite-controller-upper.md", "family_kind": "rank73-own-mixed-selected-finite-controller", "native_certificate_file": "pr588-mixed-finite-controller-native.json", "native_certificate_sha256": "c0bcc42571fb8fa0eeb397c953934428c1eff2e80e190e3ddd7c68be8806d31c", "program_fingerprint": "9eca17bd0f67f041fa89c5e35b21d1289fad25413790434385d327cbc3abe041", "program_fingerprint_scope": "Exact own selected canonical/program/orientation commitments; finite objects reconstructed from hash-pinned own recipes, not substitution of later algorithm/profile.", "invoice_fingerprint": "ffd4adb9a7ec3ab39bb7cb2c905e4d5c8d075df4e8947487f8bcb133d34592e5", "invoice_fingerprint_scope": "Fresh own selected provider/orientation primitive and wrapper census plus complete own physical owner/window/sweep/bank invoice; no prior invoice.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "400569730495803/250000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr588-mixed-finite-controller-early-upper.json", "scope": "Conditional sufficient eventual upper in the same fixed XAG/unlimited optimized-GMP model for every positive XOR tariff; own source-equivalent numeric realization.", "exact_individual_crossing": false }, "record_certificate_file": "pr588-mixed-finite-controller-record-upper.json", "record_certificate_sha256": "d05eca1ee7d1264a7d4709eb1f58961c7592ab8c0afbeaadb9c5970f6e981134", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own arbitrary-input operator-valued native phase, normalized-wrapper, ascending typed-helper and whole Gaussian endpoint contracts remain explicit; scalar specialization is not their proof.", "Exact own selected canonical/program/orientation hashes, actual scalar/frame incidence and dyadic Horner/prefix counts are checked independently. Derived objects are rebuilt from earlier hash-pinned recipes, sometimes using exact matching later archive bytes; no later supplier is imported.", "Each own PLAN/order/dispatch/OWNERS/window, complete role namespace, residual/spectator chart, primitive/wrapper invoice and no-prior-invoice finite stock is freshly checked.", "The counted parent is a primary-fixture source-equivalent numeric realization matching own physical windows; historical parent provenance metadata byte identity is not claimed.", "Common-label, mutable-source, arbitrary-input owned restore and all-size unequal-child occupied-row batching remain fixed-protocol hypotheses; completed Gaussian children have norm one under the endpoint contract.", "Own C0=2^210000 and actual512-bit payload fund the semantic precision reserve. 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The prior successful 1645-check native reconstruction is authenticated; the final source reviewer freshly checked uncached scalar/frame data and complete physical costs, and does not claim a new full native/operator/phase pipeline pass. Partial operator/absolute-phase, normalized-child, owned/common-label/all-size and analytic contracts remain explicit. 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No phase/operator endpoint is inferred from scalar specialization.", "invoice_fingerprint": "a178829d68e2d64eed68eec3da34a9d3de296a685f8db95b0b0ac51130641995", "invoice_fingerprint_scope": "Fresh own complete selected-call/physical owner/window/nonlocal/stock invoice, no prior invoice. Source-equivalent numeric parent provenance is disclosed.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "1612719427075359/1000000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "canonical_catalogue_absent_for": [], "operator_phase_proved": false, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr592-dispatched-finite-controller-early-upper.json", "scope": "Conditional sufficient eventual upper for each positive XOR tariff in the same XAG/unlimited optimized-GMP model, with explicit own full physical/phase/native interface premises.", "exact_individual_crossing": false }, "record_certificate_file": "pr592-dispatched-finite-controller-record-upper.json", "record_certificate_sha256": "6052dea307f0011102c68584cbde9614e7fafcc5c5f4b0de75b827bd79b738fa", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "selected_provider_whole_bounds.py" ], "reproduction_commands": [ [ "selected_provider_admitted_replay.py" ], [ "selected_provider_whole_bounds.py" ] ], "broader_discovery_reproduction": [ "selected_provider_dispatch.py", "--execute" ], "broader_discovery_scope": "Optional144-entry/38-numeric-input discovery replay requires additional unpriced source artifacts; the admitted scoped replay needs only these fifteen own source sets.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 596, "source_commit": "7732dd5e46863ff294b5e443661cb9d99abf4e01", "certificate_file": "pr596-mixed-finite-controller-early-upper.json", "certificate_sha256": "58419af8a1007ee6ed0f2a7ad2ad3186e5f9fec34cc0947bf95a74b557357da8", "peer_review_file": "pr596-mixed-finite-controller-peer-review.json", "peer_review_sha256": "643eedc198bb7e51c5b2533530187024d099d8e7196f876bf4fd5982a82bef10", "source_peer_review_file": "pr596-mixed-finite-controller-source-peer-review.json", "source_peer_review_sha256": "9eec641069a184409110794f8224f4283fa79a7a31d23330f5c2dcc1f4855579", "proof_file": "early-mixed-finite-controller-upper.md", "family_kind": "rank73-own-mixed-selected-finite-controller", "native_certificate_file": "pr596-mixed-finite-controller-native.json", "native_certificate_sha256": "f4aee66d547dc5381ff7ae7f093011eb8695a4dca11b57bbfee9b8134d628548", "program_fingerprint": "241dd5936f565cceb733885095a47ffd663181616a0a1b9da2322c5a8c75a860", "program_fingerprint_scope": "Exact own selected canonical/program/orientation commitments; finite objects reconstructed from hash-pinned own recipes, not substitution of later algorithm/profile.", "invoice_fingerprint": "9eb9f31d9f4470627a22b9f09e578bcdf3c5998c9d39f37b564f397e222eed62", "invoice_fingerprint_scope": "Fresh own selected provider/orientation primitive and wrapper census plus complete own physical owner/window/sweep/bank invoice; no prior invoice.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "16127213726553/10000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr596-mixed-finite-controller-early-upper.json", "scope": "Conditional sufficient eventual upper in the same fixed XAG/unlimited optimized-GMP model for every positive XOR tariff; own source-equivalent numeric realization.", "exact_individual_crossing": false }, "record_certificate_file": "pr596-mixed-finite-controller-record-upper.json", "record_certificate_sha256": "5e67ab882cdfa364a05252cb3d2e1c99874eb34255a575c983f20644241a7b47", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own arbitrary-input operator-valued native phase, normalized-wrapper, ascending typed-helper and whole Gaussian endpoint contracts remain explicit; scalar specialization is not their proof.", "Exact own selected canonical/program/orientation hashes, actual scalar/frame incidence and dyadic Horner/prefix counts are checked independently. Derived objects are rebuilt from earlier hash-pinned recipes, sometimes using exact matching later archive bytes; no later supplier is imported.", "Each own PLAN/order/dispatch/OWNERS/window, complete role namespace, residual/spectator chart, primitive/wrapper invoice and no-prior-invoice finite stock is freshly checked.", "The counted parent is a primary-fixture source-equivalent numeric realization matching own physical windows; historical parent provenance metadata byte identity is not claimed.", "Common-label, mutable-source, arbitrary-input owned restore and all-size unequal-child occupied-row batching remain fixed-protocol hypotheses; completed Gaussian children have norm one under the endpoint contract.", "Own C0=2^210000 and actual512-bit payload fund the semantic precision reserve. Same direct analytic fine-prime/boundary/recovery, candidate-only Fermat helper and repaired unlimited GMP correctness/halting interfaces." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "early_mixed_native_components.py" ], "reproduction_commands": [ [ "early_mixed_native_components.py" ], [ "early_mixed_owner_invoice.py" ], [ "early_mixed_finite_controller_upper.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 600, "source_commit": "dfb7b827990d7b586b3cd778e3d750c050dd4778", "certificate_file": "pr600-dispatched-finite-controller-early-upper.json", "certificate_sha256": "9fb7902432e62896085ff01ff990482faaa763d774b56fb92afb38c83b0d0ae0", "peer_review_file": "pr600-selected-provider-batch-peer-review.json", "peer_review_sha256": "de46756afd23856da6b78b6e5d986d6c8d6825afc2038fd30a1100b443b5e2d4", "source_peer_review_file": "pr600-dispatched-finite-controller-source-peer-review.json", "source_peer_review_sha256": "3d055872d07ba39fc40ca1ea472e7c011e304271b38f590012b532e8d0e99719", "proof_file": "selected-provider-batch-upper.md", "family_kind": "rank73-own-selected-provider-finite-controller", "native_certificate_file": "pr600-dispatched-finite-controller-native.json", "native_certificate_sha256": "4f5b718b9e4114cbba3258803c19bba413c0a5cc754a86cb4f7f50942a47cec8", "program_fingerprint": "1a1a42d77b0c8d6d3eec86f4976ad93dc1529a9b44ba4b56be317a787dd2de59", "program_fingerprint_scope": "Actual own-selected full/orientation hash-bound program; optional canonical catalogue absence is explicit. No phase/operator endpoint is inferred from scalar specialization.", "invoice_fingerprint": "a178829d68e2d64eed68eec3da34a9d3de296a685f8db95b0b0ac51130641995", "invoice_fingerprint_scope": "Fresh own complete selected-call/physical owner/window/nonlocal/stock invoice, no prior invoice. Source-equivalent numeric parent provenance is disclosed.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "1612722852614221/1000000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "canonical_catalogue_absent_for": [], "operator_phase_proved": false, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr600-dispatched-finite-controller-early-upper.json", "scope": "Conditional sufficient eventual upper for each positive XOR tariff in the same XAG/unlimited optimized-GMP model, with explicit own full physical/phase/native interface premises.", "exact_individual_crossing": false }, "record_certificate_file": "pr600-dispatched-finite-controller-record-upper.json", "record_certificate_sha256": "779034e1948a80d6cfcd571f81bdb37dd2ede4700028e533343ea2246b0136f2", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. 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Actual typed native byte and complete physical invoice replays are explicit separate reproduction jobs, with their closed source/receipt bytes bound; complete operator/phase endpoints remain stated premises.", "source_discovery_scope": "The actual own author-head MANIFEST and literal verifier select each own SPEC/PLAN/OWNERS. Exact actual typed-constructor intermediate byteobjects match every selected canonical/program/orientation commitment. Actual own selected programme/orientation commitments and newly fetched exact physical inputs are checked; no equal-kappa/profile inference or cutoff transfer.", "descriptive_entering_counter": { "source_declared_entering_helper_roles": 16344, "actual_nonzero_start_frame_roles": 16344, "width_below_9_roles": 17352, "source_declared_meter_style": "actual_initial_nonzero_frames", "source_declared_counter_matches_actual": true, "used_by_new_cost_stock_or_precision": false }, "original_global_verifier_full_PASS_claimed": false, "source_caveats": [], "record_certificate_file": "pr607-cold14-typed-finite-record-upper.json", "record_certificate_sha256": "0248e23d65d7a28e3b7a3a9fad5df1321c5b355004543b3684f83b185ef8d14a", "record_P": "230584301497830147503423480", "record_tail_input_bits": "2^(2^230584301497830147503423480)", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 608, "source_commit": "702e397432df9233cdd02e43f1f6f32e195eba84", "certificate_file": "pr608-registry-reconciled-finite-early-upper.json", "certificate_sha256": "0307df9eae5d6fd2710db34b18ce88af48140213efde8cffc2fb0ebd4167d4a3", "peer_review_file": "pr608-registry-reconciled-finite-peer-review.json", "peer_review_sha256": "ac1e0e70bcbee776aec2333ab439dbced4b83aca8387ea4c0c31ebcdc9f643f4", "source_peer_review_file": "pr608-registry-reconciled-finite-source-peer-review.json", "source_peer_review_sha256": "d5ce2a55e9fe3425e922f32071a8d0d87723972e0bad8ea2dad7560645c132f5", "proof_file": "selected-provider-v26-whole-upper.md", "family_kind": "own-registry-reconciled-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr608-registry-reconciled-finite-record-upper.json", "record_certificate_sha256": "05c513a79bcc16e8d306818dabc4bc0b758b6084b1cb953946a43a0cb2309e7d", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "322713922116043/200000000000000000", "native_certificate_file": "pr608-registry-reconciled-finite-native.json", "native_certificate_sha256": "fd3366a8f5c3d35a5ac4fed428c7679e62e993eb1dd90187ba5f1dd99c328f40", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "source_registry_metadata_reconciled": true, "original_source_PLAN_rewritten": false, "original_V23_rejection_preserved": true, "registry_metadata_reconciliation": { "schema": "own608-explicit-registry-numeric-metadata-reconciliation/1", "pr": 608, "own_head": "702e397432df9233cdd02e43f1f6f32e195eba84", "status": "four_redundant_registry_fields_reconciled_in_separate_numeric_descriptor", "original_plan_semantic_sha256": "800376d17e02d0a5182924d898817498a55b25b23d7e87d166ae897239d8754a", "derived_numeric_plan_semantic_sha256": "890afd107702483d921c026e0440a1abe17c81e6b86703c375534f90fa5a4490", "exact_changed_fields": [ { "path": [ "provider_registry", "atm3", "orientation_program_sha256" ], "source_value": { "forward": "bf24a308a5552bab4400ac2130dce64e18f3f093eb5bce288950ac05cd2b7f11", "backward": "0eb5352c4734f59c18a9d5fc48aab3efb9d408a4052b8e4ce5a8f5c8da097fe4" }, "derived_numeric_value": { "backward": "802d20d4ec675a4a52ef95ba03d640ff364b8ed2d72b62336ee1ac23c77854d7", "forward": "4f797dda98d3839539a238392810f0c235008e74db6342ec8e0901be6852a314" } }, { "path": [ "provider_registry", "atm3", "actual_paid_profile" ], "source_value": { "1": 2598, "2": 416, "3": 280, "4": 232, "5": 56, "6": 56, "8": 8 }, "derived_numeric_value": { "1": 2614, "2": 408, "3": 288, "4": 224, "5": 56, "6": 56, "8": 8 } }, { "path": [ "provider_registry", "ck", "orientation_program_sha256" ], "source_value": { "forward": "b80dbd670b2a001528a0667c94c481f4faeed4494240d4f076b6d1744bdfde78", "backward": "08366c7cfdaed343aab07a10ecd67d5b8a9adf5fa96948fa8feb0dea7447cea5" }, "derived_numeric_value": { "backward": "433a8224b14c9963f14de984a3ed520f50537fe28cd4da60b700e7eecbe22ad7", "forward": "cff18ba448e3c3823f53198d1bc6657ca749e47135e38c92538be8d8d25ec081" } }, { "path": [ "provider_registry", "ck", "actual_paid_profile" ], "source_value": { "1": 2518, "2": 496, "3": 320, "4": 192, "5": 56, "6": 56, "8": 8 }, "derived_numeric_value": { "1": 2534, "2": 488, "3": 328, "4": 184, "5": 56, "6": 56, "8": 8 } } ], "every_other_PLAN_field_unchanged": true, "actual_call_programmes_already_match_own_SPEC": true, "complete_artifact_semantics_already_match_own_SPEC": true, "old_source_PLAN_rewritten": false, "original_complete_source_verifier_PASS_claimed": false, "physical_cost_noninterference_still_requires_separate_check": true, "original_PLAN_file": "early-hyperplane-cold-own-source/608/f1a52bf3b173__PLAN.json", "original_PLAN_sha256": "4ace3e4362b713af245d5e407cc83bd4901545c6e77e50cf6dbd0ed43f229d8f", "derived_numeric_PLAN_file": "selected-provider-dispatch-v26-source/608/derived-numeric-PLAN.json", "derived_numeric_PLAN_sha256": "09c473b9ff1a8a7f0579fed89b9856e2fc50fa0163323e236c90cb97a44cb1f5", "reconciliation_module_sha256": "90a800f87fa1ff6e86763b4af2e349f55c8f46215256ece5a7c86de0d0b248e2", "complete_physical_context_identical": true, "complete_role_receipt_identical": true, "all_six_negative_controls_identical": true }, "original_global_verifier_full_PASS_claimed": false, "descriptive_entering_counter": { "source_declared_entering_helper_roles": 16416, "actual_nonzero_start_frame_roles": 16416, "width_below_9_roles": 16416, "source_declared_meter_style": "actual_initial_nonzero_frames", "source_declared_counter_matches_actual": true, "used_by_new_cost_stock_or_precision": false }, "source_report_counter_mismatch": false, "scope": "A new direct Gaussian realization uses the exact own608 selected native words and physical schedule. Its original PLAN contains four redundant registry fields with stale programme/profile values; a separate numeric descriptor updates only those four fields. Actual full artefact semantics and every call-programme digest were already current and are mandatory. Every other PLAN field, all36288 roles, six negative controls and the complete fresh invoice agree exactly. The original source PLAN and its V23 rejection are preserved; no original CLI or universal native/operator/phase PASS is claimed. A subsequent cached-replay defect was repaired by moving the existing integer profile-key restoration before the exact equality guard; two cached passes agree and only provenance hashes changed. Partial operator/absolute-phase, normalized-child, owned/common-label/all-size and analytic contracts remain explicit. No prior invoice or cutoff is transferred; no actual first crossing is known.", "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "prepare_selected_provider_v26.py" ], [ "selected_provider_dispatch_v26.py", "--execute" ], [ "own608_registry_metadata_audit.py" ], [ "prepare_selected_provider_v26_whole_costs.py" ], [ "registry_reconciled_descriptive_counter_audit.py" ], [ "selected_provider_v26_whole_bounds.py" ], [ "verify_v26_cached_profile_key_portability_repair.py" ] ], "optional_selected_byte_object_recovery_command": [ "recover_early_hyperplane_cold_native.py" ], "supplementary_source_audit_file": "v26-cached-profile-key-portability-repair.json", "supplementary_source_audit_sha256": "61ddcf816656e93dcf48487d4b4c490f0a0c0bc4c2dc4149ec50f9e0570879b2", "supplementary_source_audit_proof_file": "v26-cached-profile-key-portability-repair.md", "supplementary_source_audit_replay_driver": "verify_v26_cached_profile_key_portability_repair.py", "supplementary_source_audit_replay_driver_sha256": "4d39dfd670bf9f822d74b96ce36feee7872037bda937018b83a86e0041264618", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 609, "source_commit": "10255d48152ed9f159f7c51028b1fc34a4ccc982", "certificate_file": "pr609-cold14-typed-finite-early-upper.json", "certificate_sha256": "a63eac467d89610ea7e5d0f435dfcbcd618fe18fa41f1a607473fd6a83873482", "peer_review_file": "pr609-cold14-typed-finite-peer-review.json", "peer_review_sha256": "71652159d8db3c10ddf10e7dab7fb2335881369c7a6ca8a69f797fab9c367dd2", "source_peer_review_file": "pr609-cold14-typed-finite-source-peer-review.json", "source_peer_review_sha256": "3d3f35b9242e663802a5293054847b6592c230426c9248b842e2fc2047d87a8e", "proof_file": "selected-provider-v12-whole-upper.md", "family_kind": "rank73-exact-own-selected-typed-cold14-early-Gaussian-no-BIT", "native_certificate_file": "pr609-cold14-typed-finite-native.json", "native_certificate_sha256": "01d23b1e64ece5783a861a2e56f1c0a255aa10e2731d26ec0144db0b263d7f26", "program_fingerprint": "8395d8b79f6bca9f144ff72b12d519cb89b148708b4e942d3ee60d08a3f476f3", "program_fingerprint_scope": "Actual complete selected programme/canonical byteobjects and both orientation commitments are exact. Full operator-valued required-boundary and absolute-phase contract remains explicit.", "invoice_fingerprint": "0cbe4cf54c1c6f2fdbbcd6e7427186045db608d60df47b69ab267d92ebd2a28e", "invoice_fingerprint_scope": "Fresh complete own PLAN/OWNERS/calls/windows/charts/profile and no-prior full invoice, with disclosed new numeric parent provenance.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "324457099582947/200000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_quantified": true, "record_tail_scope": "Own original record exponent is separately quantified by this new direct Gaussian circuit.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr609-cold14-typed-finite-early-upper.json", "scope": "Conditional sufficient eventual bound for the explicitly weaker early exponent1/5000, all positive XOR tariffs, same repaired unlimited optimized-GMP reference; retained native/frame/phase/all-size/analytic interfaces.", "exact_individual_crossing": false }, "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "recover_cold14_chain_native_bytes.py" ], [ "prepare_selected_provider_v12.py" ], [ "selected_provider_dispatch_v12.py", "--execute" ], [ "cold14_descriptive_counter_audit.py" ], [ "selected_provider_v12_whole_bounds.py" ] ], "offline_verification_commands": [ [ "cold14_descriptive_counter_audit.py" ], [ "selected_provider_v12_whole_bounds.py" ] ], "offline_verification_scope": "Fast complete numerical envelope replay from bound source censuses. Actual typed native byte and complete physical invoice replays are explicit separate reproduction jobs, with their closed source/receipt bytes bound; complete operator/phase endpoints remain stated premises.", "source_discovery_scope": "The actual own author-head MANIFEST and literal verifier select each own SPEC/PLAN/OWNERS. Exact actual typed-constructor intermediate byteobjects match every selected canonical/program/orientation commitment. Actual own selected programme/orientation commitments and newly fetched exact physical inputs are checked; no equal-kappa/profile inference or cutoff transfer.", "descriptive_entering_counter": { "source_declared_entering_helper_roles": 16344, "actual_nonzero_start_frame_roles": 16344, "width_below_9_roles": 17352, "source_declared_meter_style": "actual_initial_nonzero_frames", "source_declared_counter_matches_actual": true, "used_by_new_cost_stock_or_precision": false }, "original_global_verifier_full_PASS_claimed": false, "source_caveats": [], "record_certificate_file": "pr609-cold14-typed-finite-record-upper.json", "record_certificate_sha256": "2929b7fa684e53764863c37034172af8caa555b5b07a073cf859bcb753936ed7", "record_P": "230584301497830147503423480", "record_tail_input_bits": "2^(2^230584301497830147503423480)", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 610, "source_commit": "b7c680ea38b9a25a89fce189bb927b45842362d0", "certificate_file": "pr610-cold14-typed-finite-early-upper.json", "certificate_sha256": "f7b954701ee1f8eb0955fa2b611d570bb672bd7d8ae268b44899dd49f7c2f8ff", "peer_review_file": "pr610-cold14-typed-finite-peer-review.json", "peer_review_sha256": "a0b89e8202e066bac7c1e2c2fa5b465d48a5909d8a985adaa106c2666091658e", "source_peer_review_file": "pr610-cold14-typed-finite-source-peer-review.json", "source_peer_review_sha256": "7696653c98eb4c746530491e405192467c44c0af506f0404b3824b8c8f784fe7", "proof_file": "selected-provider-v12-whole-upper.md", "family_kind": "rank73-exact-own-selected-typed-cold14-early-Gaussian-no-BIT", "native_certificate_file": "pr610-cold14-typed-finite-native.json", "native_certificate_sha256": "b7042e449d58d3da284fd77c135be4c569e0040eeb95467b5f86976f7c01b873", "program_fingerprint": "212eb9989662c1575a4c042de74388611f556352411da3cded8cdd9db20d82b8", "program_fingerprint_scope": "Actual complete selected programme/canonical byteobjects and both orientation commitments are exact. Full operator-valued required-boundary and absolute-phase contract remains explicit.", "invoice_fingerprint": "9ad4b03016285c8d8e13465b83103d3c68bcd1cdb55e678810d2f7c4c71b6dc3", "invoice_fingerprint_scope": "Fresh complete own PLAN/OWNERS/calls/windows/charts/profile and no-prior full invoice, with disclosed new numeric parent provenance.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "162536523418317/100000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_quantified": true, "record_tail_scope": "Own original record exponent is separately quantified by this new direct Gaussian circuit.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr610-cold14-typed-finite-early-upper.json", "scope": "Conditional sufficient eventual bound for the explicitly weaker early exponent1/5000, all positive XOR tariffs, same repaired unlimited optimized-GMP reference; retained native/frame/phase/all-size/analytic interfaces.", "exact_individual_crossing": false }, "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts.", "Own source descriptive entering counter 16344 differs from actual nonzero initial-frame roles 15564; width-below9 roles are 16572. The new complete invoice/stock/precision bound is independently verified not to read that counter. Historical metadata is preserved; original global verifier full PASS is not claimed." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "recover_cold14_chain_native_bytes.py" ], [ "prepare_selected_provider_v12.py" ], [ "selected_provider_dispatch_v12.py", "--execute" ], [ "cold14_descriptive_counter_audit.py" ], [ "selected_provider_v12_whole_bounds.py" ] ], "offline_verification_commands": [ [ "cold14_descriptive_counter_audit.py" ], [ "selected_provider_v12_whole_bounds.py" ] ], "offline_verification_scope": "Fast complete numerical envelope replay from bound source censuses. Actual typed native byte and complete physical invoice replays are explicit separate reproduction jobs, with their closed source/receipt bytes bound; complete operator/phase endpoints remain stated premises.", "source_discovery_scope": "The actual own author-head MANIFEST and literal verifier select each own SPEC/PLAN/OWNERS. Exact actual typed-constructor intermediate byteobjects match every selected canonical/program/orientation commitment. Actual own selected programme/orientation commitments and newly fetched exact physical inputs are checked; no equal-kappa/profile inference or cutoff transfer.", "descriptive_entering_counter": { "source_declared_entering_helper_roles": 16344, "actual_nonzero_start_frame_roles": 15564, "width_below_9_roles": 16572, "source_declared_meter_style": "unreproduced_descriptive_metadata", "source_declared_counter_matches_actual": false, "used_by_new_cost_stock_or_precision": false }, "original_global_verifier_full_PASS_claimed": false, "source_caveats": [ "Own source descriptive entering counter 16344 differs from actual nonzero initial-frame roles 15564; width-below9 roles are 16572. The new complete invoice/stock/precision bound is independently verified not to read that counter. Historical metadata is preserved; original global verifier full PASS is not claimed." ], "record_certificate_file": "pr610-cold14-typed-finite-record-upper.json", "record_certificate_sha256": "25f2c331e8bfeb849be5a93d14c38a21e99b78be1f66136f3ffed1c339ca5142", "record_P": "230584301497830147503423480", "record_tail_input_bits": "2^(2^230584301497830147503423480)", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 614, "source_commit": "6cfd7e2039078f80a8a39dec5e958d8df304cb90", "certificate_file": "pr614-cold14-typed-finite-early-upper.json", "certificate_sha256": "fe46611251e05e81261e1f8e6211f973366d9edbd4d64c4823d5f2215e068ffb", "peer_review_file": "pr614-cold14-typed-finite-peer-review.json", "peer_review_sha256": "a9ebf613b481378f38688de06cbe031ea8f3c9beb71accd44a1e11316c5e6c2b", "source_peer_review_file": "pr614-cold14-typed-finite-source-peer-review.json", "source_peer_review_sha256": "c9e46148307861190e6095e8d3783ef9b2b20df25180d8af1e133f20de9229d5", "proof_file": "selected-provider-v12-whole-upper.md", "family_kind": "rank73-exact-own-selected-typed-cold14-early-Gaussian-no-BIT", "native_certificate_file": "pr614-cold14-typed-finite-native.json", "native_certificate_sha256": "a6e86148f3fd29f0a1bcf17b7dbd08f7e88346232654ce78d9192e4e99714435", "program_fingerprint": "da083a30c6d28aa7594a2e06214c3023873353ea2bf835e99cd0282add68a2f7", "program_fingerprint_scope": "Actual complete selected programme/canonical byteobjects and both orientation commitments are exact. Full operator-valued required-boundary and absolute-phase contract remains explicit.", "invoice_fingerprint": "f34c0dfc766b7cb5f4f63dd5d29f2e82f62a45cee54e3eaa76a077a71bffb255", "invoice_fingerprint_scope": "Fresh complete own PLAN/OWNERS/calls/windows/charts/profile and no-prior full invoice, with disclosed new numeric parent provenance.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "1625715867072461/1000000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_quantified": true, "record_tail_scope": "Own original record exponent is separately quantified by this new direct Gaussian circuit.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr614-cold14-typed-finite-early-upper.json", "scope": "Conditional sufficient eventual bound for the explicitly weaker early exponent1/5000, all positive XOR tariffs, same repaired unlimited optimized-GMP reference; retained native/frame/phase/all-size/analytic interfaces.", "exact_individual_crossing": false }, "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts.", "Own source descriptive entering counter 16584 differs from actual nonzero initial-frame roles 15576; width-below9 roles are 16584. The new complete invoice/stock/precision bound is independently verified not to read that counter. Historical metadata is preserved; original global verifier full PASS is not claimed." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "recover_cold14_chain_native_bytes.py" ], [ "prepare_selected_provider_v12.py" ], [ "selected_provider_dispatch_v12.py", "--execute" ], [ "cold14_descriptive_counter_audit.py" ], [ "selected_provider_v12_whole_bounds.py" ] ], "offline_verification_commands": [ [ "cold14_descriptive_counter_audit.py" ], [ "selected_provider_v12_whole_bounds.py" ] ], "offline_verification_scope": "Fast complete numerical envelope replay from bound source censuses. Actual typed native byte and complete physical invoice replays are explicit separate reproduction jobs, with their closed source/receipt bytes bound; complete operator/phase endpoints remain stated premises.", "source_discovery_scope": "The actual own author-head MANIFEST and literal verifier select each own SPEC/PLAN/OWNERS. Exact actual typed-constructor intermediate byteobjects match every selected canonical/program/orientation commitment. Actual own selected programme/orientation commitments and newly fetched exact physical inputs are checked; no equal-kappa/profile inference or cutoff transfer.", "descriptive_entering_counter": { "source_declared_entering_helper_roles": 16584, "actual_nonzero_start_frame_roles": 15576, "width_below_9_roles": 16584, "source_declared_meter_style": "legacy_width_below_9", "source_declared_counter_matches_actual": false, "used_by_new_cost_stock_or_precision": false }, "original_global_verifier_full_PASS_claimed": false, "source_caveats": [ "Own source descriptive entering counter 16584 differs from actual nonzero initial-frame roles 15576; width-below9 roles are 16584. The new complete invoice/stock/precision bound is independently verified not to read that counter. Historical metadata is preserved; original global verifier full PASS is not claimed." ], "record_certificate_file": "pr614-cold14-typed-finite-record-upper.json", "record_certificate_sha256": "87da464d6809a50fdc24aabf6d6ddf04386122ad2d62bcb92b6b6f573857eae7", "record_P": "230584301497830147503423480", "record_tail_input_bits": "2^(2^230584301497830147503423480)", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 615, "source_commit": "bf8a49a34350599763cced8592db81dc62c2c1c0", "certificate_file": "pr615-hyperplane-cold-finite-early-upper.json", "certificate_sha256": "9d1f683b90199758a51b0bd5c5e5566752cef91167adbedbd56174ce456c4015", "peer_review_file": "pr615-hyperplane-cold-finite-peer-review.json", "peer_review_sha256": "17a9516ecdef5e948432e176502fad7a7a7815083a85ef471e4be7a68c1b8b3c", "source_peer_review_file": "pr615-hyperplane-cold-finite-source-peer-review.json", "source_peer_review_sha256": "1f0e338628a8c9e4fb7d43f00475384d6d0a96171f88e275ee78a82efe345623", "proof_file": "selected-provider-v23-whole-upper.md", "family_kind": "own-hyperplane-cold-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr615-hyperplane-cold-finite-record-upper.json", "record_certificate_sha256": "27e13bb0300455c04845704a584a8dc0205f3cf8626a43357973ad71cd8ce79a", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "1626010676080313/1000000000000000000", "native_certificate_file": "pr615-hyperplane-cold-finite-native.json", "native_certificate_sha256": "2e132bc658f69566829dbd8a2a7535c1dff7d12ac210cc5f522fefd7c93c4abb", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "historical_parent_byte_identity_claimed": false, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": false, "source_report_counter_mismatch": true, "descriptive_entering_counter": { "source_declared_entering_helper_roles": 16608, "actual_nonzero_start_frame_roles": 15600, "width_below_9_roles": 16608, "source_declared_meter_style": "legacy_width_below_9", "source_declared_counter_matches_actual": false, "used_by_new_cost_stock_or_precision": false }, "scope": "New direct Gaussian realization of the exact own-selected native words and complete owner map, with a fresh physical invoice. The prior successful 1645-check native reconstruction is authenticated; the final source reviewer freshly checked uncached scalar/frame data and complete physical costs, and does not claim a new full native/operator/phase pipeline pass. Partial operator/absolute-phase, normalized-child, owned/common-label/all-size and analytic contracts remain explicit. No prior invoice or cutoff is transferred; no actual first crossing is known. The source descriptive entering count16608 differs from actual initial-frame roles15600; the source value is preserved and independently proved unused by work, stock or precision. No original global-verifier PASS is claimed.", "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "prepare_selected_provider_v23.py" ], [ "selected_provider_dispatch_v23.py", "--execute" ], [ "prepare_selected_provider_v23_whole_costs.py" ], [ "hyperplane_cold_descriptive_counter_audit.py" ], [ "selected_provider_v23_whole_bounds.py" ] ], "optional_original_native_recovery_command": [ "recover_early_hyperplane_cold_native.py" ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 616, "source_commit": "5611a9048e4388bb2f330520796379926084c69e", "certificate_file": "pr616-cold14-typed-finite-early-upper.json", "certificate_sha256": "878117ee3033602bc4c3bfaec6f997ec3dca17702eb19820223874d5b9e69cac", "peer_review_file": "pr616-cold14-typed-finite-peer-review.json", "peer_review_sha256": "525b5b15203987980611db838e8e1e8fe0d98da22bd60608fcda446fd03e10d0", "source_peer_review_file": "pr616-cold14-typed-finite-source-peer-review.json", "source_peer_review_sha256": "2968e17c80efd8043b6e3f441c0e5e113b25e8b95e61a10bfc697821eb0c0697", "proof_file": "selected-provider-v12-whole-upper.md", "family_kind": "rank73-exact-own-selected-typed-cold14-early-Gaussian-no-BIT", "native_certificate_file": "pr616-cold14-typed-finite-native.json", "native_certificate_sha256": "650320500487684aecea957f069a7415a03049b9681812df1b398818ea73e15c", "program_fingerprint": "da083a30c6d28aa7594a2e06214c3023873353ea2bf835e99cd0282add68a2f7", "program_fingerprint_scope": "Actual complete selected programme/canonical byteobjects and both orientation commitments are exact. Full operator-valued required-boundary and absolute-phase contract remains explicit.", "invoice_fingerprint": "f34c0dfc766b7cb5f4f63dd5d29f2e82f62a45cee54e3eaa76a077a71bffb255", "invoice_fingerprint_scope": "Fresh complete own PLAN/OWNERS/calls/windows/charts/profile and no-prior full invoice, with disclosed new numeric parent provenance.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "325148945201257/200000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_quantified": true, "record_tail_scope": "Own original record exponent is separately quantified by this new direct Gaussian circuit.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr616-cold14-typed-finite-early-upper.json", "scope": "Conditional sufficient eventual bound for the explicitly weaker early exponent1/5000, all positive XOR tariffs, same repaired unlimited optimized-GMP reference; retained native/frame/phase/all-size/analytic interfaces.", "exact_individual_crossing": false }, "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts.", "Own source descriptive entering counter 16584 differs from actual nonzero initial-frame roles 15576; width-below9 roles are 16584. The new complete invoice/stock/precision bound is independently verified not to read that counter. Historical metadata is preserved; original global verifier full PASS is not claimed." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "recover_cold14_chain_native_bytes.py" ], [ "prepare_selected_provider_v12.py" ], [ "selected_provider_dispatch_v12.py", "--execute" ], [ "cold14_descriptive_counter_audit.py" ], [ "selected_provider_v12_whole_bounds.py" ] ], "offline_verification_commands": [ [ "cold14_descriptive_counter_audit.py" ], [ "selected_provider_v12_whole_bounds.py" ] ], "offline_verification_scope": "Fast complete numerical envelope replay from bound source censuses. Actual typed native byte and complete physical invoice replays are explicit separate reproduction jobs, with their closed source/receipt bytes bound; complete operator/phase endpoints remain stated premises.", "source_discovery_scope": "The actual own author-head MANIFEST and literal verifier select each own SPEC/PLAN/OWNERS. Exact actual typed-constructor intermediate byteobjects match every selected canonical/program/orientation commitment. Actual own selected programme/orientation commitments and newly fetched exact physical inputs are checked; no equal-kappa/profile inference or cutoff transfer.", "descriptive_entering_counter": { "source_declared_entering_helper_roles": 16584, "actual_nonzero_start_frame_roles": 15576, "width_below_9_roles": 16584, "source_declared_meter_style": "legacy_width_below_9", "source_declared_counter_matches_actual": false, "used_by_new_cost_stock_or_precision": false }, "original_global_verifier_full_PASS_claimed": false, "source_caveats": [ "Own source descriptive entering counter 16584 differs from actual nonzero initial-frame roles 15576; width-below9 roles are 16584. The new complete invoice/stock/precision bound is independently verified not to read that counter. Historical metadata is preserved; original global verifier full PASS is not claimed." ], "record_certificate_file": "pr616-cold14-typed-finite-record-upper.json", "record_certificate_sha256": "2bdcbc95e9084a1184d535ac069c0def6e7fef040e98918a6bc281f93d162baa", "record_P": "230584301497830147503423480", "record_tail_input_bits": "2^(2^230584301497830147503423480)", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 617, "source_commit": "904d62855723c00f8acef9a287a10768598fdeb2", "certificate_file": "pr617-mixed-finite-controller-early-upper.json", "certificate_sha256": "f8e70fbe46c1e54f34a8ff0fe5bf3c481cc52fe263475c1ae7686dee2ca15c1e", "peer_review_file": "pr617-mixed-finite-controller-peer-review.json", "peer_review_sha256": "28aa668db5991f28ed75d59f6ee0de6fe14f6a85979171e7460c1db5108e821c", "source_peer_review_file": "pr617-mixed-finite-controller-source-peer-review.json", "source_peer_review_sha256": "0cc586fff1129280efade41192656b37ea013fac4caf53a9d1342d69932a4c09", "proof_file": "early-mixed-finite-controller-upper.md", "family_kind": "rank73-own-mixed-selected-finite-controller", "native_certificate_file": "pr617-mixed-finite-controller-native.json", "native_certificate_sha256": "f4465c63fe29b16ec55bd9b1dec8f44a3053d723212b8eb9adf6690d37235f14", "program_fingerprint": "ead37c7212239feb4da606f18e380f906c817e0e2da359a937ddaa08ff7e7f1b", "program_fingerprint_scope": "Exact own selected canonical/program/orientation commitments; finite objects reconstructed from hash-pinned own recipes, not substitution of later algorithm/profile.", "invoice_fingerprint": "d9e3c693535021ca2f89259b251e7426ecfe7e5a4ec76eb82c3dc3b26a160cb5", "invoice_fingerprint_scope": "Fresh own selected provider/orientation primitive and wrapper census plus complete own physical owner/window/sweep/bank invoice; no prior invoice.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "817591864627889/500000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr617-mixed-finite-controller-early-upper.json", "scope": "Conditional sufficient eventual upper in the same fixed XAG/unlimited optimized-GMP model for every positive XOR tariff; own source-equivalent numeric realization.", "exact_individual_crossing": false }, "record_certificate_file": "pr617-mixed-finite-controller-record-upper.json", "record_certificate_sha256": "738a0d29b76a926d9eb21769b33a5ab2f463d7e20717e037c766c7bb85d1f828", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own arbitrary-input operator-valued native phase, normalized-wrapper, ascending typed-helper and whole Gaussian endpoint contracts remain explicit; scalar specialization is not their proof.", "Exact own selected canonical/program/orientation hashes, actual scalar/frame incidence and dyadic Horner/prefix counts are checked independently. Derived objects are rebuilt from earlier hash-pinned recipes, sometimes using exact matching later archive bytes; no later supplier is imported.", "Each own PLAN/order/dispatch/OWNERS/window, complete role namespace, residual/spectator chart, primitive/wrapper invoice and no-prior-invoice finite stock is freshly checked.", "The counted parent is a primary-fixture source-equivalent numeric realization matching own physical windows; historical parent provenance metadata byte identity is not claimed.", "Common-label, mutable-source, arbitrary-input owned restore and all-size unequal-child occupied-row batching remain fixed-protocol hypotheses; completed Gaussian children have norm one under the endpoint contract.", "Own C0=2^210000 and actual512-bit payload fund the semantic precision reserve. Same direct analytic fine-prime/boundary/recovery, candidate-only Fermat helper and repaired unlimited GMP correctness/halting interfaces." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "early_mixed_native_components.py" ], "reproduction_commands": [ [ "early_mixed_native_components.py" ], [ "early_mixed_owner_invoice.py" ], [ "early_mixed_finite_controller_upper.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 618, "source_commit": "a0d472c7459952f5e55fd9d829adb0484cc0f648", "certificate_file": "pr618-cold14-typed-finite-early-upper.json", "certificate_sha256": "ebe67326a4613d25decba1101983e940e0016915e4229a3e39f3118b77294ef9", "peer_review_file": "pr618-cold14-typed-finite-peer-review.json", "peer_review_sha256": "31dabb7630693d30d6cd9ec60e43258e3482b849072863c492847fb3a7c200ab", "source_peer_review_file": "pr618-cold14-typed-finite-source-peer-review.json", "source_peer_review_sha256": "1e9a8e510517352d38d073240328b99b370db0260308f8879ca8f47f8383a20a", "proof_file": "selected-provider-v12-whole-upper.md", "family_kind": "rank73-exact-own-selected-typed-cold14-early-Gaussian-no-BIT", "native_certificate_file": "pr618-cold14-typed-finite-native.json", "native_certificate_sha256": "2db8b4baf65eb6540cfcbcded30d5bfd02af64ae2232110d70947233053ee584", "program_fingerprint": "212eb9989662c1575a4c042de74388611f556352411da3cded8cdd9db20d82b8", "program_fingerprint_scope": "Actual complete selected programme/canonical byteobjects and both orientation commitments are exact. Full operator-valued required-boundary and absolute-phase contract remains explicit.", "invoice_fingerprint": "9ad4b03016285c8d8e13465b83103d3c68bcd1cdb55e678810d2f7c4c71b6dc3", "invoice_fingerprint_scope": "Fresh complete own PLAN/OWNERS/calls/windows/charts/profile and no-prior full invoice, with disclosed new numeric parent provenance.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "406358675913763/250000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_quantified": true, "record_tail_scope": "Own original record exponent is separately quantified by this new direct Gaussian circuit.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr618-cold14-typed-finite-early-upper.json", "scope": "Conditional sufficient eventual bound for the explicitly weaker early exponent1/5000, all positive XOR tariffs, same repaired unlimited optimized-GMP reference; retained native/frame/phase/all-size/analytic interfaces.", "exact_individual_crossing": false }, "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts.", "Own source descriptive entering counter 16344 differs from actual nonzero initial-frame roles 15564; width-below9 roles are 16572. The new complete invoice/stock/precision bound is independently verified not to read that counter. Historical metadata is preserved; original global verifier full PASS is not claimed." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "recover_cold14_chain_native_bytes.py" ], [ "prepare_selected_provider_v12.py" ], [ "selected_provider_dispatch_v12.py", "--execute" ], [ "cold14_descriptive_counter_audit.py" ], [ "selected_provider_v12_whole_bounds.py" ] ], "offline_verification_commands": [ [ "cold14_descriptive_counter_audit.py" ], [ "selected_provider_v12_whole_bounds.py" ] ], "offline_verification_scope": "Fast complete numerical envelope replay from bound source censuses. Actual typed native byte and complete physical invoice replays are explicit separate reproduction jobs, with their closed source/receipt bytes bound; complete operator/phase endpoints remain stated premises.", "source_discovery_scope": "The actual own author-head MANIFEST and literal verifier select each own SPEC/PLAN/OWNERS. Exact actual typed-constructor intermediate byteobjects match every selected canonical/program/orientation commitment. Actual own selected programme/orientation commitments and newly fetched exact physical inputs are checked; no equal-kappa/profile inference or cutoff transfer.", "descriptive_entering_counter": { "source_declared_entering_helper_roles": 16344, "actual_nonzero_start_frame_roles": 15564, "width_below_9_roles": 16572, "source_declared_meter_style": "unreproduced_descriptive_metadata", "source_declared_counter_matches_actual": false, "used_by_new_cost_stock_or_precision": false }, "original_global_verifier_full_PASS_claimed": false, "source_caveats": [ "Own source descriptive entering counter 16344 differs from actual nonzero initial-frame roles 15564; width-below9 roles are 16572. The new complete invoice/stock/precision bound is independently verified not to read that counter. Historical metadata is preserved; original global verifier full PASS is not claimed." ], "record_certificate_file": "pr618-cold14-typed-finite-record-upper.json", "record_certificate_sha256": "09d0467ba1b84188993c2c6fa1a60752105819106f29794f0a818aaa259c0d07", "record_P": "230584301497830147503423480", "record_tail_input_bits": "2^(2^230584301497830147503423480)", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 619, "source_commit": "9879380b4e9fd922842a35cb3edefd712debfdac", "certificate_file": "pr619-ceiling-refined-finite-early-upper.json", "certificate_sha256": "91f323669fae97c626bc4fd5debb2015b94a3b7e505b8a2ca908c6258000ed43", "peer_review_file": "pr619-ceiling-refined-finite-peer-review.json", "peer_review_sha256": "c17419c7f8b2a9abfd631104ae7212bd1f803bcb8b3741d085fa628ef8b76ef1", "source_peer_review_file": "pr619-ceiling-refined-finite-source-peer-review.json", "source_peer_review_sha256": "24555ec123d3ac3f3e524a0c19a2643a8ec9aa6ad2a12f0d5e70d88f921128b5", "proof_file": "selected-provider-v25-whole-upper.md", "family_kind": "own-fine-grid-selected-core-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr619-ceiling-refined-finite-record-upper.json", "record_certificate_sha256": "3eee12df69c2e2a0507b0eae823219e76b637bc7dab55c64bb1a350f2815e828", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "1626010676080313339567/1000000000000000000000000", "native_certificate_file": "pr619-ceiling-refined-finite-native.json", "native_certificate_sha256": "ed80606dc80a3fc8ee56c616c6de6f5f3756a0179552996fb8b82fd390e3b39d", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "historical_parent_byte_identity_claimed": false, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": false, "source_report_counter_mismatch": true, "descriptive_entering_counter": { "source_declared_entering_helper_roles": 16608, "actual_nonzero_start_frame_roles": 15600, "width_below_9_roles": 16608, "source_declared_meter_style": "legacy_width_below_9", "source_declared_counter_matches_actual": false, "used_by_new_cost_stock_or_precision": false }, "scope": "PR619 retains the PR615 native core and refines the output grid. Its own complete289-file manifest, literal selector and exact native/physical commitments are checked; a fresh direct Gaussian invoice and both runtime schedules are computed. The prior successful1645-check source615 byte recovery is used only where its actual RAW/canonical/programme/both-orientation objects match direct own619 commitments. No fresh619 native constructor, complete CLI or operator/phase pipeline pass is claimed. The final source reviewer independently checked own289API/blob bindings, the exact eight SPEC changes, uncached scalar/frame data and complete physical costs. Partial operator/absolute-phase, normalized-child, owned/common-label/all-size and analytic contracts remain explicit. No prior invoice or cutoff is transferred; no actual first crossing is known. The source descriptive entering count16608 differs from actual initial-frame roles15600; the source value is preserved and independently proved unused by work, stock or precision. No original global-verifier PASS is claimed.", "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "prepare_selected_provider_v25.py" ], [ "selected_provider_dispatch_v25.py", "--execute" ], [ "prepare_selected_provider_v25_whole_costs.py" ], [ "ceiling_refinement_descriptive_counter_audit.py" ], [ "selected_provider_v25_whole_bounds.py" ] ], "optional_selected_byte_object_recovery_command": [ "recover_early_hyperplane_cold_native.py" ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 622, "source_commit": "f69477f4f6d3c7eb1f740b166881bffed4ffa9f6", "certificate_file": "pr622-dispatched-finite-controller-early-upper.json", "certificate_sha256": "9db7e21e2f9c64a9fbd3f3198c9eaac47893120640e248bc93cd8a514d2a936c", "peer_review_file": "pr622-selected-provider-batch-peer-review.json", "peer_review_sha256": "00715eb1bcd9009ddd29d4feb43c7717606f45caf41f4176c66638a3fc07fe0a", "source_peer_review_file": "pr622-dispatched-finite-controller-source-peer-review.json", "source_peer_review_sha256": "0304ecf097eb2c6df21cbd8dfc88e16b96e429951e52ad67331038c9266fa752", "proof_file": "selected-provider-batch-upper.md", "family_kind": "rank73-own-selected-provider-finite-controller", "native_certificate_file": "pr622-dispatched-finite-controller-native.json", "native_certificate_sha256": "5d0c98b025a20a512e590079ac6ea1efa3c53af4bb9a227e578bb71e41cd5efa", "program_fingerprint": "c8471775c961e373d1d10352929929fc844438b48f84c85f25b07abb6f96bb46", "program_fingerprint_scope": "Actual own-selected full/orientation hash-bound program; optional canonical catalogue absence is explicit. No phase/operator endpoint is inferred from scalar specialization.", "invoice_fingerprint": "76bdf606ed90c3932f415409f82818398e55f96c9691ecc04705086077522c32", "invoice_fingerprint_scope": "Fresh own complete selected-call/physical owner/window/nonlocal/stock invoice, no prior invoice. Source-equivalent numeric parent provenance is disclosed.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "10221389468793/6250000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "canonical_catalogue_absent_for": [], "operator_phase_proved": false, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr622-dispatched-finite-controller-early-upper.json", "scope": "Conditional sufficient eventual upper for each positive XOR tariff in the same XAG/unlimited optimized-GMP model, with explicit own full physical/phase/native interface premises.", "exact_individual_crossing": false }, "record_certificate_file": "pr622-dispatched-finite-controller-record-upper.json", "record_certificate_sha256": "a547d54342744e511618e0879776450496a6b20632412152becabfdc1bb3cc59", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "selected_provider_whole_bounds.py" ], "reproduction_commands": [ [ "selected_provider_admitted_replay.py" ], [ "selected_provider_whole_bounds.py" ] ], "broader_discovery_reproduction": [ "selected_provider_dispatch.py", "--execute" ], "broader_discovery_scope": "Optional144-entry/38-numeric-input discovery replay requires additional unpriced source artifacts; the admitted scoped replay needs only these fifteen own source sets.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 623, "source_commit": "e39a615ca601ce5d62abeb24f3fcdb8644ca1005", "certificate_file": "pr623-dispatched-finite-controller-early-upper.json", "certificate_sha256": "61a067c1f28a3e8a934c3a20d038f1ceaf9b3d10659997f4adf3cf2e7615abe8", "peer_review_file": "pr623-selected-provider-batch-peer-review.json", "peer_review_sha256": "5091167d46d56e11c33a1b2d4b4d66fa8e78aaaeeda3280718e9d7bef745d428", "source_peer_review_file": "pr623-dispatched-finite-controller-source-peer-review.json", "source_peer_review_sha256": "4a2e343f026344a39cff8827d0c6c6ef4b46f705d06914b8b702a9da291faa8c", "proof_file": "selected-provider-batch-upper.md", "family_kind": "rank73-own-selected-provider-finite-controller", "native_certificate_file": "pr623-dispatched-finite-controller-native.json", "native_certificate_sha256": "50cf5114106c0cde11caf5e5bdbc3539789ab448da874cf243f023585555ccb0", "program_fingerprint": "c8471775c961e373d1d10352929929fc844438b48f84c85f25b07abb6f96bb46", "program_fingerprint_scope": "Actual own-selected full/orientation hash-bound program; optional canonical catalogue absence is explicit. No phase/operator endpoint is inferred from scalar specialization.", "invoice_fingerprint": "e7c8d270a0d7384112e610005382d8a461d9d66dbc1d5e192246c3c3303b2640", "invoice_fingerprint_scope": "Fresh own complete selected-call/physical owner/window/nonlocal/stock invoice, no prior invoice. Source-equivalent numeric parent provenance is disclosed.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "327098132984091/200000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "canonical_catalogue_absent_for": [], "operator_phase_proved": false, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr623-dispatched-finite-controller-early-upper.json", "scope": "Conditional sufficient eventual upper for each positive XOR tariff in the same XAG/unlimited optimized-GMP model, with explicit own full physical/phase/native interface premises.", "exact_individual_crossing": false }, "record_certificate_file": "pr623-dispatched-finite-controller-record-upper.json", "record_certificate_sha256": "b65002610a2bd2867ff3e80c135e8dcf27e804a7aa3f457d3fc8bc4f37b0a073", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "selected_provider_whole_bounds.py" ], "reproduction_commands": [ [ "selected_provider_admitted_replay.py" ], [ "selected_provider_whole_bounds.py" ] ], "broader_discovery_reproduction": [ "selected_provider_dispatch.py", "--execute" ], "broader_discovery_scope": "Optional144-entry/38-numeric-input discovery replay requires additional unpriced source artifacts; the admitted scoped replay needs only these fifteen own source sets.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 624, "source_commit": "036753ed33d4e620932262646e3d02a1927256a6", "certificate_file": "pr624-dispatched-finite-controller-early-upper.json", "certificate_sha256": "183b72ac4a8cdede38258d01b917dcf0b290781935ae5aded00c7b1d8225f53a", "peer_review_file": "pr624-selected-provider-batch-peer-review.json", "peer_review_sha256": "71e59565549f790cb835f007aa28abbc576f5af0ee8b43069c6ebc9067bfc373", "source_peer_review_file": "pr624-dispatched-finite-controller-source-peer-review.json", "source_peer_review_sha256": "898088cb76819dc446ec35566d7829d4665fd0c919d33aedfc513aec4b11c981", "proof_file": "selected-provider-batch-upper.md", "family_kind": "rank73-own-selected-provider-finite-controller", "native_certificate_file": "pr624-dispatched-finite-controller-native.json", "native_certificate_sha256": "99169cdc0a8c666310fcfcdaf0e1d2759bb3d6f291ce92566f15795ebd29e507", "program_fingerprint": "c8471775c961e373d1d10352929929fc844438b48f84c85f25b07abb6f96bb46", "program_fingerprint_scope": "Actual own-selected full/orientation hash-bound program; optional canonical catalogue absence is explicit. No phase/operator endpoint is inferred from scalar specialization.", "invoice_fingerprint": "76bdf606ed90c3932f415409f82818398e55f96c9691ecc04705086077522c32", "invoice_fingerprint_scope": "Fresh own complete selected-call/physical owner/window/nonlocal/stock invoice, no prior invoice. Source-equivalent numeric parent provenance is disclosed.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "408856367695223/250000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "canonical_catalogue_absent_for": [], "operator_phase_proved": false, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr624-dispatched-finite-controller-early-upper.json", "scope": "Conditional sufficient eventual upper for each positive XOR tariff in the same XAG/unlimited optimized-GMP model, with explicit own full physical/phase/native interface premises.", "exact_individual_crossing": false }, "record_certificate_file": "pr624-dispatched-finite-controller-record-upper.json", "record_certificate_sha256": "95e2d3c8d2976eca895c6bc456bc642cec662e880cc66544130d811d677dd8a4", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "selected_provider_whole_bounds.py" ], "reproduction_commands": [ [ "selected_provider_admitted_replay.py" ], [ "selected_provider_whole_bounds.py" ] ], "broader_discovery_reproduction": [ "selected_provider_dispatch.py", "--execute" ], "broader_discovery_scope": "Optional144-entry/38-numeric-input discovery replay requires additional unpriced source artifacts; the admitted scoped replay needs only these fifteen own source sets.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 625, "source_commit": "386712d06fe4b163596370af4646fec390bd7eb3", "certificate_file": "pr625-dispatched-finite-controller-early-upper.json", "certificate_sha256": "abf7ddc8ec896d696a5dea9ad6180a6139e25d74d7b5bfa67b0aaae13d7e08d4", "peer_review_file": "pr625-selected-provider-batch-peer-review.json", "peer_review_sha256": "d57c68ffd56d928048147552e71143967c7903237f1146b3d84661bef98109ca", "source_peer_review_file": "pr625-dispatched-finite-controller-source-peer-review.json", "source_peer_review_sha256": "96e642c1510cf0d5fefafc51e913127d842f7f551e0f5132c468a723d2cc99a3", "proof_file": "selected-provider-batch-upper.md", "family_kind": "rank73-own-selected-provider-finite-controller", "native_certificate_file": "pr625-dispatched-finite-controller-native.json", "native_certificate_sha256": "d688b3ad5bb071192ba68d62a40b0b3cec49f1feb268780b9179e757e2c0cbcf", "program_fingerprint": "c8471775c961e373d1d10352929929fc844438b48f84c85f25b07abb6f96bb46", "program_fingerprint_scope": "Actual own-selected full/orientation hash-bound program; optional canonical catalogue absence is explicit. No phase/operator endpoint is inferred from scalar specialization.", "invoice_fingerprint": "e7c8d270a0d7384112e610005382d8a461d9d66dbc1d5e192246c3c3303b2640", "invoice_fingerprint_scope": "Fresh own complete selected-call/physical owner/window/nonlocal/stock invoice, no prior invoice. Source-equivalent numeric parent provenance is disclosed.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "817751370453741/500000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "canonical_catalogue_absent_for": [], "operator_phase_proved": false, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr625-dispatched-finite-controller-early-upper.json", "scope": "Conditional sufficient eventual upper for each positive XOR tariff in the same XAG/unlimited optimized-GMP model, with explicit own full physical/phase/native interface premises.", "exact_individual_crossing": false }, "record_certificate_file": "pr625-dispatched-finite-controller-record-upper.json", "record_certificate_sha256": "784056414a10b2f6ba8b7e33ea2d24cdbef339972445e3cb80388e5461eb60ea", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "selected_provider_whole_bounds.py" ], "reproduction_commands": [ [ "selected_provider_admitted_replay.py" ], [ "selected_provider_whole_bounds.py" ] ], "broader_discovery_reproduction": [ "selected_provider_dispatch.py", "--execute" ], "broader_discovery_scope": "Optional144-entry/38-numeric-input discovery replay requires additional unpriced source artifacts; the admitted scoped replay needs only these fifteen own source sets.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 626, "source_commit": "660de893d27bb7abd1d5b01b1640207528a5c851", "certificate_file": "pr626-mixed-finite-controller-early-upper.json", "certificate_sha256": "5c13c0e2f1bc613cf96ca8238faab9c24c30c9adabdd57499e26dcee32169c71", "peer_review_file": "pr626-mixed-finite-controller-peer-review.json", "peer_review_sha256": "f3ab926a8d1beae9025ef43e9136fbe0811eaee3b7e20c4ee9dea914b4935188", "source_peer_review_file": "pr626-mixed-finite-controller-source-peer-review.json", "source_peer_review_sha256": "425dadbe54e5aaabe36952001894d44a5fc371f5595ec91943246e535f558a83", "proof_file": "early-mixed-finite-controller-upper.md", "family_kind": "rank73-own-mixed-selected-finite-controller", "native_certificate_file": "pr626-mixed-finite-controller-native.json", "native_certificate_sha256": "1601402625f4a6d030e993af5d778f5a68302b257f4f9fd97169484823913bc2", "program_fingerprint": "87b19ea95e349f451655c1149fe71bc0faf92d07c907e72409efc10c92be2de3", "program_fingerprint_scope": "Exact own selected canonical/program/orientation commitments; finite objects reconstructed from hash-pinned own recipes, not substitution of later algorithm/profile.", "invoice_fingerprint": "1c22a3fa7332caaf9446c02a17bcfc2d766d4977e6be75dc2891fa2819ebe051", "invoice_fingerprint_scope": "Fresh own selected provider/orientation primitive and wrapper census plus complete own physical owner/window/sweep/bank invoice; no prior invoice.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "51110230636731/31250000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr626-mixed-finite-controller-early-upper.json", "scope": "Conditional sufficient eventual upper in the same fixed XAG/unlimited optimized-GMP model for every positive XOR tariff; own source-equivalent numeric realization.", "exact_individual_crossing": false }, "record_certificate_file": "pr626-mixed-finite-controller-record-upper.json", "record_certificate_sha256": "198694c6f9ca095a4a5668974cc7e539c1343d59021e7eda7f90c7496e8774b9", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own arbitrary-input operator-valued native phase, normalized-wrapper, ascending typed-helper and whole Gaussian endpoint contracts remain explicit; scalar specialization is not their proof.", "Exact own selected canonical/program/orientation hashes, actual scalar/frame incidence and dyadic Horner/prefix counts are checked independently. Derived objects are rebuilt from earlier hash-pinned recipes, sometimes using exact matching later archive bytes; no later supplier is imported.", "Each own PLAN/order/dispatch/OWNERS/window, complete role namespace, residual/spectator chart, primitive/wrapper invoice and no-prior-invoice finite stock is freshly checked.", "The counted parent is a primary-fixture source-equivalent numeric realization matching own physical windows; historical parent provenance metadata byte identity is not claimed.", "Common-label, mutable-source, arbitrary-input owned restore and all-size unequal-child occupied-row batching remain fixed-protocol hypotheses; completed Gaussian children have norm one under the endpoint contract.", "Own C0=2^210000 and actual512-bit payload fund the semantic precision reserve. Same direct analytic fine-prime/boundary/recovery, candidate-only Fermat helper and repaired unlimited GMP correctness/halting interfaces." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "early_mixed_native_components.py" ], "reproduction_commands": [ [ "early_mixed_native_components.py" ], [ "early_mixed_owner_invoice.py" ], [ "early_mixed_finite_controller_upper.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 636, "source_commit": "679621828a85bac68af869fb0e55b54508e6b14b", "certificate_file": "pr636-k492-mixed-finite-early-upper.json", "certificate_sha256": "414e6a9e7293db6cf4ce01c141dbd4b13ae3e1784dd5239685fb1b8fdf5d96af", "peer_review_file": "pr636-k492-mixed-finite-peer-review.json", "peer_review_sha256": "6cce883dfab3bcbf7b0444823a16a6756385fadc07a2a401ad2a3d16fb56048b", "source_peer_review_file": "pr636-k492-mixed-finite-source-peer-review.json", "source_peer_review_sha256": "fceb32dfc1286e7f1ad6df4e6f02e6054e154017009712fe93c16c476c24708a", "proof_file": "selected-provider-v17-whole-upper.md", "family_kind": "own-selected-K492-mixed-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr636-k492-mixed-finite-record-upper.json", "record_certificate_sha256": "6d570f662b43f2f0b85e4b9a497a1c1e006d634370825ac96aa8e41498ca1e96", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "204533720305051/125000000000000000", "native_certificate_file": "pr636-k492-mixed-finite-native.json", "native_certificate_sha256": "244700a92b56b7188e6b525d6979f4cec2dad4fe4b3c557f5bbf6148d41ba4cf", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "historical_parent_byte_identity_claimed": false, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": false, "source_report_counter_mismatch": true, "descriptive_entering_counter": { "source_declared_entering_helper_roles": 16572, "actual_nonzero_start_frame_roles": 14700, "width_below_9_roles": 16714, "source_declared_meter_style": "unreproduced_descriptive_metadata", "source_declared_counter_matches_actual": false, "used_by_new_cost_stock_or_precision": false }, "source_caveats": [ "The historical descriptive global entering meter differs from the actual nonzero initial-frame count. Its value is preserved, not repaired; complete numerical cost/stock noninterference is separately checked, and no original global-verifier PASS is claimed.", "All required partial native/operator/absolute-phase/all-size interfaces remain explicit. Native-byte recovery does not prove those universal interfaces." ], "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "verify_late_cold_mixed_native_recovery.py" ], [ "prepare_selected_provider_v17.py" ], [ "selected_provider_dispatch_v17.py", "--execute" ], [ "prepare_selected_provider_v17_whole_costs.py" ], [ "late_cold_mixed_descriptive_counter_audit.py" ], [ "selected_provider_v17_whole_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 638, "source_commit": "a77f4a358b5129cda3e510a11a7f9a818aba5274", "certificate_file": "pr638-k492-mixed-finite-early-upper.json", "certificate_sha256": "00a2e38c6970cbd66cda8aaa7e954ac050b397e27bed94ea4e1e1574f0c2f45d", "peer_review_file": "pr638-k492-mixed-finite-peer-review.json", "peer_review_sha256": "6a7db108395adb96643b22b8745d0885dbb350c5b52f0b282e1e89f165aa7c6e", "source_peer_review_file": "pr638-k492-mixed-finite-source-peer-review.json", "source_peer_review_sha256": "a9cc62d26f5720b2a8b92be4e8153426adaa867f6e14c61cfbfd94c01f11a2b8", "proof_file": "selected-provider-v17-whole-upper.md", "family_kind": "own-selected-K492-mixed-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr638-k492-mixed-finite-record-upper.json", "record_certificate_sha256": "4a97147ecd535c511bc0adfff60253f21b83af64d802a4d833696a881a4f740a", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "818228405207427/500000000000000000", "native_certificate_file": "pr638-k492-mixed-finite-native.json", "native_certificate_sha256": "7ac2064d2b60268ce1eb28d947519a0a89fb93ab818a1146c9041d440ee79099", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "historical_parent_byte_identity_claimed": false, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": false, "source_report_counter_mismatch": true, "descriptive_entering_counter": { "source_declared_entering_helper_roles": 16998, "actual_nonzero_start_frame_roles": 14700, "width_below_9_roles": 16998, "source_declared_meter_style": "legacy_width_below_9", "source_declared_counter_matches_actual": false, "used_by_new_cost_stock_or_precision": false }, "source_caveats": [ "The historical descriptive global entering meter differs from the actual nonzero initial-frame count. Its value is preserved, not repaired; complete numerical cost/stock noninterference is separately checked, and no original global-verifier PASS is claimed.", "All required partial native/operator/absolute-phase/all-size interfaces remain explicit. Native-byte recovery does not prove those universal interfaces." ], "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "verify_late_cold_mixed_native_recovery.py" ], [ "prepare_selected_provider_v17.py" ], [ "selected_provider_dispatch_v17.py", "--execute" ], [ "prepare_selected_provider_v17_whole_costs.py" ], [ "late_cold_mixed_descriptive_counter_audit.py" ], [ "selected_provider_v17_whole_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 639, "source_commit": "a374528ad44924951514067c3e104b7afb0e54c3", "certificate_file": "pr639-k492-mixed-finite-early-upper.json", "certificate_sha256": "8b3f2d48ea13e863c4b02c591898232e12aec21ee269b9fd5c5d2a12926d4d38", "peer_review_file": "pr639-k492-mixed-finite-peer-review.json", "peer_review_sha256": "c16d9dbad211ab31475d91bbecddad0131e18c731a20291f262022ff13ec92a3", "source_peer_review_file": "pr639-k492-mixed-finite-source-peer-review.json", "source_peer_review_sha256": "7e9f1dbe4532661e8540cca8f0e1ff05e2c6e438d4fc75e9071495eaefe9babb", "proof_file": "selected-provider-v17-whole-upper.md", "family_kind": "own-selected-K492-mixed-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr639-k492-mixed-finite-record-upper.json", "record_certificate_sha256": "6f2ed69413d13ef307d54520cb3f1f01ec2b0434a9a40174063179d4043036b1", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "409115398194279/250000000000000000", "native_certificate_file": "pr639-k492-mixed-finite-native.json", "native_certificate_sha256": "3a941644a42d47c9c4c9065f0d45ff07cbad7d0410807a4a30a9c4dad8388970", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "historical_parent_byte_identity_claimed": false, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": false, "source_report_counter_mismatch": true, "descriptive_entering_counter": { "source_declared_entering_helper_roles": 16998, "actual_nonzero_start_frame_roles": 14700, "width_below_9_roles": 16998, "source_declared_meter_style": "legacy_width_below_9", "source_declared_counter_matches_actual": false, "used_by_new_cost_stock_or_precision": false }, "source_caveats": [ "The historical descriptive global entering meter differs from the actual nonzero initial-frame count. Its value is preserved, not repaired; complete numerical cost/stock noninterference is separately checked, and no original global-verifier PASS is claimed.", "All required partial native/operator/absolute-phase/all-size interfaces remain explicit. Native-byte recovery does not prove those universal interfaces." ], "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "verify_late_cold_mixed_native_recovery.py" ], [ "prepare_selected_provider_v17.py" ], [ "selected_provider_dispatch_v17.py", "--execute" ], [ "prepare_selected_provider_v17_whole_costs.py" ], [ "late_cold_mixed_descriptive_counter_audit.py" ], [ "selected_provider_v17_whole_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 640, "source_commit": "8ef4414fc65c8189f37fc43dc51915cb565d041e", "certificate_file": "pr640-k492-mixed-finite-early-upper.json", "certificate_sha256": "1ea3d3f47cc9f05c2eb46f7f4b00b828a997e690cba4b7dbddc654d333d0ee0b", "peer_review_file": "pr640-k492-mixed-finite-peer-review.json", "peer_review_sha256": "3824886ecfb75f7c07cdc3d9b55e9c754dd0b3f1b9f308fd41aefad0f01b01cb", "source_peer_review_file": "pr640-k492-mixed-finite-source-peer-review.json", "source_peer_review_sha256": "15348c11cf8a53143eb1659622c8e36eff4a8e928f313c231160d395698429e6", "proof_file": "selected-provider-v17-whole-upper.md", "family_kind": "own-selected-K492-mixed-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr640-k492-mixed-finite-record-upper.json", "record_certificate_sha256": "50fb1d7b0efc98e1e10f7ad620583e49ba5b88f87f58d0fe7a963452bb89989e", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "327292937952659/200000000000000000", "native_certificate_file": "pr640-k492-mixed-finite-native.json", "native_certificate_sha256": "ee37fd2c3d3eeea67e2f5e9f2373c1ef6f72db80040c82a4c48960569d30ec04", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "historical_parent_byte_identity_claimed": false, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": false, "source_report_counter_mismatch": true, "descriptive_entering_counter": { "source_declared_entering_helper_roles": 16998, "actual_nonzero_start_frame_roles": 14700, "width_below_9_roles": 17002, "source_declared_meter_style": "unreproduced_descriptive_metadata", "source_declared_counter_matches_actual": false, "used_by_new_cost_stock_or_precision": false }, "source_caveats": [ "The historical descriptive global entering meter differs from the actual nonzero initial-frame count. Its value is preserved, not repaired; complete numerical cost/stock noninterference is separately checked, and no original global-verifier PASS is claimed.", "All required partial native/operator/absolute-phase/all-size interfaces remain explicit. Native-byte recovery does not prove those universal interfaces." ], "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "verify_late_cold_mixed_native_recovery.py" ], [ "prepare_selected_provider_v17.py" ], [ "selected_provider_dispatch_v17.py", "--execute" ], [ "prepare_selected_provider_v17_whole_costs.py" ], [ "late_cold_mixed_descriptive_counter_audit.py" ], [ "selected_provider_v17_whole_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 642, "source_commit": "d1154e23e13d85fdbf64d4b41fa20bb0f56a428f", "certificate_file": "pr642-k492-mixed-finite-early-upper.json", "certificate_sha256": "4114f61a637591acf0b6e0dc8e09b2e809dba297f03df4a85881dd853f6a251e", "peer_review_file": "pr642-k492-mixed-finite-peer-review.json", "peer_review_sha256": "1c9014d91c423895624790617852c010318d342a99629766ecca6e68be1242b6", "source_peer_review_file": "pr642-k492-mixed-finite-source-peer-review.json", "source_peer_review_sha256": "840a21f8acd8055204196935de09dd3335485f5725670e0b6a6ac88f3315baea", "proof_file": "selected-provider-v17-whole-upper.md", "family_kind": "own-selected-K492-mixed-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr642-k492-mixed-finite-record-upper.json", "record_certificate_sha256": "4afdb7b75aead082638c570c8645c64f16b1cee0bdc449454332b8c2ae386bff", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "818236049242189/500000000000000000", "native_certificate_file": "pr642-k492-mixed-finite-native.json", "native_certificate_sha256": "c5cf647c1fb4f945b90151861eae187ce4407ffc97adce4f305851d7473ba167", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "historical_parent_byte_identity_claimed": false, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": false, "source_report_counter_mismatch": true, "descriptive_entering_counter": { "source_declared_entering_helper_roles": 16998, "actual_nonzero_start_frame_roles": 14700, "width_below_9_roles": 17010, "source_declared_meter_style": "unreproduced_descriptive_metadata", "source_declared_counter_matches_actual": false, "used_by_new_cost_stock_or_precision": false }, "source_caveats": [ "The historical descriptive global entering meter differs from the actual nonzero initial-frame count. Its value is preserved, not repaired; complete numerical cost/stock noninterference is separately checked, and no original global-verifier PASS is claimed.", "All required partial native/operator/absolute-phase/all-size interfaces remain explicit. Native-byte recovery does not prove those universal interfaces." ], "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "verify_late_cold_mixed_native_recovery.py" ], [ "prepare_selected_provider_v17.py" ], [ "selected_provider_dispatch_v17.py", "--execute" ], [ "prepare_selected_provider_v17_whole_costs.py" ], [ "late_cold_mixed_descriptive_counter_audit.py" ], [ "selected_provider_v17_whole_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 644, "source_commit": "5d9427d492b0d3f22a895e2c519624f293eac44e", "certificate_file": "pr644-k492-mixed-finite-early-upper.json", "certificate_sha256": "2b1749ffa29092c3ca29fb2da52d613adbd757b0d7ae709472cda25aeb3fe030", "peer_review_file": "pr644-k492-mixed-finite-peer-review.json", "peer_review_sha256": "005d788d02782a1a1fb6803a67ea5a71c37fdc72d8d645d14d8be25eda14c9f4", "source_peer_review_file": "pr644-k492-mixed-finite-source-peer-review.json", "source_peer_review_sha256": "11436a91563ae64c18c6c2a5cd3b592b1f436ab863970cdf192b0b20565b1cbd", "proof_file": "selected-provider-v17-whole-upper.md", "family_kind": "own-selected-K492-mixed-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr644-k492-mixed-finite-record-upper.json", "record_certificate_sha256": "0030141afb5f7f97581ff05cac5dea0b0ddf5529c3299ee75843dea8ab9778e9", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "1636569158555067/1000000000000000000", "native_certificate_file": "pr644-k492-mixed-finite-native.json", "native_certificate_sha256": "9ac714e5d0426682a3b2ca2a20c45168907c49c219a403bd3b3eb66b2a414722", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "historical_parent_byte_identity_claimed": false, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": false, "source_report_counter_mismatch": true, "descriptive_entering_counter": { "source_declared_entering_helper_roles": 16988, "actual_nonzero_start_frame_roles": 14688, "width_below_9_roles": 16988, "source_declared_meter_style": "legacy_width_below_9", "source_declared_counter_matches_actual": false, "used_by_new_cost_stock_or_precision": false }, "source_caveats": [ "The historical descriptive global entering meter differs from the actual nonzero initial-frame count. Its value is preserved, not repaired; complete numerical cost/stock noninterference is separately checked, and no original global-verifier PASS is claimed.", "All required partial native/operator/absolute-phase/all-size interfaces remain explicit. Native-byte recovery does not prove those universal interfaces." ], "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "verify_late_cold_mixed_native_recovery.py" ], [ "prepare_selected_provider_v17.py" ], [ "selected_provider_dispatch_v17.py", "--execute" ], [ "prepare_selected_provider_v17_whole_costs.py" ], [ "late_cold_mixed_descriptive_counter_audit.py" ], [ "selected_provider_v17_whole_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 646, "source_commit": "cdfe8273bb5054e0a837a3594309c6262e995b1f", "certificate_file": "pr646-signed-root-K480-finite-early-upper.json", "certificate_sha256": "4f7afd466ea093a8a25517d2548765f07e476c5869b80529e210baec6c160722", "peer_review_file": "pr646-signed-root-K480-finite-peer-review.json", "peer_review_sha256": "7b375feda56a6d183d3e3a7a9df62702b745a81b9995d7b324d8fee8e1b698e7", "source_peer_review_file": "pr646-signed-root-K480-finite-source-peer-review.json", "source_peer_review_sha256": "fd25d2adb38d843d8ab55886b0d1dba7118797ce606515144ea523f2c2b65ad0", "proof_file": "selected-provider-v20-whole-upper.md", "family_kind": "own-signed-root-K480-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr646-signed-root-K480-finite-record-upper.json", "record_certificate_sha256": "3afae3b9b284824108a444406ab742173cfcd22d3bee33f48a6ccd4f3b352d27", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "813551628351031/500000000000000000", "native_certificate_file": "pr646-signed-root-K480-finite-native.json", "native_certificate_sha256": "1c10e71fe9dcbae45e761b11d58c449797ef4e6ac1baeb4b7648923e6cfa9489", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": false, "source_report_counter_mismatch": false, "descriptive_entering_counter": { "source_declared_entering_helper_roles": 13836, "actual_nonzero_start_frame_roles": 13836, "width_below_9_roles": 15708, "source_declared_meter_style": "actual_initial_nonzero_frames", "source_declared_counter_matches_actual": true, "used_by_new_cost_stock_or_precision": false }, "distinct_K480_own_invoice_not_K492_transfer": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "recover_signed_root_646_native_bytes.py" ], [ "prepare_selected_provider_v20.py" ], [ "selected_provider_dispatch_v20.py", "--execute" ], [ "prepare_selected_provider_v20_whole_costs.py" ], [ "signed_root_K480_descriptive_counter_audit.py" ], [ "selected_provider_v20_whole_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 654, "source_commit": "a935a545760946489bd6f26fe5349a10820316c2", "certificate_file": "pr654-gaussian-only-finite-early-upper.json", "certificate_sha256": "02d1ad29f488ac027a453af8c2d3e98db4a3546342f8764f52d01bbd9c3ec573", "peer_review_file": "pr654-gaussian-only-finite-peer-review.json", "peer_review_sha256": "67d77759e755849d3a198cdf10bd41fd1e7c15b5ab4c2b081b416d2b5d0f450e", "source_peer_review_file": "pr654-gaussian-only-finite-source-peer-review.json", "source_peer_review_sha256": "dc8f40ad13d11475b6099413ee509111183a08c91cd2c75da1251296a223380c", "proof_file": "gaussian-only-selected-provider-upper.md", "family_kind": "rank73-own-selected-direct-Gaussian-no-BIT", "native_certificate_file": "pr654-gaussian-only-finite-native.json", "native_certificate_sha256": "e66182cc33428aafdd21e181a56b966d33c5ccbda837142e8f8a691c36276a32", "program_fingerprint": "7d7d79fd7d7204999e8211be4fc4ad5321a02998724742e021f4deec5a41cb22", "program_fingerprint_scope": "Actual own-selected full/orientation hash-bound program; optional canonical catalogue absence is explicit. No phase/operator endpoint is inferred from scalar specialization.", "invoice_fingerprint": "9d50d1144640471e01959b07a01acae671f5f6ac5995f7a7ad9a72cbe9dd9f8b", "invoice_fingerprint_scope": "Fresh own complete selected-call/physical owner/window/nonlocal/stock invoice, no prior invoice. Source-equivalent numeric parent provenance is disclosed.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "412847614269303/250000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "canonical_catalogue_absent_for": [ "gauge44" ], "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_scope": "New direct Gaussian realization of the same selected source core; literal historical dual-supplier implementation is not claimed.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr654-gaussian-only-finite-early-upper.json", "scope": "Conditional sufficient eventual upper for each positive XOR tariff in the same XAG/unlimited optimized-GMP model, with explicit own full physical/phase/native interface premises.", "exact_individual_crossing": false }, "record_certificate_file": "pr654-gaussian-only-finite-record-upper.json", "record_certificate_sha256": "b2997a12014d05bca9025048bb19ead440f08b6c3ef23429abe385a5a36d9463", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "gaussian_only_selected_provider_bounds.py" ], "reproduction_commands": [ [ "gaussian_only_admitted_replay.py" ], [ "gaussian_only_selected_provider_bounds.py" ] ], "broader_discovery_reproduction": [ "selected_provider_dispatch.py", "--execute" ], "broader_discovery_scope": "Optional144-entry/38-numeric-input discovery replay requires additional unpriced source artifacts; the admitted scoped replay needs only these fifteen own source sets.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 685, "source_commit": "5fc2a0c4e10558f09f03a8e42559dcf8e381e57e", "certificate_file": "pr685-cold72-finite-early-upper.json", "certificate_sha256": "a4c8fca60829dc941476a2da8a7cf63437ca1abb7f709541846dd946f5c273c4", "peer_review_file": "pr685-cold72-finite-peer-review.json", "peer_review_sha256": "74bcd1b67f1911e123015561fb2929dfaaa2e263fea63234e28e339525dc997a", "source_peer_review_file": "pr685-cold72-finite-source-peer-review.json", "source_peer_review_sha256": "f8a04d76b2a577787f24eae525e029bf054ac220018fd7f03e112ad19c6d9ad4", "proof_file": "selected-provider-v9-whole-upper.md", "family_kind": "rank73-exact-own-selected-cold72-early-Gaussian-no-BIT", "native_certificate_file": "pr685-cold72-finite-native.json", "native_certificate_sha256": "815de4eeecbe36452d24b1d159bbffd6d6555ec2fda491b33d0089a05a19323d", "program_fingerprint": "89c1add1a336e2fe89168ff6a507b43e659f280d3a0dc5da43dbdf889a8654cb", "program_fingerprint_scope": "Actual selected programme and both orientation commitments are exact. Canonical catalogue is absent; full operator-valued required-boundary and absolute-phase contract remains explicit.", "invoice_fingerprint": "9101173649e440edb3bc1f5d2002fe835efd610494feb8359776564157c00828", "invoice_fingerprint_scope": "Fresh complete own PLAN/OWNERS/calls/windows/charts/profile and no-prior full invoice, with disclosed new numeric parent provenance.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "1660339298410333/1000000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_quantified": true, "record_tail_scope": "Own original record exponent is separately quantified by this new direct Gaussian circuit.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr685-cold72-finite-early-upper.json", "scope": "Conditional sufficient eventual bound for the explicitly weaker early exponent1/5000, all positive XOR tariffs, same repaired unlimited optimized-GMP reference; retained native/frame/phase/all-size/analytic interfaces.", "exact_individual_crossing": false }, "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "selected_provider_dispatch_v9.py", "--execute" ], [ "selected_provider_v9_whole_bounds.py" ] ], "offline_verification_commands": [ [ "selected_provider_v9_whole_bounds.py" ] ], "offline_verification_scope": "Fast complete numerical envelope replay from bound source censuses. Actual source scalar/physical invoice replay is the first reproduction job; complete operator/phase endpoints remain stated premises.", "source_discovery_scope": "Each own author-head MANIFEST and actual verifier selects its exact kernel SPEC. Actual own selected programme/orientation commitments and newly fetched exact physical inputs are checked; no equal-kappa/profile inference or cutoff transfer.", "record_certificate_file": "pr685-cold72-finite-record-upper.json", "record_certificate_sha256": "9775f04b2e5305ee3ab26ca9f6ff9e6096607030ed0956a9ba05d0e32f72a092", "record_P": "230584301497830147503423480", "record_tail_input_bits": "2^(2^230584301497830147503423480)", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 777, "source_commit": "eca5c317d8176401a1f71a5ea1e81384c2eab1e0", "certificate_file": "pr777-frame-retimed-finite-early-upper.json", "certificate_sha256": "c40dcd3c9e0182695f55133489c5e38132c1272d439cb55fa9ffd56afa5d892a", "peer_review_file": "pr777-frame-retimed-finite-peer-review.json", "peer_review_sha256": "02a41a84f74da379530f2869f7a4b5afc1b57ef17e154ceedf9e47aea0667e54", "source_peer_review_file": "pr777-frame-retimed-finite-source-peer-review.json", "source_peer_review_sha256": "97d0a94a900975fc3ed52222ba59c7fdc8912c739c4c3430e4477ad8f9863b83", "proof_file": "selected-provider-v27-whole-upper.md", "family_kind": "own-frame-retimed-selected-core-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr777-frame-retimed-finite-record-upper.json", "record_certificate_sha256": "f623b7dff122a5597a2cce4de48dcc740ece3003fda5d91abdb966d5790035d9", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "1661202643272239/1000000000000000000", "native_certificate_file": "pr777-frame-retimed-finite-native.json", "native_certificate_sha256": "e54912d0437eaa086ee424648d770723550da01663957ea706b7ab5c27e7038d", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "historical_parent_byte_identity_claimed": false, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": true, "source_report_counter_mismatch": false, "descriptive_entering_counter": { "source_declared_entering_helper_roles": null, "actual_nonzero_start_frame_roles": 15552, "width_below_9_roles": 20736, "source_declared_meter_style": "not_declared_in_own_expected", "source_declared_counter_matches_actual": null, "used_by_new_cost_stock_or_precision": false }, "scope": "PR777 own complete26-file manifest, literal verifier and direct own native/physical commitments are checked. A fresh direct Gaussian invoice and both runtime schedules are computed. Actual earlier741 canonical and programme bytes are reused only where their full canonical, complete programme and both-orientation hashes match the direct own777 SPEC. No741 invoice, exponent or cutoff is transferred; no original777 native constructor, complete CLI or operator/phase pipeline pass is claimed. Actual canonical initial/final frames, all36288 roles and six owner controls are checked. The source does not declare an expected entering-role counter; actual15552 initial-frame roles and width-below-nine20736 are distinguished. Universal operator/absolute-phase, normalized-child, owned/common-label/all-size and analytic contracts remain explicit. No actual first crossing is known.", "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "prepare_selected_provider_v27.py" ], [ "selected_provider_dispatch_v27.py", "--execute" ], [ "prepare_selected_provider_v27_whole_costs.py" ], [ "frame_retiming_descriptive_counter_audit.py" ], [ "selected_provider_v27_whole_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 869, "source_commit": "73e86f69bf9a391e3c334999f7bbe3825dc42759", "certificate_file": "pr869-u8-selected-finite-early-upper.json", "certificate_sha256": "3027779b74e9607a22679056db268cfcc0dae5ac95917211c5eff9656a239f27", "peer_review_file": "pr869-u8-selected-finite-peer-review.json", "peer_review_sha256": "eaac26799118f8f03957cd8a91997dbb3617d46957e4fa75a7ceaeae57c061f4", "source_peer_review_file": "pr869-u8-selected-finite-source-peer-review.json", "source_peer_review_sha256": "3921b7648417ca7ed20011d4ad3da4809f80ed1bee88766de5cfe494c75effe5", "proof_file": "selected-provider-v16-whole-upper.md", "family_kind": "own-selected-U8-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr869-u8-selected-finite-record-upper.json", "record_certificate_sha256": "ae76264d345d14c1d4f9ea59c6174cc8de99b0c92ef5f1a1109570018cf7f016", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "830974347582517/500000000000000000", "native_certificate_file": "pr869-u8-selected-finite-native.json", "native_certificate_sha256": "d9fdcb70f4c18f9d7fabfa49b56428f9317fe2d86d6f6d3919017131ac7390ad", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "historical_parent_byte_identity_claimed": false, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": true, "source_report_counter_mismatch": false, "descriptive_entering_counter": { "source_declared_entering_helper_roles": null, "actual_nonzero_start_frame_roles": 15552, "width_below_9_roles": 20736, "source_declared_meter_style": "not_declared_in_own_expected", "source_declared_counter_matches_actual": null, "used_by_new_cost_stock_or_precision": false }, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "recover_u8_selected_archive_bytes.py" ], [ "prepare_selected_provider_v16.py" ], [ "selected_provider_dispatch_v16.py", "--execute" ], [ "prepare_selected_provider_v16_whole_costs.py" ], [ "u8_descriptive_counter_audit.py" ], [ "selected_provider_v16_whole_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 870, "source_commit": "b734850dc348800942f0ffd1f0723fdec7539b2b", "certificate_file": "pr870-u8-selected-finite-early-upper.json", "certificate_sha256": "dd1a90a436b60fcaacc927456c127e8069512f948df60561c8879df038ad5054", "peer_review_file": "pr870-u8-selected-finite-peer-review.json", "peer_review_sha256": "65d575ffa68e1b71f778a63ce1f7ba813a4c2c13562452db31cf1f8c7555c382", "source_peer_review_file": "pr870-u8-selected-finite-source-peer-review.json", "source_peer_review_sha256": "533ea36bd83f8cb13c08d619242a99037c222e760c7df32031fb8a95d9214de6", "proof_file": "selected-provider-v16-whole-upper.md", "family_kind": "own-selected-U8-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr870-u8-selected-finite-record-upper.json", "record_certificate_sha256": "4d467e32b42a9d4c544be8b1fecd00b9734a48be1e302f2958763e61e7f1de2b", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "415489074974971/250000000000000000", "native_certificate_file": "pr870-u8-selected-finite-native.json", "native_certificate_sha256": "fb94387197e6ab6883f7f923d77a48baacf6002c4ad4cc6cc7340a5190675574", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "historical_parent_byte_identity_claimed": false, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": true, "source_report_counter_mismatch": false, "descriptive_entering_counter": { "source_declared_entering_helper_roles": null, "actual_nonzero_start_frame_roles": 31104, "width_below_9_roles": 41472, "source_declared_meter_style": "not_declared_in_own_expected", "source_declared_counter_matches_actual": null, "used_by_new_cost_stock_or_precision": false }, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "recover_u8_selected_archive_bytes.py" ], [ "prepare_selected_provider_v16.py" ], [ "selected_provider_dispatch_v16.py", "--execute" ], [ "prepare_selected_provider_v16_whole_costs.py" ], [ "u8_descriptive_counter_audit.py" ], [ "selected_provider_v16_whole_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 890, "source_commit": "4b3bd8cbe8e3e81c44161017c9b72c905a8040a8", "certificate_file": "pr890-finite73-literal-cover-range.json", "certificate_sha256": "c9f78b1fd659f492d3d091faa91e2484073dd50b373745fa89b8de4e3cd4bd3c", "peer_review_file": "pr890-finite73-literal-cover-range-peer-review.json", "peer_review_sha256": "7a1234fcb679245f0e47c277916cf8945dcf571a9ff16673210f2d4d71492f26", "source_peer_review_file": "pr890-finite73-literal-cover-source-peer-review.json", "source_peer_review_sha256": "381be1d17392c825fec8870d9dbb7b41d893f2da7cd4106d94edc9bc710b57f2", "proof_file": "finite73-literal-cover-ranges.md", "family_kind": "finite-literal-complete-cover-source-core", "effective_kappa": "1/5000", "kappa_record": "1661957774647029/1000000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr890-finite73-literal-cover-range.json", "scope": "Existence of the bound counted literal early Gaussian schedule above its verified domain; this is not an upper for every switching policy.", "exact_individual_crossing": false }, "lower": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "Declared own literal complete O(73,2) early/record Gaussian enhancement family. Every active counted source body retains all cover vertices and the actual selected public ADD with no pruning, aggregation, quotienting or bypass; any no-native synthesis returns the identical optimized GMP reference. This is an added comparison-family policy and excludes other historical BIT/original hybrid or compressed implementations.", "source": "data/operation-audit/pr890-finite73-literal-cover-lower.json", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source_explanation": "Own complete O(73,2) invocation prescription and surviving actual selected U8 ADD, with the independently closed same-reference1875 upper; no coefficient-coordinate multiplier." }, "lower_certificate_file": "pr890-finite73-literal-cover-lower.json", "lower_certificate_sha256": "656c89d358b7b480ce396ff71bbf1095a2d86aa5f5da558e178b4f9b753ee68d", "record_tail_quantified": true, "necessary_lower_quantifier": "all_valid_literal_family_public_policies", "sufficient_upper_policy": "the_bound_counted_early_schedule_above_its_verified_domain", "upper_not_for_all_switching_policies": true, "source_base_upper_certificate": "pr890-finite-controller-early-upper.json", "source_base_upper_certificate_sha256": "a70856547d0843aef3ff92152df6e4565a932caed488c7bb6c0b244cc4b926aa", "baseline_upper_refinement_file": "optimized-gmp-degree8-compact-upper.json", "baseline_upper_refinement_sha256": "2bad0e4989947e2ef601613c1ad49ba54088c83a4827fd2feacb9f5b69c24956", "baseline_refinement_scope": "Necessary lower calculation only; reference algorithm and old sufficient upper certificate are unchanged.", "scope": [ "The source exact absolute-phase/normalized-wrapper and whole Gaussian endpoint contracts, together with common-label/mutable-source and all-size unequal-child realization interfaces, remain explicit hypotheses of the fixed comparison protocol.", "Actual selected native scalar/frame columns were replayed; own whole-owner physical windows/charts, padded parent banks and complete numeric invoices were checked afresh. Original full phase engines are not claimed rerun.", "The numeric PLAN is a newly checked source-equivalent realization with identical selected program/owner/order/window/profile semantics. It does not claim historical parent-template or PLAN provenance-string byte identity.", "Completed exact Gaussian children have semantic norm one under the source endpoint interface; own finite literal inequalities fund C0=2^210000 and the full own 512/1024 payload charges.", "Same direct Gaussian/fine-prime/finite-section/boundary/recovery analytic conditions, exact candidate-only Fermat helper, fixed XAG tariff and repaired unlimited optimized-GMP correctness/halting assumptions.", "Declared own literal complete O(73,2) early/record Gaussian enhancement family. Every active counted source body retains all cover vertices and the actual selected public ADD with no pruning, aggregation, quotienting or bypass; any no-native synthesis returns the identical optimized GMP reference. This is an added comparison-family policy and excludes other historical BIT/original hybrid or compressed implementations.", "Declared own literal complete O(73,2) early/record Gaussian enhancement family. Every active counted source body retains all cover vertices and the actual selected public ADD with no pruning, aggregation, quotienting or bypass; any no-native synthesis returns the identical optimized GMP reference. This is an added comparison-family policy and excludes other historical BIT/original hybrid or compressed implementations.", "Full same own counted source body and complete group E; own early and record verified domains both contain a nonempty native H stage above the full stopped base. No optional unrelated original-record hybrid is included." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "finite73_literal_cover_ranges.py" ], "reproduction_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "finite73_literal_cover_source_floor.py" ], [ "finite73_literal_cover_ranges.py" ] ], "offline_verification_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "finite73_literal_cover_source_floor.py" ], [ "finite73_literal_cover_ranges.py" ] ], "offline_verification_scope": "Fresh source/control/opcode/native component checks, same-reference degree8 induction and own literal-family lower/upper compatibility. No expensive original universal native/phase pipeline is asserted by these jobs.", "record_certificate_file": "pr890-finite-controller-record-upper.json", "record_certificate_sha256": "2764d636daafd3abdab847e12ed05ae3dea7eddd117df8522bec61ea79195b65", "record_P": "230584301497830147503423480", "record_tail_input_bits": "2^(2^230584301497830147503423480)", "record_tail_policy": "the_bound_counted_same_core_record_schedule_above_its_separately_verified_domain", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 937, "source_commit": "b303fed6dfe2066dcd78c0d8ed74d2a3b153ba72", "certificate_file": "pr937-historical-two-shear-gaussian-early-upper.json", "certificate_sha256": "f6f2c95d24a4faea421140ea3f43222ddc740f06f9344d53109f3c3e2111e14e", "peer_review_file": "pr937-historical-two-shear-gaussian-peer-review.json", "peer_review_sha256": "ee16675ec35d06cc7307a29d178651abf8461d541fd528152a88c65607f5a60e", "source_peer_review_file": "pr937-historical-two-shear-gaussian-source-peer-review.json", "source_peer_review_sha256": "de810a5c6964a4310439ab68b06c28ee839b14b23e2ddba9bf05c02c4d0c9f87", "proof_file": "pr937-historical-two-shear-gaussian-bounds.md", "family_kind": "own-historical-two-shear-nonlinear-native-direct-Gaussian", "upper": { "input_bits": "2^(2^1717986918404294967288)", "exact_log2log2_integer": "1717986918404294967288" }, "lower": null, "record_certificate_file": "pr937-historical-two-shear-gaussian-record-upper.json", "record_certificate_sha256": "385e191a00bf3eb448706e9bd64733157d6ae706a3e6e69c8a24c521166c39d3", "record_P": "1717986918404294967288", "effective_kappa": "1/1000000000", "kappa_record": "1/2147483648", "native_certificate_file": "pr937-historical-two-shear-gaussian-native.json", "native_certificate_sha256": "8dcda6a72aa29fba6452b8f1e54932ee6f9a4e3e6277caf948cf580d2b2dfbaa", "native_coordinate_rank": 17576, "record_tail_quantified": true, "nonlinear_native_precision": true, "native_precision_C1": "1801/1000", "source_selected_kappa_correction": true, "frozen_metadata_kappa": "1661957774647029/1000000000000000000", "source_selected_kappa_correction_basis": "Own actual historical h26 complex construction retains2^-31 in own scripts/audit_complex_centers.py and explicit own historical research note. The preserved contemporary BASE-SELECTED PR799 quote is unrelated context and is not implemented or improved by937.", "source_selected_kappa_correction_note": "This prices PR937\u2019s historical h26 two-shear complex core at its own2^-31 target. Its contemporary PR799 BASE-SELECTED quote is an unrelated referenced result, preserved here; PR937 neither implements nor improves that PR799 algorithm and does not claim a new accepted exponent record.", "unrelated_contemporary_BASE_SELECTED_kappa": "1661634653669567/1000000000000000000", "new_accepted_exponent_record_claimed": false, "costed_variant": "new_direct_Gaussian_realization_of_own_historical_two_shear_core", "source_chronology": { "schema": "own937-actual-merge-source-chronology/1", "pr": 937, "own_head": "b303fed6dfe2066dcd78c0d8ed74d2a3b153ba72", "merged_at": "2026-10-13T15:57:09Z", "merge_commit": "44c8a60d3970ec8585757ee61050f7d5ec011bb5", "direct_source_parent_number": 2, "source_included_at_actual_merge": true, "source_primary_sha256": { "pr937-finite-source/own-pr-api.json": "8b2353782270ece79fa4fb7076eb3cdfb2b81d74b886092b231622e97e60eddc", "pr937-finite-source/own-merge-api.json": "4bc51b0b373a3c291a9d2893607f9c1658ea6ed535ef0304421818c0391fafc3" }, "script_sha256": "cf6603bac1cadb850ccfa4f06b16c602cbe011ce3fb636578f5006dd5436bfa6" }, "outer_protocol": { "epsilon": "51/100", "beta": "1/200", "delta": "1/100000000000", "Q": 100000000000, "A": "400000000001", "native_stop": "4/5" }, "scope": [ "Own historical937 full all-role native circuit, required physical entry/output maps and absolute phases; arbitrary dirty auxiliaries are restored. Finite scalar/frame checks are not a universal operator theorem.", "Own common-label/all-column/whole-call/all-size phase-transfer and normalized Gaussian endpoint contracts, with source nonlinear stopped-depth recurrence at arbitrary fixedtheta.", "New fixed-wiring arbitrary-rank complete-row realization and once-only padding; no free data arithmetic or unbounded descriptors are assumed.", "Exact dyadic augmented-grid native arithmetic, completed Gaussian-integer H return and disjoint complete coefficient blocks with nonlinear convexity are those of the closed global proof, with ownC0/C1 paid in full.", "Concrete normalized accretivity/finite-LDU/FFT/narrow/cyclic convolution/boundary/recovery and repaired optimized-reference correctness/halting remain explicit; the false scale-free general theorem is not imported." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "replay_pr937_finite_source.py" ], [ "pr937_historical_two_shear_gaussian_bounds.py" ] ], "actual_own_selected_kappa": "1/2147483648", "source_kappa_correction_primary_receipt": "pr937-finite-source/chronology.json", "source_revision_included_at_merge": "2026-10-13T15:57:09Z", "source_revision_merge_commit": "44c8a60d3970ec8585757ee61050f7d5ec011bb5", "source_revision_merge_parents": [ "a4d01ac6010c2fe59b0aed8e7051d714f5b0ccbc", "b303fed6dfe2066dcd78c0d8ed74d2a3b153ba72" ], "source_correction_chronology_kind": "reviewed_primary_direct_merge_parent", "source_kappa_correction_primary_sha256": "d64d45a96dce3fec3e1b96238a42f28b977203db223cfc05cdd27b19abf4efcc", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null, "kappa_fraction": "1661957774647029/1000000000000000000", "kappa_decimal": "0.001661957774647029", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities." } }, { "pr": 942, "source_commit": "1960cfa919a0945d0ca4cb14ea96237000037903", "certificate_file": "pr942-finite73-literal-cover-range.json", "certificate_sha256": "9bc1ae3623d6ee6759863f266acdad11f5720db3e049b4059a2e6e4138643667", "peer_review_file": "pr942-finite73-literal-cover-range-peer-review.json", "peer_review_sha256": "0a945f050519311b15c92e2711efb4abff295313a8f8913cdd1d167cd42c11f4", "source_peer_review_file": "pr942-finite73-literal-cover-source-peer-review.json", "source_peer_review_sha256": "bee63d06ce2eb6b190455898dff44f828cc2cce7f8fd403c7995ab3f4de915f5", "proof_file": "finite73-literal-cover-ranges.md", "family_kind": "finite-literal-complete-cover-source-core", "effective_kappa": "1/5000", "kappa_record": "1661960547713947/1000000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr942-finite73-literal-cover-range.json", "scope": "Existence of the bound counted literal early Gaussian schedule above its verified domain; this is not an upper for every switching policy.", "exact_individual_crossing": false }, "lower": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "Declared own literal complete O(73,2) early/record Gaussian enhancement family. Every active counted source body retains all cover vertices and the actual selected public ADD with no pruning, aggregation, quotienting or bypass; any no-native synthesis returns the identical optimized GMP reference. This is an added comparison-family policy and excludes other historical BIT/original hybrid or compressed implementations.", "source": "data/operation-audit/pr942-finite73-literal-cover-lower.json", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source_explanation": "Own complete O(73,2) invocation prescription and surviving actual selected U8 ADD, with the independently closed same-reference1875 upper; no coefficient-coordinate multiplier." }, "lower_certificate_file": "pr942-finite73-literal-cover-lower.json", "lower_certificate_sha256": "b0e34f4e949eca0ee46c74fdd7264669b412601e37ce587cb1773e8ff9d98eaf", "record_tail_quantified": true, "necessary_lower_quantifier": "all_valid_literal_family_public_policies", "sufficient_upper_policy": "the_bound_counted_early_schedule_above_its_verified_domain", "upper_not_for_all_switching_policies": true, "source_base_upper_certificate": "pr942-finite-controller-early-upper.json", "source_base_upper_certificate_sha256": "6ec3fa19d62da5a064f9ea1c830c804c3a1402a91f3832b1afb4d4b29fe56e9c", "baseline_upper_refinement_file": "optimized-gmp-degree8-compact-upper.json", "baseline_upper_refinement_sha256": "2bad0e4989947e2ef601613c1ad49ba54088c83a4827fd2feacb9f5b69c24956", "baseline_refinement_scope": "Necessary lower calculation only; reference algorithm and old sufficient upper certificate are unchanged.", "scope": [ "The source exact absolute-phase/normalized-wrapper and whole Gaussian endpoint contracts, together with common-label/mutable-source and all-size unequal-child realization interfaces, remain explicit hypotheses of the fixed comparison protocol.", "Actual selected native scalar/frame columns were replayed; own whole-owner physical windows/charts, padded parent banks and complete numeric invoices were checked afresh. 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No optional unrelated original-record hybrid is included." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "finite73_literal_cover_ranges.py" ], "reproduction_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "finite73_literal_cover_source_floor.py" ], [ "finite73_literal_cover_ranges.py" ] ], "offline_verification_commands": [ [ "audit_optimized_gmp_native_loops.py" ], [ "optimized_gmp_opcode_arity.py" ], [ "optimized_gmp_finite_control_v2.py" ], [ "optimized_gmp_degree8_compact_upper.py" ], [ "finite73_literal_cover_source_floor.py" ], [ "finite73_literal_cover_ranges.py" ] ], "offline_verification_scope": "Fresh source/control/opcode/native component checks, same-reference degree8 induction and own literal-family lower/upper compatibility. No expensive original universal native/phase pipeline is asserted by these jobs.", "record_certificate_file": "pr942-finite-controller-record-upper.json", "record_certificate_sha256": "799a37c800b6f9e17bf66e7cdc1f3042565806e872b7b505f40e75c344f74113", "record_P": "230584301497830147503423480", "record_tail_input_bits": "2^(2^230584301497830147503423480)", "record_tail_policy": "the_bound_counted_same_core_record_schedule_above_its_separately_verified_domain", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 962, "source_commit": "50c6ae8151493af21d284afe34fb35f68f6d4934", "certificate_file": "pr962-generated-U8-t37-finite-early-upper.json", "certificate_sha256": "d19cd8cc76fe5fdc717b2c0643034b7eb99c1cd764ca0a03c0cc2a6537c61332", "peer_review_file": "pr962-generated-U8-t37-finite-peer-review.json", "peer_review_sha256": "d760b4a92f98e1e7e903883f6e884c94ca7592aa5bc558180d96e43bbd34e0e8", "source_peer_review_file": "pr962-generated-U8-t37-finite-source-peer-review.json", "source_peer_review_sha256": "552ed062f78dc4159602c7f9eded65dcccc45946645c64e6ff855458817fdfcb", "proof_file": "selected-provider-v19-whole-upper.md", "family_kind": "own-generated-U8-T37-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr962-generated-U8-t37-finite-record-upper.json", "record_certificate_sha256": "2be6a3386cea458e179ae5dfa0cdd3d32291e4b4653618390fa91a93b257b7b4", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "1661960547713947/1000000000000000000", "native_certificate_file": "pr962-generated-U8-t37-finite-native.json", "native_certificate_sha256": "22ef3c59fa6a71849fbab3187d1a08bb075e7e85a4c9619a57324b57dbf0d582", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "historical_parent_byte_identity_claimed": false, "exact_own_mathematical_PLAN_OWNER_semantics_recovered": true, "only_own_authorized_raw_container_portability_fields_rebound": true, "opaque_parent_hint_used": false, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": true, "source_report_counter_mismatch": false, "descriptive_entering_counter": { "source_declared_entering_helper_roles": null, "actual_nonzero_start_frame_roles": 71928, "width_below_9_roles": 95904, "source_declared_meter_style": "not_declared_in_own_expected", "source_declared_counter_matches_actual": null, "used_by_new_cost_stock_or_precision": false }, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "recover_u8_selected_archive_bytes.py" ], [ "recover_u8_t37_generated_data.py" ], [ "prepare_selected_provider_v19.py" ], [ "selected_provider_dispatch_v19.py", "--execute" ], [ "prepare_selected_provider_v19_whole_costs.py" ], [ "generated_u8_t37_descriptive_counter_audit.py" ], [ "selected_provider_v19_whole_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 991, "source_commit": "69f989511a3f0c6f7a26da1c1608b265fbb1668a", "certificate_file": "pr991-generated-U8-t37-finite-early-upper.json", "certificate_sha256": "7bc5f529f9777b81c2e01a3504a99fd74caf7a3b85903bc217a0ce78057a880c", "peer_review_file": "pr991-generated-U8-t37-finite-peer-review.json", "peer_review_sha256": "af16dd40b294881c00c41d05837f159ddb1607deefefd47282ab748590c5fcb3", "source_peer_review_file": "pr991-generated-U8-t37-finite-source-peer-review.json", "source_peer_review_sha256": "f13b587421afcf013f998585dfaaf295525936f73693a962157314dc1506df15", "proof_file": "selected-provider-v19-whole-upper.md", "family_kind": "own-generated-U8-T37-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr991-generated-U8-t37-finite-record-upper.json", "record_certificate_sha256": "2c7e9f072f6da908e9309f74c95447ad26eef245870a3d55bd54ae7b1a4106cd", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "1661960547713947/1000000000000000000", "native_certificate_file": "pr991-generated-U8-t37-finite-native.json", "native_certificate_sha256": "e13b88e0f8af589e426b2f0c7f6906fa96c2e9bbeadacca053545e7612beced8", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "historical_parent_byte_identity_claimed": false, "exact_own_mathematical_PLAN_OWNER_semantics_recovered": true, "only_own_authorized_raw_container_portability_fields_rebound": true, "opaque_parent_hint_used": false, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": true, "source_report_counter_mismatch": false, "descriptive_entering_counter": { "source_declared_entering_helper_roles": null, "actual_nonzero_start_frame_roles": 71928, "width_below_9_roles": 95904, "source_declared_meter_style": "not_declared_in_own_expected", "source_declared_counter_matches_actual": null, "used_by_new_cost_stock_or_precision": false }, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "recover_u8_selected_archive_bytes.py" ], [ "recover_u8_t37_generated_data.py" ], [ "prepare_selected_provider_v19.py" ], [ "selected_provider_dispatch_v19.py", "--execute" ], [ "prepare_selected_provider_v19_whole_costs.py" ], [ "generated_u8_t37_descriptive_counter_audit.py" ], [ "selected_provider_v19_whole_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1009, "source_commit": "4740dc74a2ee2fb7aeaa0e0013cf8f997558d101", "certificate_file": "pr1009-selected-t37-gaussian-early-upper.json", "certificate_sha256": "027ad0776d977ccfb0fedb251e6de625f6eda707c42782619eac07f14c5688cc", "peer_review_file": "pr1009-selected-t37-gaussian-cost-peer-review.json", "peer_review_sha256": "cab434e288fc6e32018e23e6153a37f7b59ec8be0cd74fc385484fbde7fb219e", "source_peer_review_file": "pr1009-selected-t37-gaussian-source-peer-review.json", "source_peer_review_sha256": "9714b8d9583749d561c0c1196d1e56158996635284f2327b962501c1d9cbd6db", "proof_file": "t37-selected-core-gaussian-bounds.md", "family_kind": "own-selected-T37-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr1009-selected-t37-gaussian-record-upper.json", "record_certificate_sha256": "7fe3375ae16b14a7bb7a0e56009ddbd0bd17c331175d0342bb85bf4bc321087f", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "1661960547713947/1000000000000000000", "native_certificate_file": "pr1009-selected-t37-gaussian-native.json", "native_certificate_sha256": "fe5f64f6939060df26ae7aadf7c81a8f09bc31317a439598605fe99ed9a735ba", "scope": [ "The source exact absolute-phase/normalized-wrapper and whole Gaussian endpoint contracts, together with common-label/mutable-source and all-size unequal-child realization interfaces, remain explicit hypotheses of the fixed comparison protocol.", "Actual selected native scalar/frame columns were replayed; own whole-owner physical windows/charts, padded parent banks and complete numeric invoices were checked afresh. Original full phase engines are not claimed rerun.", "The numeric PLAN is a newly checked source-equivalent realization with identical selected program/owner/order/window/profile semantics. It does not claim historical parent-template or PLAN provenance-string byte identity.", "Completed exact Gaussian children have semantic norm one under the source endpoint interface; own finite literal inequalities fund C0=2^210000 and the full own 512/1024 payload charges.", "Same direct Gaussian/fine-prime/finite-section/boundary/recovery analytic conditions, exact candidate-only Fermat helper, fixed XAG tariff and repaired unlimited optimized-GMP correctness/halting assumptions.", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "This new direct Gaussian/Fermat realization uses the exact own explicitly selected942 T37 core. It does not execute or quantify the original six-/seven-level affine bootstrap algorithm; no cost benefit of the source bootstrap-depth improvement is inferred.", "Exact identity imports the named native/owner/invoice component only; own source arithmetic replay scope remains as recorded, with no new full native/phase or876-source verifier execution." ], "source_selected_core_reuse": true, "source_contribution_preserved": true, "original_bootstrap_cost_realized_by_this_certificate": false, "source_contribution_scope": "Own finite bootstrap-depth improvement", "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "replay_t37_source_refinements.py" ], [ "t37_refinement_source_bindings.py" ], [ "t37_selected_core_gaussian_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1018, "source_commit": "eac7547cb191f875d5f5ea5f9bbb1d2b8c51c4ef", "certificate_file": "pr1018-dispatched-finite-controller-early-upper.json", "certificate_sha256": "033014eabfe59843cf0eff53d5c634d74ef02dad4a9ce5ba74db02105427407d", "peer_review_file": "pr1018-selected-provider-batch-peer-review.json", "peer_review_sha256": "d96fa0d0156e66718528b939f73e08d064c5cd866f291b3d2bdfb10f9d7e4875", "source_peer_review_file": "pr1018-dispatched-finite-controller-source-peer-review.json", "source_peer_review_sha256": "51c1415ecb5c63566aaf4be3934eedb9d58ce36a8087ceaf14e43454acd3441a", "proof_file": "selected-provider-batch-upper.md", "family_kind": "rank73-own-selected-provider-finite-controller", "native_certificate_file": "pr1018-dispatched-finite-controller-native.json", "native_certificate_sha256": "122180bd3da21a6cc7a44c95aa27cb8304b030c4ace819a99ad66fcc0f6e0e2e", "program_fingerprint": "abe237c5841100d67813a6ee3b0cb91cb5f7db6ddba836b9f4a52cc04289b5d5", "program_fingerprint_scope": "Actual own-selected full/orientation hash-bound program; optional canonical catalogue absence is explicit. No phase/operator endpoint is inferred from scalar specialization.", "invoice_fingerprint": "42a905b259ceb57a6e27eeee3ba524597f2db5d28271bc18847dad6e85198efd", "invoice_fingerprint_scope": "Fresh own complete selected-call/physical owner/window/nonlocal/stock invoice, no prior invoice. Source-equivalent numeric parent provenance is disclosed.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "167166528321877/100000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "canonical_catalogue_absent_for": [], "operator_phase_proved": false, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr1018-dispatched-finite-controller-early-upper.json", "scope": "Conditional sufficient eventual upper for each positive XOR tariff in the same XAG/unlimited optimized-GMP model, with explicit own full physical/phase/native interface premises.", "exact_individual_crossing": false }, "record_certificate_file": "pr1018-dispatched-finite-controller-record-upper.json", "record_certificate_sha256": "4416a40e790374b200ecc7a9004c4a7b71ba8c18a2b9e1ef34874b1139706f90", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "selected_provider_whole_bounds.py" ], "reproduction_commands": [ [ "selected_provider_admitted_replay.py" ], [ "selected_provider_whole_bounds.py" ] ], "broader_discovery_reproduction": [ "selected_provider_dispatch.py", "--execute" ], "broader_discovery_scope": "Optional144-entry/38-numeric-input discovery replay requires additional unpriced source artifacts; the admitted scoped replay needs only these fifteen own source sets.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1019, "source_commit": "eff657644137971f6e31ac3c825950c770471349", "certificate_file": "pr1019-selected-t37-gaussian-early-upper.json", "certificate_sha256": "689f00d3d5ac5d186972df2357ccbf64213bfb28a68a4701f86bae17d6adc1e7", "peer_review_file": "pr1019-selected-t37-gaussian-cost-peer-review.json", "peer_review_sha256": "3f25276e86b4204c15d765cff7db8d6f9732fadadd609e183b25aab06bd63e9f", "source_peer_review_file": "pr1019-selected-t37-gaussian-source-peer-review.json", "source_peer_review_sha256": "b1978485bf07721eb8dcae66c0f150e32b2d8990569e740dee17ef92218e65a5", "proof_file": "t37-selected-core-gaussian-bounds.md", "family_kind": "own-selected-T37-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr1019-selected-t37-gaussian-record-upper.json", "record_certificate_sha256": "8937fe64d4b329328a671244a40d7c5e526bc9a6ab9d46ff340f2d0f92af76ce", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "1661960547713947858091/1000000000000000000000000", "native_certificate_file": "pr1019-selected-t37-gaussian-native.json", "native_certificate_sha256": "23f3479547ee45a2d1103049a20232c14c78a724ed3406154fd2b87aa84a40b9", "scope": [ "The source exact absolute-phase/normalized-wrapper and whole Gaussian endpoint contracts, together with common-label/mutable-source and all-size unequal-child realization interfaces, remain explicit hypotheses of the fixed comparison protocol.", "Actual selected native scalar/frame columns were replayed; own whole-owner physical windows/charts, padded parent banks and complete numeric invoices were checked afresh. Original full phase engines are not claimed rerun.", "The numeric PLAN is a newly checked source-equivalent realization with identical selected program/owner/order/window/profile semantics. It does not claim historical parent-template or PLAN provenance-string byte identity.", "Completed exact Gaussian children have semantic norm one under the source endpoint interface; own finite literal inequalities fund C0=2^210000 and the full own 512/1024 payload charges.", "Same direct Gaussian/fine-prime/finite-section/boundary/recovery analytic conditions, exact candidate-only Fermat helper, fixed XAG tariff and repaired unlimited optimized-GMP correctness/halting assumptions.", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "This new direct Gaussian/Fermat realization uses the exact own explicitly selected942 T37 core. It does not execute or quantify the original six-/seven-level affine bootstrap algorithm; no cost benefit of the source bootstrap-depth improvement is inferred.", "Exact identity imports the named native/owner/invoice component only; own source arithmetic replay scope remains as recorded, with no new full native/phase or876-source verifier execution." ], "source_selected_core_reuse": true, "source_contribution_preserved": true, "original_bootstrap_cost_realized_by_this_certificate": false, "source_contribution_scope": "Own exact rational objective refinement", "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "replay_t37_source_refinements.py" ], [ "t37_refinement_source_bindings.py" ], [ "t37_selected_core_gaussian_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1022, "source_commit": "58618bcbfe88a252467755fc283c04c3db5ca4fd", "certificate_file": "pr1022-recovered-t16-finite-early-upper.json", "certificate_sha256": "f9fbe3db86ad9e3281fc984748b25fac4160d6d759f60cc9fdc2bd0e45adad6c", "peer_review_file": "pr1022-recovered-t16-finite-peer-review.json", "peer_review_sha256": "44014fdd58108c6278d912ff4f5ee969ad627a791878873ce206229d9af772cb", "source_peer_review_file": "pr1022-recovered-t16-finite-source-peer-review.json", "source_peer_review_sha256": "52deb2b34ba3cfcdc6cb86ab189c65e8b4417b49abea9d766dcc35ff1a00b1df", "proof_file": "selected-provider-v2-whole-upper.md", "family_kind": "rank73-own-recovered-T16-direct-Gaussian-no-BIT", "native_certificate_file": "pr1022-recovered-t16-finite-native.json", "native_certificate_sha256": "20a64f804cd7cffd9b2820cdadb83cd751b52c93a4c91210ae12678b7f5843ad", "program_fingerprint": "c6c9ee324a08f7907d70aa412e93c8df87e9f52c8ea680554c85f3578ccecdae", "program_fingerprint_scope": "Actual own selected full/orientation hashes are checked. Optional canonical absence remains explicit; scalar specialization does not prove operator or phase endpoints.", "invoice_fingerprint": "73fb80fa0f09cb6e1bb08e1abe825c7ec7212261c9dc6c519eec6d8d6691219a", "invoice_fingerprint_scope": "Fresh own complete PLAN/OWNERS, whole helper widths, chronological windows, charts, stock and full no-prior invoice; source-equivalent numeric parent provenance is disclosed.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "334416251150589/200000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "canonical_catalogue_absent_for": [], "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_scope": "New direct Gaussian realization of the same own selected source core; no literal historical dual-supplier replay is claimed.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr1022-recovered-t16-finite-early-upper.json", "scope": "Conditional sufficient eventual bound for every positive XOR tariff against the same repaired unlimited optimized-GMP reference, retaining the stated own typed native/frame/phase/all-size and analytic interfaces.", "exact_individual_crossing": false }, "record_certificate_file": "pr1022-recovered-t16-finite-record-upper.json", "record_certificate_sha256": "245e81ef586e96a3db9c74cb650928448a27bdc27e81b8a447dcb88d46b2fd0a", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "selected_provider_v2_whole_bounds.py" ], "reproduction_commands": [ [ "selected_provider_dispatch_v2.py", "--execute" ], [ "selected_provider_v2_whole_bounds.py" ] ], "source_discovery_scope": "Fourteen newly recovered exact own production SPECs are screened. Eleven have complete admitted numeric inputs; three unresolved actual selected program-byte gaps receive no bound.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1028, "source_commit": "be4bd89cb4483dcee43257200cd27601f938f13d", "certificate_file": "pr1028-recovered-t16-finite-early-upper.json", "certificate_sha256": "3d96bbaf75ef5186f09c081379f8113dc3d868e30887abfaebe4be439848c13d", "peer_review_file": "pr1028-recovered-t16-finite-peer-review.json", "peer_review_sha256": "9c90a94e7738bc746964e08738cad9c06e72de9fb09108912927428a5ffe2eab", "source_peer_review_file": "pr1028-recovered-t16-finite-source-peer-review.json", "source_peer_review_sha256": "bc006f9e582e8bb59ce37671e0e84a54eed6981bfa14c7a2bf1b02eebbc421b3", "proof_file": "selected-provider-v2-whole-upper.md", "family_kind": "rank73-own-recovered-T16-direct-Gaussian-no-BIT", "native_certificate_file": "pr1028-recovered-t16-finite-native.json", "native_certificate_sha256": "8bf6116ce8183a3502f80c8830f4257c35d69351db04d089ca165f9b20650c33", "program_fingerprint": "c6c9ee324a08f7907d70aa412e93c8df87e9f52c8ea680554c85f3578ccecdae", "program_fingerprint_scope": "Actual own selected full/orientation hashes are checked. Optional canonical absence remains explicit; scalar specialization does not prove operator or phase endpoints.", "invoice_fingerprint": "73fb80fa0f09cb6e1bb08e1abe825c7ec7212261c9dc6c519eec6d8d6691219a", "invoice_fingerprint_scope": "Fresh own complete PLAN/OWNERS, whole helper widths, chronological windows, charts, stock and full no-prior invoice; source-equivalent numeric parent provenance is disclosed.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "1672166670891177/1000000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "canonical_catalogue_absent_for": [], "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_scope": "New direct Gaussian realization of the same own selected source core; no literal historical dual-supplier replay is claimed.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr1028-recovered-t16-finite-early-upper.json", "scope": "Conditional sufficient eventual bound for every positive XOR tariff against the same repaired unlimited optimized-GMP reference, retaining the stated own typed native/frame/phase/all-size and analytic interfaces.", "exact_individual_crossing": false }, "record_certificate_file": "pr1028-recovered-t16-finite-record-upper.json", "record_certificate_sha256": "0e0a838667614a487cfefd9efc44d2255ee90c549a3d5ab22be2c7c8ab1af4d5", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "selected_provider_v2_whole_bounds.py" ], "reproduction_commands": [ [ "selected_provider_dispatch_v2.py", "--execute" ], [ "selected_provider_v2_whole_bounds.py" ] ], "source_discovery_scope": "Fourteen newly recovered exact own production SPECs are screened. Eleven have complete admitted numeric inputs; three unresolved actual selected program-byte gaps receive no bound.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1031, "source_commit": "e900534f0beda892c726723524203b97471fb9a3", "certificate_file": "pr1031-recovered-t16-finite-early-upper.json", "certificate_sha256": "4a4c86e98545b1d444650a338c3c02d3215d8b658c293c5470776ff5d7a312ae", "peer_review_file": "pr1031-recovered-t16-finite-peer-review.json", "peer_review_sha256": "8ba2cded3d12a694045474bb6bc0e3a4d155fed9e7240581f08b401f389bbf4b", "source_peer_review_file": "pr1031-recovered-t16-finite-source-peer-review.json", "source_peer_review_sha256": "1a05bd5e9b87d62309dfc1a745619954ca25eb5afe393564eae3f7ca255cb7e4", "proof_file": "selected-provider-v2-whole-upper.md", "family_kind": "rank73-own-recovered-T16-direct-Gaussian-no-BIT", "native_certificate_file": "pr1031-recovered-t16-finite-native.json", "native_certificate_sha256": "b545d0b216c5ef43f6f90489bdd649fce5ce71079643e079b3b9a90f397d6af1", "program_fingerprint": "c6c9ee324a08f7907d70aa412e93c8df87e9f52c8ea680554c85f3578ccecdae", "program_fingerprint_scope": "Actual own selected full/orientation hashes are checked. Optional canonical absence remains explicit; scalar specialization does not prove operator or phase endpoints.", "invoice_fingerprint": "73fb80fa0f09cb6e1bb08e1abe825c7ec7212261c9dc6c519eec6d8d6691219a", "invoice_fingerprint_scope": "Fresh own complete PLAN/OWNERS, whole helper widths, chronological windows, charts, stock and full no-prior invoice; source-equivalent numeric parent provenance is disclosed.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "104510464417001/62500000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "canonical_catalogue_absent_for": [], "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_scope": "New direct Gaussian realization of the same own selected source core; no literal historical dual-supplier replay is claimed.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr1031-recovered-t16-finite-early-upper.json", "scope": "Conditional sufficient eventual bound for every positive XOR tariff against the same repaired unlimited optimized-GMP reference, retaining the stated own typed native/frame/phase/all-size and analytic interfaces.", "exact_individual_crossing": false }, "record_certificate_file": "pr1031-recovered-t16-finite-record-upper.json", "record_certificate_sha256": "168f22028735d5b05232759cc218e992ab0b362e8e6227749f9080879df31b9f", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "selected_provider_v2_whole_bounds.py" ], "reproduction_commands": [ [ "selected_provider_dispatch_v2.py", "--execute" ], [ "selected_provider_v2_whole_bounds.py" ] ], "source_discovery_scope": "Fourteen newly recovered exact own production SPECs are screened. Eleven have complete admitted numeric inputs; three unresolved actual selected program-byte gaps receive no bound.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1042, "source_commit": "7e8ef087c02a77038a28a337a7ee3a77039cac0d", "certificate_file": "pr1042-r480-finite-controller-early-upper.json", "certificate_sha256": "5deab51b9b6ffe7c60430b9f570eb0029f6a5181797e2fa08114d5c113b6de9e", "peer_review_file": "pr1042-r480-finite-controller-peer-review.json", "peer_review_sha256": "87b1cb731a2edad1a0a12c73cd194f74e55c286c0e1893bf968c076bc7591ae5", "source_peer_review_file": "pr1042-r480-finite-controller-source-peer-review.json", "source_peer_review_sha256": "68e34d8ee6f0bffb44c1aa46164ba9a4403f757de4a77e28c6baf497a4345b35", "proof_file": "r480-t16-finite-controller-upper.md", "family_kind": "rank73-r480-source-equivalent-finite-controller", "native_certificate_file": "pr1042-r480-finite-controller-native.json", "native_certificate_sha256": "ed96fdd57303b699920f53d6d2d0b1d7f7385d3ce50a11c86b57f592b3f9d2c6", "program_fingerprint": "9f41d53659e9be84e20c661560c5687abbf5cd0660cdecbe01ad5eb29e6b8ee3", "program_fingerprint_scope": "Exact earlier own-SPEC selected 704-column canonical/program hashes recovered from a later archive; fresh regeneration of both orientations. No later construction or profile is transferred.", "invoice_fingerprint": "56237bf23ac5d708f439a749a980003db5f227f97b42401d11f3b54534435703", "invoice_fingerprint_scope": "Fresh own selected-call native, wrapper and nonlocal invoice; own historical PLAN/order/windows/profile/owner bytes bind a newly checked source-equivalent parent realization.", "params_fingerprint": "fcfcf73bf82998446ad32b81767830def24c6d56c02b017528163ad98b3c0a89", "effective_kappa": "1/5000", "kappa_record": "1672188119205421/1000000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr1042-r480-finite-controller-early-upper.json", "scope": "Conditional sufficient eventual upper in the same fixed XAG/unlimited optimized-GMP model for every positive XOR tariff; own source-equivalent numeric realization.", "exact_individual_crossing": false }, "record_certificate_file": "pr1042-r480-finite-controller-record-upper.json", "record_certificate_sha256": "1fca558ee271b0b14635b8192706cab7f47fd90e1b7558c061a4a898634f37dd", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own exact arbitrary-input phase/normalized-wrapper, common-label/mutable-source and all-size unequal-child realization interfaces remain explicit fixed-protocol hypotheses.", "Exact earlier own-SPEC canonical/program hashes are recovered from a later archive; only identical earlier selected bytes are reused. No later owner/profile or rank supplier is substituted.", "All704 native scalar input columns, private clears, actual wrapper sweeps, dyadic Horner/prefix counts and each own whole T16 role/window/chart/profile were freshly checked; no full phase or Lean replay is claimed.", "The parent numeric realization uses an independently window-matched primary geometry fixture and source direct-sum lift. Own historical PLAN, call order, windows, profile and owner bytes are bound; historical parent provenance metadata byte identity is not claimed.", "Completed Gaussian children have semantic norm one under the endpoint contract. Own finite router/literal/C0 inequalities,512-bit payload and16469 row allowance fund the typed precision interface.", "Same direct Gaussian/fine-prime/finite-section/boundary/recovery analytic contracts, exact candidate-only Fermat helper and repaired unlimited optimized-GMP correctness/halting assumptions." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "r480_selected_native_recovery.py" ], "reproduction_commands": [ [ "r480_selected_native_recovery.py" ], [ "r480_t16_owner_invoice.py" ], [ "r480_t16_finite_controller_upper.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1050, "source_commit": "c87242f846cfab8c0b97fd889b5fecb0eacef939", "certificate_file": "pr1050-recovered-t16-finite-early-upper.json", "certificate_sha256": "5b11d1eebd55d0fb77946e0015f5207200a8c45972bdc9dce88507bb07e3f92a", "peer_review_file": "pr1050-recovered-t16-finite-peer-review.json", "peer_review_sha256": "9f13e3b40e628b2fef0ec22f84e0ce7a92834b04201802fc29eaeecb9889c168", "source_peer_review_file": "pr1050-recovered-t16-finite-source-peer-review.json", "source_peer_review_sha256": "f170b7a6a89f4daae288aa263920ab61354aa5538c0aa4676582ecaecd17f4c9", "proof_file": "selected-provider-v2-whole-upper.md", "family_kind": "rank73-own-recovered-T16-direct-Gaussian-no-BIT", "native_certificate_file": "pr1050-recovered-t16-finite-native.json", "native_certificate_sha256": "d865e11dd4cdae379d7d80cd79ba7f75567021855eb144d1420528947dfb0477", "program_fingerprint": "c6c9ee324a08f7907d70aa412e93c8df87e9f52c8ea680554c85f3578ccecdae", "program_fingerprint_scope": "Actual own selected full/orientation hashes are checked. Optional canonical absence remains explicit; scalar specialization does not prove operator or phase endpoints.", "invoice_fingerprint": "73fb80fa0f09cb6e1bb08e1abe825c7ec7212261c9dc6c519eec6d8d6691219a", "invoice_fingerprint_scope": "Fresh own complete PLAN/OWNERS, whole helper widths, chronological windows, charts, stock and full no-prior invoice; source-equivalent numeric parent provenance is disclosed.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "1672241870811633/1000000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "canonical_catalogue_absent_for": [], "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_scope": "New direct Gaussian realization of the same own selected source core; no literal historical dual-supplier replay is claimed.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr1050-recovered-t16-finite-early-upper.json", "scope": "Conditional sufficient eventual bound for every positive XOR tariff against the same repaired unlimited optimized-GMP reference, retaining the stated own typed native/frame/phase/all-size and analytic interfaces.", "exact_individual_crossing": false }, "record_certificate_file": "pr1050-recovered-t16-finite-record-upper.json", "record_certificate_sha256": "2f2ead1f0898bd39907c6ad9980408870fec53e27aab46320a9516b306a0e185", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "selected_provider_v2_whole_bounds.py" ], "reproduction_commands": [ [ "selected_provider_dispatch_v2.py", "--execute" ], [ "selected_provider_v2_whole_bounds.py" ] ], "source_discovery_scope": "Fourteen newly recovered exact own production SPECs are screened. Eleven have complete admitted numeric inputs; three unresolved actual selected program-byte gaps receive no bound.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1053, "source_commit": "6f92ce8884929c9fd4730c86a28e2e3735de02af", "certificate_file": "pr1053-recovered-t16-finite-early-upper.json", "certificate_sha256": "6af626ae827bda35ec75a88ea4281775d00c60850bf1dd5d004b5c0d7653c1c8", "peer_review_file": "pr1053-recovered-t16-finite-peer-review.json", "peer_review_sha256": "0135fddca86a9b2bb5dcc7ddebccbb60c94619ed9a5f31d5d472fd5af33c1c5d", "source_peer_review_file": "pr1053-recovered-t16-finite-source-peer-review.json", "source_peer_review_sha256": "5c8a3ebefd5f3d7f47c7306cb5bda009c5bcbbf400fb7a607772fb9ab513090d", "proof_file": "selected-provider-v2-whole-upper.md", "family_kind": "rank73-own-recovered-T16-direct-Gaussian-no-BIT", "native_certificate_file": "pr1053-recovered-t16-finite-native.json", "native_certificate_sha256": "b9c9daf4dc7bbbcdbedccf94023f5109e6b4f8ae0bcfdfd9a35ad69c51e0cec0", "program_fingerprint": "c6c9ee324a08f7907d70aa412e93c8df87e9f52c8ea680554c85f3578ccecdae", "program_fingerprint_scope": "Actual own selected full/orientation hashes are checked. Optional canonical absence remains explicit; scalar specialization does not prove operator or phase endpoints.", "invoice_fingerprint": "73fb80fa0f09cb6e1bb08e1abe825c7ec7212261c9dc6c519eec6d8d6691219a", "invoice_fingerprint_scope": "Fresh own complete PLAN/OWNERS, whole helper widths, chronological windows, charts, stock and full no-prior invoice; source-equivalent numeric parent provenance is disclosed.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "418061452383951/250000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "canonical_catalogue_absent_for": [], "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_scope": "New direct Gaussian realization of the same own selected source core; no literal historical dual-supplier replay is claimed.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr1053-recovered-t16-finite-early-upper.json", "scope": "Conditional sufficient eventual bound for every positive XOR tariff against the same repaired unlimited optimized-GMP reference, retaining the stated own typed native/frame/phase/all-size and analytic interfaces.", "exact_individual_crossing": false }, "record_certificate_file": "pr1053-recovered-t16-finite-record-upper.json", "record_certificate_sha256": "01d8302745ad237617b25064ef9bc8d01d5a0a453c57a5b60d42cdb1f536be42", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "selected_provider_v2_whole_bounds.py" ], "reproduction_commands": [ [ "selected_provider_dispatch_v2.py", "--execute" ], [ "selected_provider_v2_whole_bounds.py" ] ], "source_discovery_scope": "Fourteen newly recovered exact own production SPECs are screened. 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Source-equivalent numeric parent provenance is disclosed.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "334530612298617/200000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "canonical_catalogue_absent_for": [], "operator_phase_proved": false, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr1082-dispatched-finite-controller-early-upper.json", "scope": "Conditional sufficient eventual upper for each positive XOR tariff in the same XAG/unlimited optimized-GMP model, with explicit own full physical/phase/native interface premises.", "exact_individual_crossing": false }, "record_certificate_file": "pr1082-dispatched-finite-controller-record-upper.json", "record_certificate_sha256": "73a66c3a99929fc212ce5ac6559e6271198223193ccb8c332ed05dfa2836f21d", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "selected_provider_whole_bounds.py" ], "reproduction_commands": [ [ "selected_provider_admitted_replay.py" ], [ "selected_provider_whole_bounds.py" ] ], "broader_discovery_reproduction": [ "selected_provider_dispatch.py", "--execute" ], "broader_discovery_scope": "Optional144-entry/38-numeric-input discovery replay requires additional unpriced source artifacts; the admitted scoped replay needs only these fifteen own source sets.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1087, "source_commit": "589d1cedf5ef5f231182f4ec86408616311a8af0", "certificate_file": "pr1087-recovered-t16-finite-early-upper.json", "certificate_sha256": "827862c7ad06c4543b3d8a852a30f38548bc570324eeb6d7c4eefcb153405c77", "peer_review_file": "pr1087-recovered-t16-finite-peer-review.json", "peer_review_sha256": "a013644763538abe443128a88faae9d2d8fdc3c9efa11fe97177415ef7419ea4", "source_peer_review_file": "pr1087-recovered-t16-finite-source-peer-review.json", "source_peer_review_sha256": "f76cf7c293d67a1b1e6b5c330970cfd12c3b8608e5f7b1b24f28a7d98033408f", "proof_file": "selected-provider-v2-whole-upper.md", "family_kind": "rank73-own-recovered-T16-direct-Gaussian-no-BIT", "native_certificate_file": "pr1087-recovered-t16-finite-native.json", "native_certificate_sha256": "02c759b220c82d8e2f23a81de77aa7dd362a2e777f68508bd9001fc7da0f1de5", "program_fingerprint": "c6c9ee324a08f7907d70aa412e93c8df87e9f52c8ea680554c85f3578ccecdae", "program_fingerprint_scope": "Actual own selected full/orientation hashes are checked. Optional canonical absence remains explicit; scalar specialization does not prove operator or phase endpoints.", "invoice_fingerprint": "73fb80fa0f09cb6e1bb08e1abe825c7ec7212261c9dc6c519eec6d8d6691219a", "invoice_fingerprint_scope": "Fresh own complete PLAN/OWNERS, whole helper widths, chronological windows, charts, stock and full no-prior invoice; source-equivalent numeric parent provenance is disclosed.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "1672654541898561/1000000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "canonical_catalogue_absent_for": [], "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_scope": "New direct Gaussian realization of the same own selected source core; no literal historical dual-supplier replay is claimed.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr1087-recovered-t16-finite-early-upper.json", "scope": "Conditional sufficient eventual bound for every positive XOR tariff against the same repaired unlimited optimized-GMP reference, retaining the stated own typed native/frame/phase/all-size and analytic interfaces.", "exact_individual_crossing": false }, "record_certificate_file": "pr1087-recovered-t16-finite-record-upper.json", "record_certificate_sha256": "d781d368959539caa1b5600b9f49fa58816507826ef152a33ba9ec6a173b64f5", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "selected_provider_v2_whole_bounds.py" ], "reproduction_commands": [ [ "selected_provider_dispatch_v2.py", "--execute" ], [ "selected_provider_v2_whole_bounds.py" ] ], "source_discovery_scope": "Fourteen newly recovered exact own production SPECs are screened. Eleven have complete admitted numeric inputs; three unresolved actual selected program-byte gaps receive no bound.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1094, "source_commit": "0fc329d0bec93ca7cd288eaea1295172e8789810", "certificate_file": "pr1094-r480-finite-controller-early-upper.json", "certificate_sha256": "58275c5f06f7ec0f72c8ae332c68f5e1732e0677b2dc6f29df6999a121a0d4da", "peer_review_file": "pr1094-r480-finite-controller-peer-review.json", "peer_review_sha256": "675b21c85b9b31af0dc88fc16f87986059fdd5a3818e6d4bd7b767ebfee68d58", "source_peer_review_file": "pr1094-r480-finite-controller-source-peer-review.json", "source_peer_review_sha256": "904070e0b8b1c19a3da4c588ca2658679318da3d115b5f14de4b4e964a4e6edc", "proof_file": "r480-t16-finite-controller-upper.md", "family_kind": "rank73-r480-source-equivalent-finite-controller", "native_certificate_file": "pr1094-r480-finite-controller-native.json", "native_certificate_sha256": "68007b400bd3ebbf455dc1d105dc8a94ad1e9a0993a4d0f572edf1f14084ed06", "program_fingerprint": "9f41d53659e9be84e20c661560c5687abbf5cd0660cdecbe01ad5eb29e6b8ee3", "program_fingerprint_scope": "Exact earlier own-SPEC selected 704-column canonical/program hashes recovered from a later archive; fresh regeneration of both orientations. No later construction or profile is transferred.", "invoice_fingerprint": "539ff2f6905e6dc98e8f74f25fbe7101d4b499625ea9cdf8d9b2f295a676e68f", "invoice_fingerprint_scope": "Fresh own selected-call native, wrapper and nonlocal invoice; own historical PLAN/order/windows/profile/owner bytes bind a newly checked source-equivalent parent realization.", "params_fingerprint": "fcfcf73bf82998446ad32b81767830def24c6d56c02b017528163ad98b3c0a89", "effective_kappa": "1/5000", "kappa_record": "836330098538459/500000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr1094-r480-finite-controller-early-upper.json", "scope": "Conditional sufficient eventual upper in the same fixed XAG/unlimited optimized-GMP model for every positive XOR tariff; own source-equivalent numeric realization.", "exact_individual_crossing": false }, "record_certificate_file": "pr1094-r480-finite-controller-record-upper.json", "record_certificate_sha256": "525ddd9b2ee7c69242eb46a44013bb701a2d5d2b9097d1404146728706746190", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own exact arbitrary-input phase/normalized-wrapper, common-label/mutable-source and all-size unequal-child realization interfaces remain explicit fixed-protocol hypotheses.", "Exact earlier own-SPEC canonical/program hashes are recovered from a later archive; only identical earlier selected bytes are reused. No later owner/profile or rank supplier is substituted.", "All704 native scalar input columns, private clears, actual wrapper sweeps, dyadic Horner/prefix counts and each own whole T16 role/window/chart/profile were freshly checked; no full phase or Lean replay is claimed.", "The parent numeric realization uses an independently window-matched primary geometry fixture and source direct-sum lift. Own historical PLAN, call order, windows, profile and owner bytes are bound; historical parent provenance metadata byte identity is not claimed.", "Completed Gaussian children have semantic norm one under the endpoint contract. Own finite router/literal/C0 inequalities,512-bit payload and16469 row allowance fund the typed precision interface.", "Same direct Gaussian/fine-prime/finite-section/boundary/recovery analytic contracts, exact candidate-only Fermat helper and repaired unlimited optimized-GMP correctness/halting assumptions." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "r480_selected_native_recovery.py" ], "reproduction_commands": [ [ "r480_selected_native_recovery.py" ], [ "r480_t16_owner_invoice.py" ], [ "r480_t16_finite_controller_upper.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1104, "source_commit": "d8982686afd7ef6ce52ddeaa17011ccda558d666", "certificate_file": "pr1104-ends7-selected-finite-early-upper.json", "certificate_sha256": "dd2024e82468b4a6e89c8a79e915f2dfd971be2455772f9b36c4afef6be2f859", "peer_review_file": "pr1104-ends7-selected-finite-peer-review.json", "peer_review_sha256": "282727599ef7d2161c255b0ac782ed388f3554bf716fb750a16cecb6817a99ac", "source_peer_review_file": "pr1104-ends7-selected-finite-source-peer-review.json", "source_peer_review_sha256": "fc39689e1ffda16c366491c0ab3ea49b36e466f4fa084f5f2b8ac10a332efd59", "proof_file": "selected-provider-v13-whole-upper.md", "family_kind": "own-selected-ends7-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr1104-ends7-selected-finite-record-upper.json", "record_certificate_sha256": "8e2ca972d2f5a36d95e85ed43fc12a4f2849da2bb6ebd560d23b12220d5017bf", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "1672691689152441/1000000000000000000", "native_certificate_file": "pr1104-ends7-selected-finite-native.json", "native_certificate_sha256": "2fd13e3255445498ba392212138bcba0ca12a53d782dceb6fad5532f5a3b7db3", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "historical_parent_byte_identity_claimed": false, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": true, "source_report_counter_mismatch": false, "descriptive_entering_counter": { "source_declared_entering_helper_roles": null, "actual_nonzero_start_frame_roles": 27648, "width_below_9_roles": 34560, "source_declared_meter_style": "not_declared_in_own_expected", "source_declared_counter_matches_actual": null, "used_by_new_cost_stock_or_precision": false }, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "recover_pr1104_ends7_selected_native.py" ], [ "prepare_selected_provider_v13.py" ], [ "selected_provider_dispatch_v13.py", "--execute" ], [ "prepare_selected_provider_v13_whole_costs.py" ], [ "ends7_descriptive_counter_audit.py" ], [ "selected_provider_v13_whole_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1107, "source_commit": "6123fc5d57db16aaa3e8a26b4a11a34b46c0c391", "certificate_file": "pr1107-ends7-selected-finite-early-upper.json", "certificate_sha256": "9a3aa8b4a7d1fe20ea66e208418a5dc02be770acab8dbfd434fd55c8b3c413ac", "peer_review_file": "pr1107-ends7-selected-finite-peer-review.json", "peer_review_sha256": "f0b09ac605e2e72782089752f7e0dea720bf7f79dce94c5b3e29bac4221221d2", "source_peer_review_file": "pr1107-ends7-selected-finite-source-peer-review.json", "source_peer_review_sha256": "0292c7d9b8115103b04d7471671a6137049186e907b5fa2c57d5e071689788c3", "proof_file": "selected-provider-v13-whole-upper.md", "family_kind": "own-selected-ends7-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr1107-ends7-selected-finite-record-upper.json", "record_certificate_sha256": "001a654f665d7502ecf861db6fd0df8baa11d55ee751ae4e1235a0024fa89cdc", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "836382990093363/500000000000000000", "native_certificate_file": "pr1107-ends7-selected-finite-native.json", "native_certificate_sha256": "ca9af562c429de3ddab042d0132f7931ce261b73ae48888adfa95234a8ce3146", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "historical_parent_byte_identity_claimed": false, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": true, "source_report_counter_mismatch": false, "descriptive_entering_counter": { "source_declared_entering_helper_roles": null, "actual_nonzero_start_frame_roles": 27648, "width_below_9_roles": 34560, "source_declared_meter_style": "not_declared_in_own_expected", "source_declared_counter_matches_actual": null, "used_by_new_cost_stock_or_precision": false }, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "recover_pr1104_ends7_selected_native.py" ], [ "prepare_selected_provider_v13.py" ], [ "selected_provider_dispatch_v13.py", "--execute" ], [ "prepare_selected_provider_v13_whole_costs.py" ], [ "ends7_descriptive_counter_audit.py" ], [ "selected_provider_v13_whole_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1117, "source_commit": "342b67f23dfa8f41a520a0d58978b2875e9eb0dd", "certificate_file": "pr1117-ends7-selected-finite-early-upper.json", "certificate_sha256": "aaffa69b0e4c16e2a5ea9f414ed307255304d18f50e552ebc20fdf9a85b4e7a6", "peer_review_file": "pr1117-ends7-selected-finite-peer-review.json", "peer_review_sha256": "5036970ad67cdfa2488af5c9ec6869e9110f1746e358b19de8a504bdd4713a34", "source_peer_review_file": "pr1117-ends7-selected-finite-source-peer-review.json", "source_peer_review_sha256": "c39955e6557084c71b96e0f69bfb6274ccd4bef68481237731992c2d9b98db90", "proof_file": "selected-provider-v13-whole-upper.md", "family_kind": "own-selected-ends7-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr1117-ends7-selected-finite-record-upper.json", "record_certificate_sha256": "55ced425c2be013ce2fcae1ae2380cf952ba8f94696fbd646cb65c0ddbe3493e", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "334569399176037/200000000000000000", "native_certificate_file": "pr1117-ends7-selected-finite-native.json", "native_certificate_sha256": "4f852b440033f8b1567696acc9aba7996f69d2bf143cb2c565113479fec132e8", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "historical_parent_byte_identity_claimed": false, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": true, "source_report_counter_mismatch": false, "descriptive_entering_counter": { "source_declared_entering_helper_roles": null, "actual_nonzero_start_frame_roles": 27648, "width_below_9_roles": 34560, "source_declared_meter_style": "not_declared_in_own_expected", "source_declared_counter_matches_actual": null, "used_by_new_cost_stock_or_precision": false }, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. 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The new explicit numeric PLAN and fresh full invoice do not assert historical full PLAN byte identity or reuse the previous billed amount.", "The actual original source native/owner/invoice/assembly components were observed under a disclosed external wall-timeout-only wrapper. The literal original short-timeout command and universal operator/all-size hypotheses are not claimed fully proved." ], "original_global_verifier_full_PASS_claimed": false, "literal_original_timeout_command_PASS_claimed": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "kernel_demotions_native_owner_invoice.py" ], [ "kernel_demotions_gaussian_bounds.py" ] ], "offline_verification_commands": [ [ "kernel_demotions_gaussian_bounds.py" ] ], "offline_verification_scope": "Fresh complete numerical228-check cost envelope from independently peer-bound own native/physical/call/invoice censuses, with exact source and selected programme bytes verified. The explicit native/whole-owner/invoice producer is separately reproducible; original expensive full-source observed execution is provenance, not silently rerun or claimed deterministic by this fast job.", "optional_original_component_replay_command": [ "run_kernel_demotions_original.py" ], "optional_original_component_replay_scope": "Observed native/phase/owner/invoice/assembly producer with explicitly disclosed external timeout wrapper; raw timing-bearing reports are not byte-stable mathematical outputs.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1157, "source_commit": "c5647aecc8ff44e49776860bb75520bfe3e88f1e", "certificate_file": "pr1157-gaussian-only-finite-early-upper.json", "certificate_sha256": "3ff0123aff33366c44ce4e095e8b59c080d3c7d0c81e26efa8ae7d172c62f821", "peer_review_file": "pr1157-gaussian-only-finite-peer-review.json", "peer_review_sha256": "4e542dcb7c4a5e715e871105f7be263faacc9e427f952bd30455831e6ed9dd90", "source_peer_review_file": "pr1157-gaussian-only-finite-source-peer-review.json", "source_peer_review_sha256": "9bc7c9c3677c263ee32fd6e5a9a49fcc141f0a984f28619e9e19bfc79106d5e4", "proof_file": "gaussian-only-selected-provider-upper.md", "family_kind": "rank73-own-selected-direct-Gaussian-no-BIT", "native_certificate_file": "pr1157-gaussian-only-finite-native.json", "native_certificate_sha256": "6400b518d2940395f73edc7f415572e712794525bf33e600f5e99afe20f650ea", "program_fingerprint": "a2fd9d1c037e08e0b5af26976e5ac0a597a5e409d1a86d02cfcc8755d8f09a41", "program_fingerprint_scope": "Actual own-selected full/orientation hash-bound program; optional canonical catalogue absence is explicit. No phase/operator endpoint is inferred from scalar specialization.", "invoice_fingerprint": "fabe97d64ea09e528ac65c3e0b36fe5043ad63899c3b9b2b73380bb29f5f1d88", "invoice_fingerprint_scope": "Fresh own complete selected-call/physical owner/window/nonlocal/stock invoice, no prior invoice. Source-equivalent numeric parent provenance is disclosed.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "334827562021037/200000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "canonical_catalogue_absent_for": [ "gauge44" ], "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_scope": "New direct Gaussian realization of the same selected source core; literal historical dual-supplier implementation is not claimed.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr1157-gaussian-only-finite-early-upper.json", "scope": "Conditional sufficient eventual upper for each positive XOR tariff in the same XAG/unlimited optimized-GMP model, with explicit own full physical/phase/native interface premises.", "exact_individual_crossing": false }, "record_certificate_file": "pr1157-gaussian-only-finite-record-upper.json", "record_certificate_sha256": "10cd9540e1877de6204fcd3d95cf8b88e220945b6eaac69b2ac4a55d3c55b5cd", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "gaussian_only_selected_provider_bounds.py" ], "reproduction_commands": [ [ "gaussian_only_admitted_replay.py" ], [ "gaussian_only_selected_provider_bounds.py" ] ], "broader_discovery_reproduction": [ "selected_provider_dispatch.py", "--execute" ], "broader_discovery_scope": "Optional144-entry/38-numeric-input discovery replay requires additional unpriced source artifacts; the admitted scoped replay needs only these fifteen own source sets.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1169, "source_commit": "13d02293a7af67d7e3bd2e4d7f1a2943ac20537e", "certificate_file": "pr1169-joint-entrance-finite-early-upper.json", "certificate_sha256": "8b5c313bcd879482ce0f2dd495ad1f5f7d10062e4fee0884d31abde64765a9bc", "peer_review_file": "pr1169-joint-entrance-finite-peer-review.json", "peer_review_sha256": "09282102ed3186fd456c56cc5bbb43f7f36b17eccfb1791d8d05344884821fb2", "source_peer_review_file": "pr1169-joint-entrance-finite-source-peer-review.json", "source_peer_review_sha256": "408ac900a083afa3bc2f0e18aac485fe1da542f802d46c8a2636fea3321a30ab", "proof_file": "selected-provider-v21-whole-upper.md", "family_kind": "own-joint-entrance-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr1169-joint-entrance-finite-record-upper.json", "record_certificate_sha256": "08fa92a91786232639046e4834ea9cdb1086c89a2aed7b517ea4502d91506daa", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "1675568675201533/1000000000000000000", "native_certificate_file": "pr1169-joint-entrance-finite-native.json", "native_certificate_sha256": "c751ee442624e99483ba78d50c0d36a2f20998c43b2ab78f6055511cf7811696", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "historical_parent_byte_identity_claimed": false, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": true, "source_report_counter_mismatch": false, "descriptive_entering_counter": { "source_declared_entering_helper_roles": null, "actual_nonzero_start_frame_roles": 63936, "width_below_9_roles": 79920, "source_declared_meter_style": "not_declared_in_own_expected", "source_declared_counter_matches_actual": null, "used_by_new_cost_stock_or_precision": false }, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "recover_joint_entrance_selected_native.py" ], [ "recover_joint_entrance_extra_native.py" ], [ "prepare_selected_provider_v21.py" ], [ "selected_provider_dispatch_v21.py", "--execute" ], [ "prepare_selected_provider_v21_whole_costs.py" ], [ "joint_entrance_descriptive_counter_audit.py" ], [ "selected_provider_v21_whole_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1172, "source_commit": "4d2cc9df55ed5a17786b7c0a200d70332afbe41e", "certificate_file": "pr1172-ends7-exchange-finite-early-upper.json", "certificate_sha256": "6693ca966902627ffd32efb6b8ff013137928cf164640f509598a485f561cee4", "peer_review_file": "pr1172-ends7-exchange-finite-peer-review.json", "peer_review_sha256": "c4748007d35bdaf9a7b19d14a2a15e2952d498739fe9c94032629822b05addc8", "source_peer_review_file": "pr1172-ends7-exchange-finite-source-peer-review.json", "source_peer_review_sha256": "249cae59c2c41b345a35ffee6033791e056f0e3e3bc41b20d01062da7648f1be", "proof_file": "selected-provider-v15-whole-upper.md", "family_kind": "own-selected-ends7-exchange-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr1172-ends7-exchange-finite-record-upper.json", "record_certificate_sha256": "36d4efaaa93040a8e1520dd07ed05366ddf5e0924a649780c9ba10f673ea058a", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "6691209629869/4000000000000000", "native_certificate_file": "pr1172-ends7-exchange-finite-native.json", "native_certificate_sha256": "d6782bf24c9929e429f949b440d66b850ec45385ea21b8f26574df2a0adf331e", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "historical_parent_byte_identity_claimed": false, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": true, "source_report_counter_mismatch": false, "descriptive_entering_counter": { "source_declared_entering_helper_roles": null, "actual_nonzero_start_frame_roles": 27648, "width_below_9_roles": 34560, "source_declared_meter_style": "not_declared_in_own_expected", "source_declared_counter_matches_actual": null, "used_by_new_cost_stock_or_precision": false }, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "recover_pr1104_ends7_selected_native.py" ], [ "prepare_selected_provider_v15.py" ], [ "selected_provider_dispatch_v15.py", "--execute" ], [ "prepare_selected_provider_v15_whole_costs.py" ], [ "ends7_exchange_descriptive_counter_audit.py" ], [ "selected_provider_v15_whole_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1175, "source_commit": "007a7c64280053e2ddabdb92e60b51bfd9105119", "certificate_file": "pr1175-final-mixed-finite-early-upper.json", "certificate_sha256": "a070a1f23b16a5ca77ae532632dd664859c80336450bef003a39ed1c7efa169d", "peer_review_file": "pr1175-final-mixed-finite-peer-review.json", "peer_review_sha256": "02981a0bd1a382a441567fb45b93aa3f7b602ac781d4080f61bfa7b6e8192ec4", "source_peer_review_file": "pr1175-final-mixed-finite-source-peer-review.json", "source_peer_review_sha256": "19563cac84d9e0170b77db7d81773cb07f1d43790b749eff1aa5e3379c5730b1", "proof_file": "selected-provider-v8-whole-upper.md", "family_kind": "rank73-exact-own-final-mixed1175-early-Gaussian-no-BIT", "native_certificate_file": "pr1175-final-mixed-finite-native.json", "native_certificate_sha256": "765e491e60ce3e1e4122f5ba4cfd199c2ac002bd6360ee0bb478bbb2cbd6dca1", "program_fingerprint": "fd26c05ffdf9aa57384e8933ef44cb0b8755bfbc61c1047207b186419a2328cf", "program_fingerprint_scope": "Actual full selected programme, canonical and both orientation commitments are checked. Full operator-valued required-boundary and absolute-phase contract remains explicit.", "invoice_fingerprint": "42a905b259ceb57a6e27eeee3ba524597f2db5d28271bc18847dad6e85198efd", "invoice_fingerprint_scope": "Fresh complete own PLAN/OWNERS/calls/windows/charts/profile and no-prior full invoice, with disclosed new numeric parent provenance.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "104741720899017/62500000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_quantified": true, "record_tail_scope": "Own original record exponent is separately quantified by this new direct Gaussian circuit.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr1175-final-mixed-finite-early-upper.json", "scope": "Conditional sufficient eventual bound for the explicitly weaker early exponent1/5000, all positive XOR tariffs, same repaired unlimited optimized-GMP reference; retained native/frame/phase/all-size/analytic interfaces.", "exact_individual_crossing": false }, "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "pr1175_final_source_chronology.py" ], [ "pr1175_plot_source_chronology.py" ], [ "recover_pr1175_final_mixed_native.py" ], [ "selected_provider_dispatch_v8.py", "--execute" ], [ "selected_provider_v8_whole_bounds.py" ] ], "offline_verification_commands": [ [ "selected_provider_v8_whole_bounds.py" ] ], "offline_verification_scope": "Fast complete numerical envelope replay from bound source censuses. The distinct921-check actual source reconstruction is available as the first reproduction job and authenticated by its separate frozen receipt.", "source_discovery_scope": "Each own author-head MANIFEST and actual verifier selects its exact kernel SPEC. Raw source words and unchanged own1175mixed source archive reconstruct exactly those canonical/program/orientation commitments; no equal-kappa/profile inference or cutoff transfer.", "record_certificate_file": "pr1175-final-mixed-finite-record-upper.json", "record_certificate_sha256": "d31e29c48c82c18fe9f74c18136f096fa2e3897fa69d06c4004c78573eeea240", "record_P": "230584301497830147503423480", "record_tail_input_bits": "2^(2^230584301497830147503423480)", "source_selected_kappa_correction": true, "frozen_metadata_kappa": "1675338871723469/1000000000000000000", "actual_own_selected_kappa": "104741720899017/62500000000000000", "source_selected_kappa_correction_basis": "Actual final own CLAIM names the sixth-layer mixed-arcflow head package; own MANIFEST/RESULT/verifier/SPEC agree. Exact raw recipes and two complete native providers plus full PLAN/OWNERS/invoice are independently reconstructed. Earlier historical title/body arcflow fixture is preserved separately, not selected.", "source_revision_committed_at": "2026-10-15T18:34:53Z", "source_revision_included_at_merge": "2026-10-16T13:35:38Z", "source_revision_merge_commit": "050d1ad521415e977aa9be563cb3db419afab37b", "source_kappa_correction_scope": "MUST visibly annotate actual included-at-merge own final1175 mixed source\u03ba separately from the earlier frozen parsed title/body fixture. Preserve original metadata and never date this source revision at PR creation. Own head is sixth of23 merge parents.", "source_kappa_correction_primary_receipt": "pr1175-final-mixed-source/plot-chronology-primary-receipt.json", "source_kappa_correction_primary_sha256": "099049825a13e6f4f3c72c091c9cc8a9a12034249b3ef743bc5084273beb6f6e", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null, "kappa_fraction": "1675338871723469/1000000000000000000", "kappa_decimal": "0.001675338871723469", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews." } }, { "pr": 1176, "source_commit": "3a0d419341879a395d921693112c3b826de93677", "certificate_file": "pr1176-dynamic-kernel-finite-early-upper.json", "certificate_sha256": "4e20c76d0c3d4171545de8aca8e19a54b9248339b7dbb8fa69a3516e7f207169", "peer_review_file": "pr1176-dynamic-kernel-finite-peer-review.json", "peer_review_sha256": "a0bf030190a97786bd1741a517b321a665ac946c07070ab44b63cb8d481e5d2e", "source_peer_review_file": "pr1176-dynamic-kernel-finite-source-peer-review.json", "source_peer_review_sha256": "178eeda1e417459ec2b04272f06349f9f750ed6006962597950dfd9738c98a80", "proof_file": "kernel-demotions-gaussian-bounds.md", "family_kind": "own-dynamic-selected-kernel-demotions-direct-Gaussian", "native_certificate_file": "pr1176-dynamic-kernel-finite-native.json", "native_certificate_sha256": "a26e01ae398047a591f8046d3117c3e4a9a58dc43ba13bba390a9db342b5a462", "record_certificate_file": "pr1176-dynamic-kernel-finite-record-upper.json", "record_certificate_sha256": "23f9a035957821a69849f9ef2fedc7f5d77fb992108be445fc67dd9224b9b6bd", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "effective_kappa": "1/5000", "kappa_record": "1675224519162937/1000000000000000000", "native_coordinate_rank": 73, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "exact_individual_crossing": false, "source": "data/operation-audit/pr1176-dynamic-kernel-finite-early-upper.json" }, "lower": null, "scope": [ "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "Own required physical partial initial/output Gaussian operators, identity on spectators, absolute phases, bounded73-axis affine/even-Z4 monomial grammar and normalized completed-child identities remain explicit; scalar/rank checks alone do not prove them.", "Own arbitrary dirty restoration, common-label, whole-call/all-column/all-size hosting and fixed group/compiler interfaces.", "A new complete numeric parent and full operation invoice are priced; no historical full PLAN byte identity or old billed amount is claimed.", "The original optional BIT supplier is not consumed by this direct Gaussian realization." ], "source_caveats": [ "The complete own dynamic provider dispatch and all literal owner edits are retained. The new explicit numeric PLAN and fresh full invoice do not assert historical full PLAN byte identity or reuse the previous billed amount.", "The actual original source native/owner/invoice/assembly components were observed under a disclosed external wall-timeout-only wrapper. The literal original short-timeout command and universal operator/all-size hypotheses are not claimed fully proved." ], "original_global_verifier_full_PASS_claimed": false, "literal_original_timeout_command_PASS_claimed": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "kernel_demotions_native_owner_invoice.py" ], [ "kernel_demotions_gaussian_bounds.py" ] ], "offline_verification_commands": [ [ "kernel_demotions_gaussian_bounds.py" ] ], "offline_verification_scope": "Fresh complete numerical228-check cost envelope from independently peer-bound own native/physical/call/invoice censuses, with exact source and selected programme bytes verified. The explicit native/whole-owner/invoice producer is separately reproducible; original expensive full-source observed execution is provenance, not silently rerun or claimed deterministic by this fast job.", "optional_original_component_replay_command": [ "run_kernel_demotions_original.py" ], "optional_original_component_replay_scope": "Observed native/phase/owner/invoice/assembly producer with explicitly disclosed external timeout wrapper; raw timing-bearing reports are not byte-stable mathematical outputs.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1178, "source_commit": "6d4d0dd1c2df531a3350495dd15e00105793c52d", "certificate_file": "pr1178-recovered-x54-finite-early-upper.json", "certificate_sha256": "9b2f701d532c758c835f6a4b1a7a2cdd307c1c9238a10d9f40d8eaef22ae8fb5", "peer_review_file": "pr1178-recovered-x54-finite-peer-review.json", "peer_review_sha256": "f66d7f4d0c3546ef30bd330a469238118559b45273940ff8d3083f62703ba332", "source_peer_review_file": "pr1178-recovered-x54-finite-source-peer-review.json", "source_peer_review_sha256": "8d4728c0e9ce5f921d955bf9b4198e2489931c2af917e22af0f7011dfb138669", "proof_file": "selected-provider-v5-whole-upper.md", "family_kind": "rank73-own-recovered-X54-source-direct-Gaussian-no-BIT", "native_certificate_file": "pr1178-recovered-x54-finite-native.json", "native_certificate_sha256": "f65f0257a5ac16c1bf6fdf75d0fec0eb172e93881f442398e3ead011de6d53ac", "program_fingerprint": "f3d45f055e75e0445ff6c930520fece272b353b71cf64f1ba4598c7c4d175f31", "program_fingerprint_scope": "Actual own selected full/orientation hashes are checked. Optional canonical absence remains explicit; scalar specialization does not prove operator or phase endpoints.", "invoice_fingerprint": "f83303bef6466a27947c176fce7e3cc1437c4ac9c70c555c38cef14249807ebd", "invoice_fingerprint_scope": "Fresh own complete PLAN/OWNERS, whole helper widths, chronological windows, charts, stock and full no-prior invoice; source-equivalent numeric parent provenance is disclosed.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "1675161536733127/1000000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "canonical_catalogue_absent_for": [], "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_scope": "New direct Gaussian realization of the same own selected source core; no literal historical dual-supplier replay is claimed.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr1178-recovered-x54-finite-early-upper.json", "scope": "Conditional sufficient eventual bound for every positive XOR tariff against the same repaired unlimited optimized-GMP reference, retaining the stated own typed native/frame/phase/all-size and analytic interfaces.", "exact_individual_crossing": false }, "record_certificate_file": "pr1178-recovered-x54-finite-record-upper.json", "record_certificate_sha256": "0d5fda40566036e870ad3963e3fb5e4e962a7ef639fb820a62a4d98c6991e192", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "selected_provider_v5_whole_bounds.py" ], "reproduction_commands": [ [ "selected_provider_dispatch_v5.py", "--execute" ], [ "selected_provider_v5_whole_bounds.py" ] ], "source_discovery_scope": "Own raw seed/recipe and unchanged own-pinned constructor, scalar/frame transporter, emitter, replay and wrapper checker produce complete selected canonical/program/orientation commitments. Own gzip PLAN and SOURCE-PINS OWNERS are exact-bound. No later program, profile, invoice or cutoff transfer.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1183, "source_commit": "9e7ccda21f28f5dd0397aa04a596e4f0e1d75d1d", "certificate_file": "pr1183-joint-entrance-finite-early-upper.json", "certificate_sha256": "74505e0c88202a762349e909534b411f1ed420bdb7a34828526af0041e903e4a", "peer_review_file": "pr1183-joint-entrance-finite-peer-review.json", "peer_review_sha256": "31956124bdae55abaf0678251630973d72c4c4ec1bb87cb3331321aca5cc49ac", "source_peer_review_file": "pr1183-joint-entrance-finite-source-peer-review.json", "source_peer_review_sha256": "4083a05ee8f716b998cfc5cbe8d2ca17b0f32fd4bf36bac262eec79ce94af7a1", "proof_file": "selected-provider-v21-whole-upper.md", "family_kind": "own-joint-entrance-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr1183-joint-entrance-finite-record-upper.json", "record_certificate_sha256": "65ca37ac56b4af8425ae2a3c0f527679b93e79a22d2593cb13e0c6f982dad2da", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "837801590300651/500000000000000000", "native_certificate_file": "pr1183-joint-entrance-finite-native.json", "native_certificate_sha256": "b9efa879a0c6259b354001329983c875cccc6fd2900b470998cd420e803d5ecb", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "historical_parent_byte_identity_claimed": false, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": true, "source_report_counter_mismatch": false, "descriptive_entering_counter": { "source_declared_entering_helper_roles": null, "actual_nonzero_start_frame_roles": 63936, "width_below_9_roles": 79920, "source_declared_meter_style": "not_declared_in_own_expected", "source_declared_counter_matches_actual": null, "used_by_new_cost_stock_or_precision": false }, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "recover_joint_entrance_selected_native.py" ], [ "recover_joint_entrance_extra_native.py" ], [ "prepare_selected_provider_v21.py" ], [ "selected_provider_dispatch_v21.py", "--execute" ], [ "prepare_selected_provider_v21_whole_costs.py" ], [ "joint_entrance_descriptive_counter_audit.py" ], [ "selected_provider_v21_whole_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1192, "source_commit": "970793428d346b4aa8d8fa2af03aa6dd5ad6f994", "certificate_file": "pr1192-joint-entrance-finite-early-upper.json", "certificate_sha256": "73a7a6fa221877f5ea0d2c90c2499a3666a07835ce24fc744e4ef9aa7b7be622", "peer_review_file": "pr1192-joint-entrance-finite-peer-review.json", "peer_review_sha256": "01e464f05bcdd3681c23dcae908dd5b95f3e616b7e49ec6c528a9907e25771e5", "source_peer_review_file": "pr1192-joint-entrance-finite-source-peer-review.json", "source_peer_review_sha256": "6c0ae0a8637c50ea1eb524a6296976547784538a6ef9f90f3ab326226d290e76", "proof_file": "selected-provider-v21-whole-upper.md", "family_kind": "own-joint-entrance-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr1192-joint-entrance-finite-record-upper.json", "record_certificate_sha256": "83d2de0e8c7675162e18653de0246af6bd44dfbf08e2f2d435ff8b15e07c3c83", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "837835347653851/500000000000000000", "native_certificate_file": "pr1192-joint-entrance-finite-native.json", "native_certificate_sha256": "3a83925ae190a6e9a70666e7b06f6e842a669cecb0e242ad8a34cbf8627fc462", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "historical_parent_byte_identity_claimed": false, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": true, "source_report_counter_mismatch": false, "descriptive_entering_counter": { "source_declared_entering_helper_roles": null, "actual_nonzero_start_frame_roles": 63936, "width_below_9_roles": 79920, "source_declared_meter_style": "not_declared_in_own_expected", "source_declared_counter_matches_actual": null, "used_by_new_cost_stock_or_precision": false }, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. 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Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "recover_joint_entrance_selected_native.py" ], [ "recover_joint_entrance_extra_native.py" ], [ "prepare_selected_provider_v21.py" ], [ "selected_provider_dispatch_v21.py", "--execute" ], [ "prepare_selected_provider_v21_whole_costs.py" ], [ "joint_entrance_descriptive_counter_audit.py" ], [ "selected_provider_v21_whole_bounds.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1297, "source_commit": "4abf710a7f0d2a46f522f3f13c15769d003f9495", "certificate_file": "pr1297-dispatched-finite-controller-early-upper.json", "certificate_sha256": "d271d82ccbb0eadb7be3d2910cdfb9c0aa6982558a9fd540299edff77c735587", "peer_review_file": "pr1297-selected-provider-batch-peer-review.json", "peer_review_sha256": "73c4c80ab6df872a68f804feafe95c4916cd012912f51b4b921cefb966ed6e89", "source_peer_review_file": "pr1297-dispatched-finite-controller-source-peer-review.json", "source_peer_review_sha256": "2ee822b572c50264259d88487b12b164b325fc3151111413505a2d0624d636c4", "proof_file": "selected-provider-batch-upper.md", "family_kind": "rank73-own-selected-provider-finite-controller", "native_certificate_file": "pr1297-dispatched-finite-controller-native.json", "native_certificate_sha256": "e10af9ba9894bc0c1c7d30af96164907ed93a24a828ba5e9950ab20a36385f06", "program_fingerprint": "526008ef1f4926fa36d757e84f16afbf4253924ac76027a67dde3ca8a80519f3", "program_fingerprint_scope": "Actual own-selected full/orientation hash-bound program; optional canonical catalogue absence is explicit. No phase/operator endpoint is inferred from scalar specialization.", "invoice_fingerprint": "34028fe3123338a14413364e91dc383e3207a60f3d703542bbf8601b8ea9a453", "invoice_fingerprint_scope": "Fresh own complete selected-call/physical owner/window/nonlocal/stock invoice, no prior invoice. Source-equivalent numeric parent provenance is disclosed.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "13414839829209/8000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "canonical_catalogue_absent_for": [ "extra", "gauge44" ], "operator_phase_proved": false, "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr1297-dispatched-finite-controller-early-upper.json", "scope": "Conditional sufficient eventual upper for each positive XOR tariff in the same XAG/unlimited optimized-GMP model, with explicit own full physical/phase/native interface premises.", "exact_individual_crossing": false }, "record_certificate_file": "pr1297-dispatched-finite-controller-record-upper.json", "record_certificate_sha256": "53fdbd065d94df2c2943b6d7ca51ef823a2632274ad4aa62f38d4fb5730c968e", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. 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No equal-kappa inference or cutoff transfer.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1601, "source_commit": "6986056504a372b8a2dd74c66000da108a549be6", "certificate_file": "pr1601-gaussian-only-finite-early-upper.json", "certificate_sha256": "1782bf165db958172e4f0d3a531b2464ac4168f63415ef3352013ab6485b2fb9", "peer_review_file": "pr1601-gaussian-only-finite-peer-review.json", "peer_review_sha256": "db5d7fc53f17135a7ed7002d42a7649116359964dff814900006d03280d5ae19", "source_peer_review_file": "pr1601-gaussian-only-finite-source-peer-review.json", "source_peer_review_sha256": "9055a9ec5dd46ac408a73f57d7df9b437da2f54ab416da79fdca16b47f65f74b", "proof_file": "gaussian-only-selected-provider-upper.md", "family_kind": "rank73-own-selected-direct-Gaussian-no-BIT", "native_certificate_file": "pr1601-gaussian-only-finite-native.json", "native_certificate_sha256": "3918e31276020bb93c0bdbbc47beca9cd05f91f38baad3d210fe5d852a8e1f77", "program_fingerprint": "526008ef1f4926fa36d757e84f16afbf4253924ac76027a67dde3ca8a80519f3", "program_fingerprint_scope": "Actual own-selected full/orientation hash-bound program; optional canonical catalogue absence is explicit. 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Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "gaussian_only_selected_provider_bounds.py" ], "reproduction_commands": [ [ "gaussian_only_admitted_replay.py" ], [ "gaussian_only_selected_provider_bounds.py" ] ], "broader_discovery_reproduction": [ "selected_provider_dispatch.py", "--execute" ], "broader_discovery_scope": "Optional144-entry/38-numeric-input discovery replay requires additional unpriced source artifacts; the admitted scoped replay needs only these fifteen own source sets.", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1625, "source_commit": "c7cac07823caabefb2439a9fc5c222639b487cbd", "certificate_file": "pr1625-pivot566-kernel-finite-early-upper.json", "certificate_sha256": "37917db0a78589ec5b73a46de7a8ead15d25c58f2f45bb14edebc9c21f3ed376", "peer_review_file": "pr1625-pivot566-kernel-finite-peer-review.json", "peer_review_sha256": "c3fc3df195f98d1aa0bab0995e2e5b57754c515c394e3ccb09a6fe261b364c0b", "source_peer_review_file": "pr1625-pivot566-kernel-finite-source-peer-review.json", "source_peer_review_sha256": "3b4ca5dac2d930c104972c700bd700d5969b0992bbabd936ef563bc6f20e343f", "proof_file": "selected-provider-v11-whole-upper.md", "family_kind": "rank73-exact-own-selected-pivot566kernel-early-Gaussian-no-BIT", "native_certificate_file": "pr1625-pivot566-kernel-finite-native.json", "native_certificate_sha256": "e2378b72a7cbc46793e6ef3fc50a3facf3ddff0115907bb42082806815599f79", "program_fingerprint": "7f45160c7474b19908b1804338b3916ec5f05ea51c93c05bd720647261acbe4d", "program_fingerprint_scope": "Actual complete selected programme/canonical byteobjects and both orientation commitments are exact. Full operator-valued required-boundary and absolute-phase contract remains explicit.", "invoice_fingerprint": "a8939d7127dbcc257d35a94b4bcfbf1e65ca994428dfe80574e5bff2b991bdb9", "invoice_fingerprint_scope": "Fresh complete own PLAN/OWNERS/calls/windows/charts/profile and no-prior full invoice, with disclosed new numeric parent provenance.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "1676896669021299/1000000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_quantified": true, "record_tail_scope": "Own original record exponent is separately quantified by this new direct Gaussian circuit.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr1625-pivot566-kernel-finite-early-upper.json", "scope": "Conditional sufficient eventual bound for the explicitly weaker early exponent1/5000, all positive XOR tariffs, same repaired unlimited optimized-GMP reference; retained native/frame/phase/all-size/analytic interfaces.", "exact_individual_crossing": false }, "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. 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Source-equivalent numeric parent provenance is disclosed.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "83842761453566094310322838613729630975622436975523763140168259552557832760600482475789234582069227149646377190519710903155084826441014256114676959358785932254564306415247343968165291277223407451719907616357667505695722536458932689349901836826724303468796430964746760140669873971381414520570792032059913582652631304839020072875394198229006615603806542742261584224261783534908521340102134811580084913544911088424771284404446526522819813946082601173024941541423681517459/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "canonical_catalogue_absent_for": [ "extra", "gauge44" ], "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_scope": "New direct Gaussian realization of the same selected source core; literal historical dual-supplier implementation is not claimed.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr1629-gaussian-only-finite-early-upper.json", "scope": "Conditional sufficient eventual upper for each positive XOR tariff in the same XAG/unlimited optimized-GMP model, with explicit own full physical/phase/native interface premises.", "exact_individual_crossing": false }, "record_certificate_file": "pr1629-gaussian-only-finite-record-upper.json", "record_certificate_sha256": "41657b3154b1b43f2bf2b6c9b257c5a5c6b1203fcc20b67dec06c82be19089a1", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. 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Full operator-valued required-boundary and absolute-phase contract remains explicit.", "invoice_fingerprint": "a8939d7127dbcc257d35a94b4bcfbf1e65ca994428dfe80574e5bff2b991bdb9", "invoice_fingerprint_scope": "Fresh complete own PLAN/OWNERS/calls/windows/charts/profile and no-prior full invoice, with disclosed new numeric parent provenance.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "33537933380425986155014219945359253432229800326783192213169281110298673603459706163329665915797520678218701299211456271548826432677658295931657193791562920984105784745217696422385398714479277544968453414772033493372169367078156499518480327645874504365738204887153552163687338864241214294743928488251436018263025236927183355949981660265363464492686936318041530634356948094604590286323620537151/20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_quantified": true, "record_tail_scope": "Own original record exponent is separately quantified by this new direct Gaussian circuit.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr1644-selected-p566-finite-early-upper.json", "scope": "Conditional sufficient eventual bound for the explicitly weaker early exponent1/5000, all positive XOR tariffs, same repaired unlimited optimized-GMP reference; retained native/frame/phase/all-size/analytic interfaces.", "exact_individual_crossing": false }, "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. 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Raw source words and unchanged own1644 source archive reconstruct exactly those canonical/program/orientation commitments; no equal-kappa/profile inference or cutoff transfer.", "record_certificate_file": "pr1644-selected-p566-finite-record-upper.json", "record_certificate_sha256": "3441eb65dcf89ba719c106ab465e36aa181047c65ad435f963c7da450a1a422d", "record_P": "230584301497830147503423480", "record_tail_input_bits": "2^(2^230584301497830147503423480)", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1661, "source_commit": "f852af5e178ce035cd46181a29d9330bcbcaa206", "certificate_file": "pr1661-selected-p566-finite-early-upper.json", "certificate_sha256": "341baa6f084cb25bff1c9d064d6a119c13578bfda2c7c56956bfaa40b219f275", "peer_review_file": "pr1661-selected-p566-finite-peer-review.json", "peer_review_sha256": "9b35317e28f5ee7a72dd0dfe7ba42a84e27e0d1dfd3b804909e656edb2485937", "source_peer_review_file": "pr1661-selected-p566-finite-source-peer-review.json", "source_peer_review_sha256": "5077f74192f7e7795e96050a3761e86a90a47674d9ee10e327ebc979c464e266", "proof_file": "selected-provider-v7-whole-upper.md", "family_kind": "rank73-exact-own-selected-p566-early-Gaussian-no-BIT", "native_certificate_file": "pr1661-selected-p566-finite-native.json", "native_certificate_sha256": "35c1734bd8bdfd17f81a9c2ec51fb707b6e618915d6cefcfa04ade9de6652b31", "program_fingerprint": "8a8f35bc4d8d4837215538a794a405ae556bfbe586e9aa3d61606f219919555f", "program_fingerprint_scope": "Actual full selected programme, canonical and both orientation commitments are checked. 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Raw source words and unchanged own1672 source archive reconstruct exactly those canonical/program/orientation commitments; no equal-kappa/profile inference or cutoff transfer.", "original_record_tail_unquantified": true, "original_record_kappa_is_provenance_only": true, "failed_inherited_tax_endpoint_preserved": true, "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 1875, "source_commit": "bb40dfc8e155d0b4daad1d910ba3ee751669b52c", "certificate_file": "pr1875-selected-k554-finite-early-upper.json", "certificate_sha256": "83495c8f9dd50eb9dabf15dd5923c2b1b69f364535cc95536d3f9c810d7f2ab1", "peer_review_file": "pr1875-selected-k554-finite-peer-review.json", "peer_review_sha256": "42658e6f34d4a39c632f219dc24a4214448c2ad124b90002f5b9109e7eae00f6", "source_peer_review_file": "pr1875-selected-k554-finite-source-peer-review.json", "source_peer_review_sha256": "afc9505db63ff53f0ea055d7dd3d5b34b6b68308669a609fabeb736d6a0a31ad", "proof_file": "selected-provider-v6-whole-upper.md", "family_kind": "rank73-exact-own-selected-k554-early-Gaussian-no-BIT", "native_certificate_file": "pr1875-selected-k554-finite-native.json", "native_certificate_sha256": "ee1650be3649199fcf3340c5d686b0ff0c58e9a0e26c726f4860d50607293639", "program_fingerprint": "26d1a663f0c4fc1245f18afcc43e1d78430a3a4e4445e0a050a83e62c032d3d2", "program_fingerprint_scope": "Actual full selected programme, canonical and both orientation commitments are checked. Full operator-valued required-boundary and absolute-phase contract remains explicit.", "invoice_fingerprint": "741942fd0d1f8501111a4d2f52a81a83eaebd2ba0c48df319e248f186d62f478", "invoice_fingerprint_scope": "Fresh complete own PLAN/OWNERS/calls/windows/charts/profile and no-prior full invoice, with disclosed new numeric parent provenance.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "8398774780627722606678354969603512884991557192512901477301637600814322741301628194131528280664223161372256584542931104860352240600827060713856503183464783578674812636953114638574227090497768781685562377794069883920702765193372789409782809399003446270856098837437418473378465284913944613786596277824999999998998320245043374455478664329006079297/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_quantified": false, "record_tail_scope": "Own historical record kappa is provenance only. This certificate proves only the explicitly weaker early exponent1/5000; its inherited finite-envelope tax is NOT removed and no same-XAG record tail is quantified.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr1875-selected-k554-finite-early-upper.json", "scope": "Conditional sufficient eventual bound for the explicitly weaker early exponent1/5000, all positive XOR tariffs, same repaired unlimited optimized-GMP reference; retained native/frame/phase/all-size/analytic interfaces.", "exact_individual_crossing": false }, "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "recover_pr1672_selected_native.py" ], [ "selected_provider_dispatch_v6.py", "--execute" ], [ "selected_provider_v6_whole_bounds.py" ] ], "offline_verification_commands": [ [ "selected_provider_v6_whole_bounds.py" ] ], "offline_verification_scope": "Fast complete numerical envelope replay from bound source censuses. The distinct807-check actual source reconstruction is available as the first reproduction job and authenticated by its separate frozen receipt.", "source_discovery_scope": "Each own author-head MANIFEST and actual verifier selects its exact kernel SPEC. Raw source words and unchanged own1672 source archive reconstruct exactly those canonical/program/orientation commitments; no equal-kappa/profile inference or cutoff transfer.", "original_record_tail_unquantified": true, "original_record_kappa_is_provenance_only": true, "failed_inherited_tax_endpoint_preserved": true, "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 2077, "source_commit": "407712103b605a662a89a56f9c42b93dca69126b", "certificate_file": "pr2077-vacancy-chain-finite-early-upper.json", "certificate_sha256": "b1032cf07278a9bc5ac7da21d14e394c81971b96dc2375a44f7c9538164f41ef", "peer_review_file": "pr2077-vacancy-chain-finite-peer-review.json", "peer_review_sha256": "173b19bbcf960c01ad15744a70aa3940e10f0a6400d3d18ada54eb0af2ad0cec", "source_peer_review_file": "pr2077-vacancy-chain-finite-source-peer-review.json", "source_peer_review_sha256": "a5ea2f5adce1fea767bb431cffd50d4a31934001aa3ea70c3dbc963fa5fe2d01", "proof_file": "selected-provider-v18-whole-upper.md", "family_kind": "own-selected-vacancy-chain-direct-Gaussian", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968" }, "lower": null, "record_certificate_file": "pr2077-vacancy-chain-finite-record-upper.json", "record_certificate_sha256": "9ffa4d80de66e93410f9878ef5dc064092d255019d3ae9e7aa3736cd41dc240d", "record_P": "230584301497830147503423480", "effective_kappa": "1/5000", "kappa_record": "418166011373521/250000000000000000", "native_certificate_file": "pr2077-vacancy-chain-finite-native.json", "native_certificate_sha256": "b953423d764981d4262b6275147d37761c065ff9f9ed8bff5c3f4335036c9880", "native_coordinate_rank": 73, "record_tail_quantified": true, "source_equivalent_numeric_realization": true, "historical_parent_byte_identity_claimed": false, "original_global_verifier_full_PASS_claimed": false, "source_report_counter_not_declared": true, "source_report_counter_mismatch": false, "descriptive_entering_counter": { "source_declared_entering_helper_roles": null, "actual_nonzero_start_frame_roles": 27648, "width_below_9_roles": 34560, "source_declared_meter_style": "not_declared_in_own_expected", "source_declared_counter_matches_actual": null, "used_by_new_cost_stock_or_precision": false }, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "recover_pr2077_selected_data.py" ], [ "prepare_selected_provider_v18.py" ], [ "selected_provider_dispatch_v18.py", "--execute" ], [ "prepare_selected_provider_v18_whole_costs.py" ], [ "vacancy_chain_descriptive_counter_audit.py" ], [ "selected_provider_v18_whole_bounds.py" ] ], "source_selected_kappa_correction": true, "frozen_metadata_kappa": "836330098538459/500000000000000000", "actual_own_selected_kappa": "418166011373521/250000000000000000", "source_selected_kappa_correction_basis": "Own immutable MANIFEST/verify/build reconstruct all3complete data bytes; own SPEC and CANDIDATE.expected_updates select actual target, while CANDIDATE baseline is the preserved frozen parser quote.", "source_kappa_correction_primary_receipt": "pr2077-source-chronology/chronology.json", "source_revision_included_at_merge": "2026-10-16T13:49:47Z", "source_revision_merge_commit": "ee997d5300167b46619f769c47bea9178a958978", "source_revision_committed_at": "2026-10-14T20:06:46Z", "source_selected_kappa_correction_note": "The preserved frozen parser quote is the explicit own CANDIDATE baseline. The actual own MANIFEST/verify/build/CANDIDATE select a distinct four-placement target, reconstructed as full own data bytes and authenticated at its actual16th-parent merge. Both values remain visible; this source-corrected cost point is not a new accepted-record-truth determination.", "new_accepted_exponent_record_claimed": false, "source_caveats": [ "The own actual selected kappa differs from its frozen baseline quote. Full raw source and actual merge chronology are peer-bound; original quote is preserved.", "Historical BIT contribution and original full global/native-phase verifier are not executed or priced by this new Gaussian realization." ], "source_kappa_correction_primary_sha256": "4b1e5f361ccc8b9c27bf90b63e11ba3bed63bef54e22f9bc4af0a68d6385dce8", "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null, "kappa_fraction": "836330098538459/500000000000000000", "kappa_decimal": "0.001672660197076918", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement." } }, { "pr": 2169, "source_commit": "4452c98ce93b83e696fd285eeb024f6669c145c0", "certificate_file": "pr2169-gaussian-only-finite-early-upper.json", "certificate_sha256": "2b33f6914f261a7ba5b5081cb26b81e996a969e9217e01c6657954279c13e848", "peer_review_file": "pr2169-gaussian-only-finite-peer-review.json", "peer_review_sha256": "62e4d6ace9af538c39089bd3c0358d0f034827319d148a230fbcca08dcd30a0c", "source_peer_review_file": "pr2169-gaussian-only-finite-source-peer-review.json", "source_peer_review_sha256": "61234edeff61d2b87683890bc872758daeff23589d75f13d2ae4b8bea5f89a09", "proof_file": "gaussian-only-selected-provider-upper.md", "family_kind": "rank73-own-selected-direct-Gaussian-no-BIT", "native_certificate_file": "pr2169-gaussian-only-finite-native.json", "native_certificate_sha256": "4c7fe5a085dbda76b65534eb77cd8582ff8ed10d40ba4149ddb71f7e102b0734", "program_fingerprint": "abe237c5841100d67813a6ee3b0cb91cb5f7db6ddba836b9f4a52cc04289b5d5", "program_fingerprint_scope": "Actual own-selected full/orientation hash-bound program; optional canonical catalogue absence is explicit. No phase/operator endpoint is inferred from scalar specialization.", "invoice_fingerprint": "73fb80fa0f09cb6e1bb08e1abe825c7ec7212261c9dc6c519eec6d8d6691219a", "invoice_fingerprint_scope": "Fresh own complete selected-call/physical owner/window/nonlocal/stock invoice, no prior invoice. Source-equivalent numeric parent provenance is disclosed.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "334722841145139/200000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "canonical_catalogue_absent_for": [], "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_scope": "New direct Gaussian realization of the same selected source core; literal historical dual-supplier implementation is not claimed.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr2169-gaussian-only-finite-early-upper.json", "scope": "Conditional sufficient eventual upper for each positive XOR tariff in the same XAG/unlimited optimized-GMP model, with explicit own full physical/phase/native interface premises.", "exact_individual_crossing": false }, "record_certificate_file": "pr2169-gaussian-only-finite-record-upper.json", "record_certificate_sha256": "313d5d4dbac1d1d233c7a862d010d33b5c1e6f5d016bde25e573bfdfa3b3addb", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. 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No phase/operator endpoint is inferred from scalar specialization.", "invoice_fingerprint": "73fb80fa0f09cb6e1bb08e1abe825c7ec7212261c9dc6c519eec6d8d6691219a", "invoice_fingerprint_scope": "Fresh own complete selected-call/physical owner/window/nonlocal/stock invoice, no prior invoice. Source-equivalent numeric parent provenance is disclosed.", "params_fingerprint": "056b5ce22092032c39b6d97461ac84b2151e4198dbe8e2869aa48e25166194bd", "effective_kappa": "1/5000", "kappa_record": "209202311361877/125000000000000000", "native_coordinate_rank": 73, "uniform_rank_H": null, "canonical_catalogue_absent_for": [], "operator_phase_proved": false, "ordinary_BIT_supplier_consumed": false, "invented_BIT_saving": null, "record_tail_scope": "New direct Gaussian realization of the same selected source core; literal historical dual-supplier implementation is not claimed.", "upper": { "input_bits": "2^(2^18014398509484968)", "exact_log2log2_integer": "18014398509484968", "source": "data/operation-audit/pr3308-gaussian-only-finite-early-upper.json", "scope": "Conditional sufficient eventual upper for each positive XOR tariff in the same XAG/unlimited optimized-GMP model, with explicit own full physical/phase/native interface premises.", "exact_individual_crossing": false }, "record_certificate_file": "pr3308-gaussian-only-finite-record-upper.json", "record_certificate_sha256": "012dc83fe30e801524a0f172b29cfb41764f213ac913df93eb40b7eed7383b4f", "record_P": "230584301497830147503423480", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^230584301497830147503423480)", "lower": null, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. 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identical optimized GMP when inactive.", "statistic": "Earliest possible strict win in the declared literal enhancement family", "exact_individual_crossing": false, "all_PR_implementations": false, "source": "data/operation-audit/pr4414-native-tensor-literal-lower.json" }, "effective_kappa": "1/500", "kappa_record": "267987/100000000", "uniform_rank_H": "473129651134046950001", "tensor_power": 150000, "scope": [ "Own exact all-fresh native and chronological tensor product with arbitrary-input required-boundary/all-column/absolute-phase/Clifford identities and clean-owned/full-spectator semantics; own raw native inventory/main phase replay is bound, full all-column base operator closure remains explicit.", "Own new uniform-rank theorem and complete chronological integer compiler with ready barriers, separate role arrays and actual child/complement endpoints.", "Concrete normalized Gaussian/finite-LDU/narrow-gap/cyclic-border/fine-prime/exact-recovery interfaces and fixed repaired reference correctness/finite-kernel halting." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "p3_p6_tensor_source_bindings.py" ], [ "p3_p6_tensor_costs.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 4433, "source_commit": "b84060c9cba91b1e76f84617a877d259621eb015", "certificate_file": "pr4433-literal-boundary-lower.json", "certificate_sha256": "2cc70d4b2f72eee5c498180070960601bfb0347ac57c12c4f4a62cf4b4fb9618", "peer_review_file": "pr4433-literal-boundary-peer-review.json", "peer_review_sha256": "2b0f6bfcc0599dbe3c1685a71009cc077b8dd5c3b7b24a55877e09fa98866cfa", "proof_file": "pr4433-literal-boundary-lower.md", "family_kind": "own-p7-boundary-literal", "kappa_record": "268647/100000000", "uniform_rank_H": "349300000000", "tensor_power": 150, "upper": null, "lower_certificate_file": "pr4433-literal-boundary-lower.json", "lower_certificate_sha256": "2cc70d4b2f72eee5c498180070960601bfb0347ac57c12c4f4a62cf4b4fb9618", "lower": { "input_bits": "2^(2^349299999997-2^69)", "plot_triple_log": { "log2_of_integer": "349299999997", "negligible_negative_correction": true }, "scope": "Own complete unreduced p7 boundary/native word when active, width at least two, strict winning uniform supplier at its stated H; identical optimized GMP when inactive.", "statistic": "Earliest input width at which a correct member of this literal enhancement family strictly beats the reference", "source": "data/operation-audit/pr4433-literal-boundary-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "scope": "Own complete unreduced p7 boundary/native word when active, width at least two, strict winning uniform supplier at its stated H; identical optimized GMP when inactive. This source has no newly derived sufficient upper. The exact first crossing remains unknown.", "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "pr4433_literal_boundary_lower.py" ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 4446, "source_commit": "e2bde8f5b9bfa2e8d51f959656d84ebcc2af81b7", "certificate_file": "pr4446-hybrid-boundary-lower.json", "certificate_sha256": "cd8e0b617aa31aac7992baeeeed058467f8db27e8cbddb2b8363d0640e587c22", "peer_review_file": "pr4446-hybrid-boundary-peer-review.json", "peer_review_sha256": "a8c47b342037142df78f1dc27104dd4fa9dca083132c88431d9314ace15e078e", "proof_file": "pr4446-hybrid-boundary-lower.md", "family_kind": "own-hybrid-p17-complete-boundary-lower", "upper": null, "lower_certificate_file": "pr4446-hybrid-boundary-lower.json", "lower_certificate_sha256": "cd8e0b617aa31aac7992baeeeed058467f8db27e8cbddb2b8363d0640e587c22", "lower": { "input_bits": "2^(2^15026650096742881962198-2^69)", "plot_triple_log": { "log2_of_integer": "15026650096742881962198", "negligible_negative_correction": true }, "scope": "Own selected hybrid supplier with complete unreduced boundary/native word when active, width at least two, whole-field/spectator rank N contract; identical optimized GMP when inactive.", "statistic": "Earliest possible strict win in the specified literal enhancement family", "source": "data/operation-audit/pr4446-hybrid-boundary-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "effective_kappa": "3001053/1000000000", "kappa_record": "3001053/1000000000", "uniform_rank_H": "15026650096742881962201", "tensor_power": 17160, "reproduction_command": [ "pr4446_hybrid_boundary_lower.py" ], "scope": [ "Own full Laurent/direct/native arbitrary-input identity, required physical entry/output frames, absolute phase and complete all-column whole-job copied/owned/spectator semantics.", "Own strictifying physical native tensor/compiler realization, literal boundary retention, exact source interval enclosures and positive winning uniform supplier at the selected H.", "Fixed repaired optimized-GMP correctness/finite-kernel halting and prescribed unreduced XAG lowering." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 4453, "source_commit": "de6869e2e4d9c6f630bac5de4a919d99a2cb884b", "certificate_file": "pr4453-separated-early-upper.json", "certificate_sha256": "e92e85599deb4a181b48d1af03845326cd60e5d96d69fd80e4f9ed67a91f5c5b", "peer_review_file": "middle-p17-separated-peer-review.json", "peer_review_sha256": "c8d025ed6cf67b0b4b8342887aa74ae9deffa3ae459953cbeaca1ff0a9effab0", "proof_file": "middle-p17-separated-bounds.md", "family_kind": "separated-product-p17", "native_certificate_file": "pr4453-separated-native-parameters.json", "native_certificate_sha256": "32710d53e92b75c7b8af435f496c4a24fd0e4fdf339f22721a9e4ede9783cbec", "program_fingerprint": "cc045a98fdd023c59ac40835c46ef78d71a83cd76307078048d315a817d28783", "program_fingerprint_scope": "Own-head selected raw payload and primary source bindings; the huge compiled full supplier is not materialized.", "invoice_fingerprint": "3020ca32669d6a93b852f5499d9c9d9ff7e12a0c1f8e410d0f244120b572c1a6", "invoice_fingerprint_scope": "Own compiler/source-envelope and freshly derived circuit interfaces, conditional on the retained physical realization; not an emitted full instruction list.", "params_fingerprint": "772203b4a772304da1284a970b783237ab43a68ee9961f2fccf7fdf8673e2d96", "effective_kappa": "1/500", "kappa_record": "7503/2500000", "uniform_rank_H": "2299850000000", "tensor_power": 675, "upper": { "input_bits": "2^(2^230055792290424752352)", "exact_log2log2_integer": "230055792290424752352", "source": "data/operation-audit/pr4453-separated-early-upper.json", "scope": "Conditional sufficient eventual upper for an own source-bound unreduced literal enhancement family member; all positive XOR/AND tariffs.", "exact_individual_crossing": false }, "record_certificate_file": "pr4453-separated-record-upper.json", "record_certificate_sha256": "b9a2a59bc8490012d008af2b578d82708eb0cfda150664b30efe7c0667f6adb8", "record_P": "1126926507495899104083251142352", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^1126926507495899104083251142352)", "reproduction_command": [ "middle_p17_separated_bounds.py" ], "lower_certificate_file": "pr4453-separated-literal-lower.json", "lower_certificate_sha256": "dcf169939a9afe2cc050eab1a458753d57de74d512ae96c55839d4e1fc3804c3", "lower": { "input_bits": "2^(2^2299849999997-2^69)", "plot_triple_log": { "log2_of_integer": "2299849999997", "negligible_negative_correction": true }, "scope": "Own complete unreduced p17 boundary/native word when active, width at least two, strict winning own uniform supplier; identical optimized GMP when inactive.", "statistic": "Earliest input width at which a correct member of this literal enhancement family strictly beats the reference", "source": "data/operation-audit/pr4453-separated-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "scope": [ "Own p17 native arbitrary-input/absolute-phase all-column endpoint and chronological owned return contracts", "Source separated-product/net-tax compiler realizes its strict winning uniform supplier at the stated own H with completed base cases paid", "Complete role fields and spectators, exact per-role Clifford endpoints, barriers and restored owned banks on fixed parent selected axes", "Own source raw nonrecursive allowance below1e9 and expanded whole-job normal-form/adapter interfaces", "Parameterized fine-prime/Gaussian/finite-section/boundary/recovery analytic branch and unchanged fixed XAG/repaired optimized-GMP semantics" ], "actual_first_crossover_known": false, "all_implementations_covered": false, "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 4480, "source_commit": "4cf054a50c5718616594ec4ca2c9114278120a8b", "certificate_file": "pr4480-separated-early-upper.json", "certificate_sha256": "c2efa88417b7dbc3783dfd507c501839c9b9ccde3a1b9e3da9aeb41d499922c5", "peer_review_file": "middle-p17-separated-peer-review.json", "peer_review_sha256": "c8d025ed6cf67b0b4b8342887aa74ae9deffa3ae459953cbeaca1ff0a9effab0", "proof_file": "middle-p17-separated-bounds.md", "family_kind": "separated-product-p17", "native_certificate_file": "pr4480-separated-native-parameters.json", "native_certificate_sha256": "024ddca098a7095a2b217ac1b422e31a2547704d8013f506fa3b65496d61c934", "program_fingerprint": "b7e50eabfa723322515844462c2d09f940c624d8f3242362ba992dd39720f03c", "program_fingerprint_scope": "Own-head selected raw payload and primary source bindings; the huge compiled full supplier is not materialized.", "invoice_fingerprint": "813c57c0e2368652f78b333b59b2d1ac6b90d6c35c636fcea5a3c92f0f2dda68", "invoice_fingerprint_scope": "Own compiler/source-envelope and freshly derived circuit interfaces, conditional on the retained physical realization; not an emitted full instruction list.", "params_fingerprint": "6d2500036c5549d3a9796da1920a2d5d8999af215b3128d7ccdce33b8515f7e1", "effective_kappa": "1/500", "kappa_record": "7503/2500000", "uniform_rank_H": "125790000000", "tensor_power": 260, "upper": { "input_bits": "2^(2^12584566141734985381)", "exact_log2log2_integer": "12584566141734985381", "source": "data/operation-audit/pr4480-separated-early-upper.json", "scope": "Conditional sufficient eventual upper for an own source-bound unreduced literal enhancement family member; all positive XOR/AND tariffs.", "exact_individual_crossing": false }, "record_certificate_file": "pr4480-separated-record-upper.json", "record_certificate_sha256": "18cc5f6034b34ed7bf947f1db9cff32b50044f426f6c5d76035026bce68d919c", "record_P": "22189356388448412157751085381", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^22189356388448412157751085381)", "reproduction_command": [ "middle_p17_separated_bounds.py" ], "lower_certificate_file": "pr4480-separated-literal-lower.json", "lower_certificate_sha256": "d2bb79a62b960f686b9efc93a35bf9b45abe8f38a15aef6d06a96a0f1e9a7ad3", "lower": { "input_bits": "2^(2^125789999997-2^69)", "plot_triple_log": { "log2_of_integer": "125789999997", "negligible_negative_correction": true }, "scope": "Own complete unreduced p17 boundary/native word when active, width at least two, strict winning own uniform supplier; identical optimized GMP when inactive.", "statistic": "Earliest input width at which a correct member of this literal enhancement family strictly beats the reference", "source": "data/operation-audit/pr4480-separated-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "scope": [ "Own p17 native arbitrary-input/absolute-phase all-column endpoint and chronological owned return contracts", "Source separated-product/net-tax compiler realizes its strict winning uniform supplier at the stated own H with completed base cases paid", "Complete role fields and spectators, exact per-role Clifford endpoints, barriers and restored owned banks on fixed parent selected axes", "Own source raw nonrecursive allowance below1e9 and expanded whole-job normal-form/adapter interfaces", "Parameterized fine-prime/Gaussian/finite-section/boundary/recovery analytic branch and unchanged fixed XAG/repaired optimized-GMP semantics" ], "actual_first_crossover_known": false, "all_implementations_covered": false, "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 4563, "source_commit": "7db8ee8d97d456f120cb534d8cf356a1b8b02ca8", "certificate_file": "pr4563-critical-early-upper.json", "certificate_sha256": "02b57759c5e2493f7a9318fbb1ac77317e3e2ae7046deaeef7e046f25d72b884", "peer_review_file": "uniform-critical-p16-batch-peer-review.json", "peer_review_sha256": "795c09bc8a29d10b70bda5915607efc566eef46112f3ee1439c3e0392ca0d01e", "proof_file": "uniform-critical-p16-batch.md", "family_kind": "critical-integer-p16", "native_certificate_file": "pr4563-critical-native-parameters.json", "native_certificate_sha256": "a9e2f1df0d7c93ce90228c59d9c4a38a881443e59aee49da4cee8cd85cdb9a84", "program_fingerprint": "68ee0a81a4eafecc743a494549160af89a02fe853742d24099509701a3c0887c", "program_fingerprint_scope": "Own-head selected raw payload and primary source bindings; 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Both early and original-record tails are priced. Native finite engine passed; all-width compiler and analytic contracts remain premises.", "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "helper621_separated_bounds.py" ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 4630, "source_commit": "f4b974db1f651250a252721cf127d0491a802699", "certificate_file": "pr4630-derived-xag-early-upper.json", "certificate_sha256": "3a6831cac439119218cb4a2055e732836070f6db5aed407a690e6e08e9eebc7f", "peer_review_file": "pr4630-derived-xag-cost-peer-review.json", "peer_review_sha256": "d28ad858a6ffd6ede0a9fc612efd4076ae0faa908271c483da84d5e53d30af01", "source_peer_review_file": "pr4630-derived-xag-source-peer-review.json", "source_peer_review_sha256": "9c359a101e57bf1f18cdb4bdd625f1e49386a15043d6fc413bf56d0827098fa9", "proof_file": "native-provider-derived-xag-costs.md", "family_kind": "own-native-provider-new-derived-xag-bit-realization", "upper": { "input_bits": "2^(2^100041795189802580144)", "exact_log2log2_integer": "100041795189802580144" }, "record_certificate_file": "pr4630-derived-xag-record-upper.json", "record_certificate_sha256": "f02dbb16c0482471b7590461c27c1a211dbbd665f8d5bf63f72bc432db2f4cad", "record_P": "4000000000017716804200612179201050144", "lower_certificate_file": "pr4630-derived-xag-literal-lower.json", "lower_certificate_sha256": "ac102aea7f0f679c327978b4e23ccdc5a0c316bd061d5b5be7f441352fb9448b", "lower": { "input_bits": "2^(2^999999999997-2^69)", "plot_triple_log": { "log2_of_integer": "999999999997", "negligible_negative_correction": true }, "scope": "Derived bit-circuit enhancement family retaining own complete unreduced raw controller/native boundary on full fields/spectators, width at least two when active; identical optimizedGMP when inactive. Not all WordRAM or bit implementations.", "statistic": "Earliest possible strict win in this own-source literal bit enhancement family", "exact_individual_crossing": false, "all_PR_implementations": false, "source": "data/operation-audit/pr4630-derived-xag-literal-lower.json" }, "effective_kappa": "1/500", "kappa_record": "6040331/2000000000", "uniform_rank_H": "1000000000000", "tensor_power": 1, "historical_machine_model": "Word RAM", "new_source_core_XAG_realization": true, "literal_Word_RAM_cost_transferred": false, "historical_bit_model_record_claimed": false, "scope": [ "NEW direct Gaussian/Fermat XAG bit realization of the own explicitly selected algebraic native core, not original Word RAM lookup/MUL/DIV instruction cost translation.", "Own actual selected arbitrary-input required Gaussian endpoint/absolute-phase/all-fiber/owned/spectator and bounded finite-Clifford monomial identities; same raw component recovered by exact source hashes, not a fresh universal native proof.", "Own chronological source/complement/exit complete integer compiler, ready barriers and nested widths with strict rank descent, and own freshly replayed critical majorant.", "Concrete normalized Gaussian/finite-LDU/narrow-gap/cyclic-border/fine-prime/exact-recovery and fixed repaired optimizedGMP correctness/finite-kernel halting." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "native_provider_xag_source_bindings.py" ], [ "native_provider_derived_xag_costs.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 4635, "source_commit": "898b0c8e2ca23897c312230988515c2553154f30", "certificate_file": "pr4635-derived-xag-early-upper.json", "certificate_sha256": "cf3c2d16b5642d0ba97695967434b9fd0dd24897707666e731c2f9cf6cd34444", "peer_review_file": "pr4635-derived-xag-cost-peer-review.json", "peer_review_sha256": "b131fd8bc4c862b742448ef040385bd89306bdbee24a6276408ac59d6bcfc25e", "source_peer_review_file": "pr4635-derived-xag-source-peer-review.json", "source_peer_review_sha256": "65b7f3fb5a84da8157b45db2683107ba791f0816865089ef536719bb17a020ae", "proof_file": "native-provider-derived-xag-costs.md", "family_kind": "own-native-provider-new-derived-xag-bit-realization", "upper": { "input_bits": "2^(2^100041795189802580144)", "exact_log2log2_integer": "100041795189802580144" }, "record_certificate_file": "pr4635-derived-xag-record-upper.json", "record_certificate_sha256": "f3695a5bb963d93c35da48be07ef756adc0e13f08193ee55b43af393c0746d91", "record_P": "4000000000017716804200612179201050144", "lower_certificate_file": "pr4635-derived-xag-literal-lower.json", "lower_certificate_sha256": "227ca21285b60343c4932cd83c9afb422922c2e7eb60cfaabcdbafcf52ee6c92", "lower": { "input_bits": "2^(2^999999999997-2^69)", "plot_triple_log": { "log2_of_integer": "999999999997", "negligible_negative_correction": true }, "scope": "Derived bit-circuit enhancement family retaining own complete unreduced raw controller/native boundary on full fields/spectators, width at least two when active; identical optimizedGMP when inactive. Not all WordRAM or bit implementations.", "statistic": "Earliest possible strict win in this own-source literal bit enhancement family", "exact_individual_crossing": false, "all_PR_implementations": false, "source": "data/operation-audit/pr4635-derived-xag-literal-lower.json" }, "effective_kappa": "1/500", "kappa_record": "15108877/5000000000", "uniform_rank_H": "1000000000000", "tensor_power": 1, "historical_machine_model": "Word RAM", "new_source_core_XAG_realization": true, "literal_Word_RAM_cost_transferred": false, "historical_bit_model_record_claimed": false, "scope": [ "NEW direct Gaussian/Fermat XAG bit realization of the own explicitly selected algebraic native core, not original Word RAM lookup/MUL/DIV instruction cost translation.", "Own actual selected arbitrary-input required Gaussian endpoint/absolute-phase/all-fiber/owned/spectator and bounded finite-Clifford monomial identities; same raw component recovered by exact source hashes, not a fresh universal native proof.", "Own chronological source/complement/exit complete integer compiler, ready barriers and nested widths with strict rank descent, and own freshly replayed critical majorant.", "Concrete normalized Gaussian/finite-LDU/narrow-gap/cyclic-border/fine-prime/exact-recovery and fixed repaired optimizedGMP correctness/finite-kernel halting." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "native_provider_xag_source_bindings.py" ], [ "native_provider_derived_xag_costs.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 4672, "source_commit": "9da43a7d1ec73f4e6000a201d9d76818a8d4548f", "certificate_file": "pr4672-hyperplane-literal-lower.json", "certificate_sha256": "19937b6ed6673a60f171629bc88a99e921107dd4cedb73ebf9f17a05e282a39f", "peer_review_file": "pr4672-hyperplane-literal-peer-review.json", "peer_review_sha256": "8f4f5b7207517ee1ae2bae11fc048e50a97ceaefc2a678eef7be7f4e9434a0b7", "proof_file": "pr4672-hyperplane-literal-lower.md", "family_kind": "own-hyperplane-retimed-literal-lower", "upper": null, "lower_certificate_file": "pr4672-hyperplane-literal-lower.json", "lower_certificate_sha256": "19937b6ed6673a60f171629bc88a99e921107dd4cedb73ebf9f17a05e282a39f", "lower": { "input_bits": "2^(2^31385199999997-2^69)", "plot_triple_log": { "log2_of_integer": "31385199999997", "negligible_negative_correction": true }, "scope": "Own selected complete unreduced hyperplane-retimed raw controller/native word, full field/spectator ranges when active, stored width at least two; identical optimized GMP when inactive.", "statistic": "Earliest possible strict win in the declared literal enhancement family", "source": "data/operation-audit/pr4672-hyperplane-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "effective_kappa": "151083/50000000", "kappa_record": "151083/50000000", "uniform_rank_H": "31385200000000", "tensor_power": 1024, "reproduction_command": [ "pr4672_hyperplane_literal_lower.py" ], "scope": [ "Own source gauge/relative-helper arbitrary-input all-column required-entry/output-frame and absolute-phase identities, complete copied/owned/spectator interface; original full native engine is authenticated but not rerun here.", "Own physical mixed tensor/completion/splitting/compiler strict supplier at the selected H, literal complete raw occurrences retained.", "Same prescribed unreduced dense ADD lowering and fixed repaired-reference correctness/finite-kernel halting contracts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 4707, "source_commit": "ccc1517daba8fa7d4a571ce72cace1789bac1cf4", "certificate_file": "pr4707-critical-early-upper.json", "certificate_sha256": "1d8ccc69c20f3a4a3105812c4817fc8c390b2a95f0d8bd3d4d1b9ab1f306ac2b", "peer_review_file": "late-critical-p16-peer-review.json", "peer_review_sha256": "2f1127ca2f0e6f3b77cb845a8d8335848058ba135a1c49eaad0adf953f07424e", "proof_file": "late-critical-p16-costs.md", "family_kind": "critical-integer-p16", "native_certificate_file": "pr4707-critical-native-parameters.json", "native_certificate_sha256": "942291c1739c4880e51289a70958a6ccdf0ce0b822167e2f0e2d403f92699aa7", "program_fingerprint": "29f4a789d969345e04c8dfa91a1c160f97c00cd54f3e48b7495077061cda5f1f", "program_fingerprint_scope": "Own-head selected raw payload and primary source bindings; the huge compiled full supplier is not materialized.", "invoice_fingerprint": "71ae9644561e03e434c8e6d8eec9d0304720b95a2b105074e42a1f7023e1ff3d", "invoice_fingerprint_scope": "Own compiler/source-envelope and freshly derived circuit interfaces, conditional on the retained physical realization; not an emitted full instruction list.", "params_fingerprint": "c2ce4014760ea21e79ddc1fff823399643478a0217538eab74199e8608990f5b", "effective_kappa": "1/500", "kappa_record": "30201659769/10000000000000", "uniform_rank_H": "1000000000000000", "tensor_power": 1, "upper": { "input_bits": "2^(2^100040004792191118061679)", "exact_log2log2_integer": "100040004792191118061679", "source": "data/operation-audit/pr4707-critical-early-upper.json", "scope": "Conditional sufficient eventual upper for an own source-bound unreduced literal enhancement family member; all positive XOR/AND tariffs.", "exact_individual_crossing": false }, "record_certificate_file": "pr4707-critical-record-upper.json", "record_certificate_sha256": "2295af2d74d4be1c8ccfbd8cbbf11e0b78ea60cda9af0981184237f9271c8224", "record_P": "4000000000000017000716804726752000179201181679", "record_tail_quantified": true, "record_tail_input_bits": "2^(2^4000000000000017000716804726752000179201181679)", "reproduction_command": [ "late_critical_p16_costs.py" ], "lower_certificate_file": "pr4707-critical-literal-lower.json", "lower_certificate_sha256": "0a309f0e90ea7810e65098d12804cf4c813eecaf359852f610e91d17e1ec24d6", "lower": { "input_bits": "2^(2^999999999999997-2^69+2)", "plot_triple_log": { "log2_of_integer": "999999999999997", "negligible_negative_correction": true }, "scope": "Identical repaired optimized GMP when inactive; unreduced complete dense raw p16 scalar word when active, under own strict-winning supplier and all-column/spectator contracts.", "statistic": "Earliest input width at which some correct member of this literal enhancement family strictly beats the reference", "source": "data/operation-audit/pr4707-critical-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "scope": [ "Own source critical-root theorem/strict integer child descent and positive uniform supplier at this explicitly authenticated H", "Own source inherits arbitrary-input/all-column, owned/spectator and physical closure for its changed fixed word; the finite checker does not prove this bridge", "Own-head selected unchanged raw p16 native and exact absolute-phase endpoints; full native engine not replayed here", "Separate role fields and parent selected axes, completed child barriers, restored owned banks, exact per-role Clifford Gaussian-dyadic endpoints", "The source-parametric fine-prime/Gaussian/finite-section/boundary/whole-integer recovery analytic branch" ], "actual_first_crossover_known": false, "all_implementations_covered": false, "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 4713, "source_commit": "9bb3f3f72925e8825c8b4851dfdc8e92b72db949", "certificate_file": "pr4713-derived-xag-early-upper.json", "certificate_sha256": "f782955509fd16edf7150cd3245cb705688afe07fef544fb53e76e10c5473125", "peer_review_file": "pr4713-derived-xag-cost-peer-review.json", "peer_review_sha256": "41b1f88315e45b1d94526e1465711c35d847e065ba478453dc091bee1fb543f6", "source_peer_review_file": "pr4713-derived-xag-source-peer-review.json", "source_peer_review_sha256": "bc03ff0da6338136d5d4735107a9d0296c193f43f635d04b21e7345525189de3", "proof_file": "pr4713-derived-native-xag-costs.md", "family_kind": "own-native-provider-new-derived-xag-bit-realization", "upper": { "input_bits": "2^(2^3858472889500089802740160)", "exact_log2log2_integer": "3858472889500089802740160" }, "record_certificate_file": "pr4713-derived-xag-record-upper.json", "record_certificate_sha256": "a7d2a820c92ea927926d140b2ecc410f29b01c39f8baa817897e4d0692da6087", "record_P": "154277200000501405616804316381079201050160", "lower_certificate_file": "pr4713-derived-xag-literal-lower.json", "lower_certificate_sha256": "ff6ca77e43010c83e8893502136d53a86d7cb6b979f8172456d01ca6570f84bc", "lower": { "input_bits": "2^(2^38569299999999997-2^69)", "plot_triple_log": { "log2_of_integer": "38569299999999997", "negligible_negative_correction": true }, "scope": "Derived bit-circuit enhancement family retaining own complete unreduced raw controller/native boundary on full fields/spectators, width at least two when active; identical optimizedGMP when inactive. Not all WordRAM or bit implementations.", "statistic": "Earliest possible strict win in this own-source literal bit enhancement family", "exact_individual_crossing": false, "all_PR_implementations": false, "source": "data/operation-audit/pr4713-derived-xag-literal-lower.json" }, "effective_kappa": "1/500", "kappa_record": "15108879/5000000000", "uniform_rank_H": "38569300000000000", "tensor_power": 1, "historical_machine_model": "Division-free Word RAM", "new_source_core_XAG_realization": true, "literal_Word_RAM_cost_transferred": false, "historical_bit_model_record_claimed": false, "scope": [ "NEW direct Gaussian/Fermat XAG bit realization of own explicitly selected algebraic native core, not original division-free Word RAM lookup/MUL instruction cost translation.", "Own actual selected arbitrary-input required Gaussian endpoint/absolute-phase/all-fiber/owned/spectator and bounded finite-Clifford monomial identities; same raw component recovered by exact source hashes, not a fresh universal native proof.", "Own chronological source/complement/exit complete integer compiler, ready barriers and nested widths with strict rank descent, and own freshly replayed critical majorant.", "Concrete normalized Gaussian/finite-LDU/narrow-gap/cyclic-border/fine-prime/exact-recovery and fixed repaired optimizedGMP correctness/finite-kernel halting." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_commands": [ [ "pr4713_native_xag_source_bindings.py" ], [ "pr4713_derived_native_xag_costs.py" ] ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 5377, "source_commit": "c448d13c71908647f968b06cddb795ce7d288139", "certificate_file": "pr5377-changed-native-literal-lower.json", "certificate_sha256": "9f18575f1dbf5b1b3936721be5bed713feca6d5f073de7e63e31fc36b969cde9", "peer_review_file": "changed-native-p16-boundary-lowers-peer-review.json", "peer_review_sha256": "4551f6ec30d3b59f4e754c8b5cec2c88ff1693bb1aec11ede03e4699bf4299b3", "proof_file": "changed-native-p16-boundary-lowers.md", "family_kind": "own-changed-native-p16-literal-lower", "kappa_record": "60447/20000000", "uniform_rank_H": "31385200000000", "tensor_power": 1024, "upper": null, "lower_certificate_file": "pr5377-changed-native-literal-lower.json", "lower_certificate_sha256": "9f18575f1dbf5b1b3936721be5bed713feca6d5f073de7e63e31fc36b969cde9", "lower": { "input_bits": "2^(2^31385199999997-2^69)", "plot_triple_log": { "log2_of_integer": "31385199999997", "negligible_negative_correction": true }, "scope": "Own complete unreduced raw controller/native word, complete field and spectators when active, stored width at least two; identical repaired optimized GMP when inactive.", "statistic": "Earliest input width at which a correct member of the declared own-source literal enhancement family strictly beats the reference", "source": "data/operation-audit/pr5377-changed-native-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "scope": "Own complete unreduced raw controller/native word, complete field and spectators when active, stored width at least two; identical repaired optimized GMP when inactive. Own native engine receipts are authenticated but not freshly replayed here. No sufficient upper has been derived.", "program_fingerprint": "645b32ff67dfd49bbe8c2287d21f12a66a775d3c5e187db6f813e17e9f8fae35", "program_fingerprint_scope": "Four public-field scalar additions retained in the own selected backward local word, called by the complete raw controller.", "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "changed_native_p16_boundary_lowers.py" ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 5383, "source_commit": "4bd6efa51a495a7c7b7754915cf0244e7e60969e", "certificate_file": "pr5383-changed-native-literal-lower.json", "certificate_sha256": "38fe1bd4653d9561be468e43db7d9e44e3256a37560b9db0cbafd4a0626573a0", "peer_review_file": "changed-native-p16-boundary-lowers-peer-review.json", "peer_review_sha256": "4551f6ec30d3b59f4e754c8b5cec2c88ff1693bb1aec11ede03e4699bf4299b3", "proof_file": "changed-native-p16-boundary-lowers.md", "family_kind": "own-changed-native-p16-literal-lower", "kappa_record": "151333/50000000", "uniform_rank_H": "31385200000000", "tensor_power": 1024, "upper": null, "lower_certificate_file": "pr5383-changed-native-literal-lower.json", "lower_certificate_sha256": "38fe1bd4653d9561be468e43db7d9e44e3256a37560b9db0cbafd4a0626573a0", "lower": { "input_bits": "2^(2^31385199999997-2^69)", "plot_triple_log": { "log2_of_integer": "31385199999997", "negligible_negative_correction": true }, "scope": "Own complete unreduced raw controller/native word, complete field and spectators when active, stored width at least two; identical repaired optimized GMP when inactive.", "statistic": "Earliest input width at which a correct member of the declared own-source literal enhancement family strictly beats the reference", "source": "data/operation-audit/pr5383-changed-native-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "scope": "Own complete unreduced raw controller/native word, complete field and spectators when active, stored width at least two; identical repaired optimized GMP when inactive. Own native engine receipts are authenticated but not freshly replayed here. No sufficient upper has been derived.", "program_fingerprint": "2aee5e997df99726fc763e510d9cb69fbe4f86114dc8d2cd33ad26c6c462a21d", "program_fingerprint_scope": "Four public-field scalar additions retained in the own selected backward local word, called by the complete raw controller.", "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "changed_native_p16_boundary_lowers.py" ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 5384, "source_commit": "411648821f0208d60099be8ca42957ca3a1c4316", "certificate_file": "pr5384-reviewed-selected-literal-lower.json", "certificate_sha256": "d1fade8d1cd453ce4bb3367b25614351a2f53805d76ad191857013d087853d91", "peer_review_file": "pr5384-reviewed-selected-literal-peer-review.json", "peer_review_sha256": "37a4051ab7417736ed763e51043fedd39cfebd71dd144c17024f75ac9252e4fc", "proof_file": "reviewed-selected-native-lowers.md", "family_kind": "own-selected-validation-literal-lower", "upper": null, "lower_certificate_file": "pr5384-reviewed-selected-literal-lower.json", "lower_certificate_sha256": "d1fade8d1cd453ce4bb3367b25614351a2f53805d76ad191857013d087853d91", "lower": { "input_bits": "2^(2^31385199999997-2^69)", "plot_triple_log": { "log2_of_integer": "31385199999997", "negligible_negative_correction": true }, "scope": "Own selected complete unreduced raw controller/native word with full field/spectator ranges when active, stored width at least two; identical optimized GMP when inactive.", "statistic": "Earliest possible strict win in the specified own-source literal enhancement family", "source": "data/operation-audit/pr5384-reviewed-selected-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "effective_kappa": "60447/20000000", "kappa_record": "60447/20000000", "uniform_rank_H": "31385200000000", "tensor_power": 1024, "reproduction_command": [ "reviewed_selected_native_lowers.py" ], "scope": [ "Own source native arbitrary-input required entry/output frames, absolute phase, all-column whole-job/owned/spectator and actual changed caller semantics. Stored validation evidence is authenticated, not a freshly rerun original native or validation engine here.", "Own physically realized strict winning uniform compiler at the selected H, literal raw occurrences/boundary instructions retained, no materialized enormous uniform-word claim.", "Prescribed unreduced dense ADD macros and the same fixed reference correctness/finite-kernel halting contracts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 5390, "source_commit": "654ab79238e957eb20eced5197c3c38d5738183f", "certificate_file": "pr5390-changed-native-literal-lower.json", "certificate_sha256": "911b5c0e939353c24dcc22aef7cb569d0c39c7433a504b1281cc14c1318a66fe", "peer_review_file": "changed-native-p16-boundary-lowers-peer-review.json", "peer_review_sha256": "4551f6ec30d3b59f4e754c8b5cec2c88ff1693bb1aec11ede03e4699bf4299b3", "proof_file": "changed-native-p16-boundary-lowers.md", "family_kind": "own-changed-native-p16-literal-lower", "kappa_record": "3783343460093/1250000000000000", "uniform_rank_H": "3634890000000000000000", "tensor_power": 757, "upper": null, "lower_certificate_file": "pr5390-changed-native-literal-lower.json", "lower_certificate_sha256": "911b5c0e939353c24dcc22aef7cb569d0c39c7433a504b1281cc14c1318a66fe", "lower": { "input_bits": "2^(2^3634889999999999999997-2^69)", "plot_triple_log": { "log2_of_integer": "3634889999999999999997", "negligible_negative_correction": true }, "scope": "Own complete unreduced raw controller/native word, complete field and spectators when active, stored width at least two; identical repaired optimized GMP when inactive.", "statistic": "Earliest input width at which a correct member of the declared own-source literal enhancement family strictly beats the reference", "source": "data/operation-audit/pr5390-changed-native-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "scope": "Own complete unreduced raw controller/native word, complete field and spectators when active, stored width at least two; identical repaired optimized GMP when inactive. Own native engine receipts are authenticated but not freshly replayed here. No sufficient upper has been derived.", "program_fingerprint": "9aa0d7112b4e13f1aa13a93dab0af6f4435ffe99b842aad841685becdafee492", "program_fingerprint_scope": "Four public-field scalar additions retained in the own selected backward local word, called by the complete raw controller.", "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "changed_native_p16_boundary_lowers.py" ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 5392, "source_commit": "329b2ff35d2994b11abbb59f770d12da75c494ac", "certificate_file": "pr5392-changed-native-literal-lower.json", "certificate_sha256": "73bca4c7017f40f6e0862451cafb3ef9a80e9d4d113c7120354e9dbf79e9e211", "peer_review_file": "changed-native-p16-boundary-lowers-peer-review.json", "peer_review_sha256": "4551f6ec30d3b59f4e754c8b5cec2c88ff1693bb1aec11ede03e4699bf4299b3", "proof_file": "changed-native-p16-boundary-lowers.md", "family_kind": "own-changed-native-p16-literal-lower", "kappa_record": "12109/4000000", "uniform_rank_H": "31385200000000", "tensor_power": 1024, "upper": null, "lower_certificate_file": "pr5392-changed-native-literal-lower.json", "lower_certificate_sha256": "73bca4c7017f40f6e0862451cafb3ef9a80e9d4d113c7120354e9dbf79e9e211", "lower": { "input_bits": "2^(2^31385199999997-2^69)", "plot_triple_log": { "log2_of_integer": "31385199999997", "negligible_negative_correction": true }, "scope": "Own complete unreduced raw controller/native word, complete field and spectators when active, stored width at least two; identical repaired optimized GMP when inactive.", "statistic": "Earliest input width at which a correct member of the declared own-source literal enhancement family strictly beats the reference", "source": "data/operation-audit/pr5392-changed-native-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "scope": "Own complete unreduced raw controller/native word, complete field and spectators when active, stored width at least two; identical repaired optimized GMP when inactive. Own native engine receipts are authenticated but not freshly replayed here. No sufficient upper has been derived.", "program_fingerprint": "737caaf8ed380ec2bdac2452839c3fb8a3ddf68136a8f6fee8c4419cfccdc076", "program_fingerprint_scope": "Four public-field scalar additions retained in the own selected backward local word, called by the complete raw controller.", "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "changed_native_p16_boundary_lowers.py" ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 5395, "source_commit": "275dc377246f91ef30dc9e05241b0f637aa807fb", "certificate_file": "pr5395-source-committed-literal-lower.json", "certificate_sha256": "35b183c48f9a3aa2666e19951cfc7b42ed6246300696cd6f4e8ac72a81d71197", "peer_review_file": "pr5395-source-committed-literal-peer-review.json", "peer_review_sha256": "85f3fc12458fe96d1b1ab663736f2281183252c846c643fcd633cfb5e73c10bb", "proof_file": "source-committed-reviewed-lowers.md", "family_kind": "own-selected-review-exact-word-committed-literal-lower", "upper": null, "lower_certificate_file": "pr5395-source-committed-literal-lower.json", "lower_certificate_sha256": "35b183c48f9a3aa2666e19951cfc7b42ed6246300696cd6f4e8ac72a81d71197", "lower": { "input_bits": "2^(2^409548999999999997-2^69)", "plot_triple_log": { "log2_of_integer": "409548999999999997", "negligible_negative_correction": true }, "scope": "Own source-selected unreduced full-field/native/complete controller enhancement family at positive multiplicity and width>=2 when active; identical repaired optimizedGMP when inactive.", "statistic": "Earliest possible strict win in this declared source-selected literal enhancement family", "exact_individual_crossing": false, "all_PR_implementations": false, "source": "data/operation-audit/pr5395-source-committed-literal-lower.json" }, "effective_kappa": "605334953/200000000000", "kappa_record": "605334953/200000000000", "uniform_rank_H": "409549000000000000", "tensor_power": 1024, "reproduction_command": [ "source_committed_reviewed_lowers.py" ], "scope": [ "Own complete required physical entry/output-frame/absolute-phase/all-column/owned/spectator native endpoint and literal complete controller, not established by source scalar statistics or formal nonzero-cut diagnostics.", "Own source physically realized strict winning uniform supplier, chronological integer compiler/fullfields and source complete-template applicability. Exact own stored evidence is authenticated, not freshly rerun original native/phase/validation engines here.", "Same prescribed unreduced dense arithmetic macros and repaired optimizedGMP correctness/finite-kernel halting." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 5396, "source_commit": "787efce72a908f92b8a8b4ebb677a6fdb7729e33", "certificate_file": "pr5396-reviewed-selected-literal-lower.json", "certificate_sha256": "46add6ef5b2d55ae230eeae3f466288e9b27e068a4a01532ff8891f85ad00b22", "peer_review_file": "pr5396-reviewed-selected-literal-peer-review.json", "peer_review_sha256": "2f0d41b30b36ab1cd98935de885cc7d303b396ff107cf56b13632ed0097f8532", "proof_file": "reviewed-selected-native-lowers.md", "family_kind": "own-selected-validation-literal-lower", "upper": null, "lower_certificate_file": "pr5396-reviewed-selected-literal-lower.json", "lower_certificate_sha256": "46add6ef5b2d55ae230eeae3f466288e9b27e068a4a01532ff8891f85ad00b22", "lower": { "input_bits": "2^(2^409548999999999997-2^69)", "plot_triple_log": { "log2_of_integer": "409548999999999997", "negligible_negative_correction": true }, "scope": "Own selected complete unreduced raw controller/native word with full field/spectator ranges when active, stored width at least two; identical optimized GMP when inactive.", "statistic": "Earliest possible strict win in the specified own-source literal enhancement family", "source": "data/operation-audit/pr5396-reviewed-selected-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "effective_kappa": "605334953/200000000000", "kappa_record": "605334953/200000000000", "uniform_rank_H": "409549000000000000", "tensor_power": 1024, "reproduction_command": [ "reviewed_selected_native_lowers.py" ], "scope": [ "Own source native arbitrary-input required entry/output frames, absolute phase, all-column whole-job/owned/spectator and actual changed caller semantics. Stored validation evidence is authenticated, not a freshly rerun original native or validation engine here.", "Own physically realized strict winning uniform compiler at the selected H, literal raw occurrences/boundary instructions retained, no materialized enormous uniform-word claim.", "Prescribed unreduced dense ADD macros and the same fixed reference correctness/finite-kernel halting contracts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 5398, "source_commit": "174fb211493b43a42210434083e9702b4fb7a2ce", "certificate_file": "pr5398-changed-native-literal-lower.json", "certificate_sha256": "ef159720c3f04e5ee84f2f4bc59801cfec77bca3dbdc96bee48ea15c2c478b65", "peer_review_file": "changed-native-p16-boundary-lowers-peer-review.json", "peer_review_sha256": "4551f6ec30d3b59f4e754c8b5cec2c88ff1693bb1aec11ede03e4699bf4299b3", "proof_file": "changed-native-p16-boundary-lowers.md", "family_kind": "own-changed-native-p16-literal-lower", "kappa_record": "302728823/100000000000", "uniform_rank_H": "38569300000000000", "tensor_power": 1024, "upper": null, "lower_certificate_file": "pr5398-changed-native-literal-lower.json", "lower_certificate_sha256": "ef159720c3f04e5ee84f2f4bc59801cfec77bca3dbdc96bee48ea15c2c478b65", "lower": { "input_bits": "2^(2^38569299999999997-2^69)", "plot_triple_log": { "log2_of_integer": "38569299999999997", "negligible_negative_correction": true }, "scope": "Own complete unreduced raw controller/native word, complete field and spectators when active, stored width at least two; identical repaired optimized GMP when inactive.", "statistic": "Earliest input width at which a correct member of the declared own-source literal enhancement family strictly beats the reference", "source": "data/operation-audit/pr5398-changed-native-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "scope": "Own complete unreduced raw controller/native word, complete field and spectators when active, stored width at least two; identical repaired optimized GMP when inactive. Own native engine receipts are authenticated but not freshly replayed here. No sufficient upper has been derived.", "program_fingerprint": "2aee5e997df99726fc763e510d9cb69fbe4f86114dc8d2cd33ad26c6c462a21d", "program_fingerprint_scope": "Four distinct-source unit-coefficient additions in the own complete raw controller boundary.", "actual_first_crossover_known": false, "all_implementations_covered": false, "reproduction_command": [ "changed_native_p16_boundary_lowers.py" ], "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } }, { "pr": 5399, "source_commit": "702fde7d0a7cde17bc51a9a0bd3a3f740fefc199", "certificate_file": "pr5399-source-committed-literal-lower.json", "certificate_sha256": "4b6d8296e3de30d37026fda1e77a8050eb187adb8add8581ce833f5bca30ce47", "peer_review_file": "pr5399-source-committed-literal-peer-review.json", "peer_review_sha256": "1487f8cd84690f48d6f2e482352ba8618488891917d7bc11de1c551369955808", "proof_file": "source-committed-reviewed-lowers.md", "family_kind": "own-selected-review-exact-word-committed-literal-lower", "upper": null, "lower_certificate_file": "pr5399-source-committed-literal-lower.json", "lower_certificate_sha256": "4b6d8296e3de30d37026fda1e77a8050eb187adb8add8581ce833f5bca30ce47", "lower": { "input_bits": "2^(2^31385199999997-2^69)", "plot_triple_log": { "log2_of_integer": "31385199999997", "negligible_negative_correction": true }, "scope": "Own source-selected unreduced full-field/native/complete controller enhancement family at positive multiplicity and width>=2 when active; identical repaired optimizedGMP when inactive.", "statistic": "Earliest possible strict win in this declared source-selected literal enhancement family", "exact_individual_crossing": false, "all_PR_implementations": false, "source": "data/operation-audit/pr5399-source-committed-literal-lower.json" }, "effective_kappa": "12109/4000000", "kappa_record": "12109/4000000", "uniform_rank_H": "31385200000000", "tensor_power": 1024, "reproduction_command": [ "source_committed_reviewed_lowers.py" ], "scope": [ "Own complete required physical entry/output-frame/absolute-phase/all-column/owned/spectator native endpoint and literal complete controller, not established by source scalar statistics or formal nonzero-cut diagnostics.", "Own source physically realized strict winning uniform supplier, chronological integer compiler/fullfields and source complete-template applicability. 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Stored validation evidence is authenticated, not a freshly rerun original native or validation engine here.", "Own physically realized strict winning uniform compiler at the selected H, literal raw occurrences/boundary instructions retained, no materialized enormous uniform-word claim.", "Prescribed unreduced dense ADD macros and the same fixed reference correctness/finite-kernel halting contracts." ], "actual_first_crossover_known": false, "all_implementations_covered": false, "schema": "own-source-crossover-overlay/1", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "previous_bound_fields": { "cost_status": "not_costed", "conditional_upper": null, "meaningful_lower_bound": null } } ], "interval_fluctuation_annotation": { "schema": "own-source-separated-family-interval-example/1", "status": "closed_exact_conditional_ordering", "model": "xag-straightline-v1", "baseline_extension_id": "gmp-630-native-skylake-unbounded-exact-constants-v2", "earlier": { "pr": 531, "source_head": "e07a8a3f9f79c22113398a0c5dbbc7601f489b3e", "merged_at": "2026-10-12T01:55:39Z", "quoted_kappa": "1517760977820331/1000000000000000000", "upper_certificate": "pr531-finite-gate-refined-upper.json", "P": "18014398509484968", "upper": "2^(2^18014398509484968)" }, "later": { "pr": 4416, "source_head": "e9058860b5c850760fdf970e796a96aefcdb1d98", "merged_at": "2026-10-21T19:27:52Z", "quoted_kappa": "268647/100000000", "lower_certificate": "p7-p17-record-crossover-bounds.json", "H": "16201843136005340321", "q": 0, "lower": "2^(2^16201843136005340318-2^69)" }, "exact_relation": "F_531 <= U_531 < L_4416 <= F_4416", "integer_separation_witness": { "P_le_H_minus_4": true, "H_minus_4_gt_69": true, "q_nonnegative": true }, "scope": "Conditional comparison of the explicitly declared own-source families: the earlier counted finite controller supplies an upper witness; the later unreduced literal supplier has the stated mandatory-work lower. All retained native, analytic and reference correctness contracts apply. This does not order all implementations of either PR idea.", "actual_individual_first_crossings_computed": false, "practical_or_hardware_claim": false, "certificate": "data/operation-audit/feasibility-interval-fluctuation.json", "proof": "data/operation-audit/feasibility-interval-fluctuation.md", "peer_review": "data/operation-audit/feasibility-interval-fluctuation-peer-review.json" }, "source_cost_coverage": { "source": "data/operation-audit/remaining-record-audit/cost-coverage-ledger.json", "summary": { "total_entries": 595, "baseline_uncosted": 577, "source_discovery_covered_among_original577": 577, "source_artifacts": 6276, "numeric_bound_entries": 222, "completed_source_dispositions_without_numeric": 196, "remaining_cost_obligation_entries": 177, "status_counts": { "closed_conditional_numeric_bound": 222, "source_scope_completed_supporting_or_restricted_result": 156, "own_source_fetched_cost_obligations_open": 177, "supporting_formal_interface_no_independent_algorithm": 2, "supporting_contract_audit_no_independent_algorithm": 2, "supporting_endpoint_audit_no_independent_algorithm": 3, "supporting_verification_tooling_no_independent_algorithm": 2, "supporting_arithmetic_audit_no_independent_algorithm": 1, "scoped_obstruction_no_independent_algorithm": 9, "scoped_decoder_bound_no_independent_algorithm": 1, "supporting_reconstruction_requires_target_cost_binding": 2, "supporting_relaxation_audit_no_independent_algorithm": 1, "supporting_native_audit_no_independent_algorithm": 1, "scoped_information_bound_no_independent_algorithm": 2, "supporting_local_identity_no_independent_algorithm": 1, "supporting_local_classification_no_independent_algorithm": 1, "verification_tooling_no_independent_algorithm": 1, "supporting_native_fault_audit_no_independent_algorithm": 1, "supporting_invoice_audit_no_independent_algorithm": 1, "documentation_maintenance_no_independent_algorithm": 1, "independent_validation_of_explicit_construction_targets": 4, "supporting_proof_audit_no_independent_algorithm": 1, "local_algebraic_result_no_integer_algorithm": 3 }, "structural_source_family_counts": { "source_bound_construction": 222, "supporting_evidence_or_tooling": 196, "finite_symbolic_bridge": 2, "source_interface_requires_individual_analysis": 138, "selected_provider_controller": 37 }, "distinct_algorithm_equivalence_cohorts_admitted": 0, "parsed_uniform_rank_candidate_entries": 40, "parse_cap_or_format_obligations": 2 }, "source_specific_gap_report": { "file": "remaining-record-audit/source-specific-cost-gaps.json", "sha256": "b9b3d1e50407345fc10f0e2b7a798831d9fc077db230e63a62f85149e123a201", "entries": 595, "originally_uncosted_entries": 577, "scope": "Source-specific authenticated interface inventory; unresolved cost obligations remain open, no numerical point admitted by inventory." }, "historical_record_stream_membership": { "file": "remaining-record-audit/record-stream-memberships.json", "sha256": "e6c915317ff36bf3485a3ec9c754eef74a26a6f5fb70f5099c303a29e1d0997b", "scope": "Separate heterogeneous announcement/observation/current-chart streams;595positive/source entries are not595record events." } }, "cohort_gap_report_source": "data/operation-audit/remaining-record-cohort-screen.md", "finite_lower_gap_report_source": "data/operation-audit/finite-controller-lower-bound-gap.md", "scope": "Frozen inventory, not a live monitor. No runtime number is inferred from kappa, merge status, proof applicability or a chosen fallback switch.", "unmerged_historical_candidates": [ { "pr": 1, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1", "title": "Refine paired parameters and derive the fixed-exponent supremum", "created_at": "2026-10-07T20:58:44Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 5, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5", "title": "Faster Gaussian resampling for a conditional 1479/10^12 > 2^-30 bound", "created_at": "2026-10-08T04:09:10Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 6, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/6", "title": "Aligned bit circuit with cheaper centers for a conditional 1624/10^12 bound", "created_at": "2026-10-08T05:23:23Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 7, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/7", "title": "Ternary five-subset networks for a conditional 373/10^11 > 2^-28 bound", "created_at": "2026-10-08T06:12:04Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 13, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/13", "title": "Auxiliary source frames for a conditional kappa = 7699/10^10 > 2^-21 bound", "created_at": "2026-10-08T09:01:22Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 14, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/14", "title": "Combine source frames and data corners for conditional kappa = 9.0799e-7", "created_at": "2026-10-08T09:16:50Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 15, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/15", "title": "Smaller h30 producer and full complex batching for conditional \u03ba > 2^-20", "created_at": "2026-10-08T09:26:21Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 17, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/17", "title": "Compose nested geometry and smaller h30 producer for conditional \u03ba = 1.248342e-6 > 2^-20", "created_at": "2026-10-08T09:53:37Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 19, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/19", "title": "Partial-swap ternary geometry for conditional \u03ba = 2.093495e-6 > 2^-19", "created_at": "2026-10-08T10:19:19Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 20, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/20", "title": "Source-framed h53 conditional witness above 2^-20: attributed research record", "created_at": "2026-10-08T10:20:40Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 21, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/21", "title": "Translated partial-swap frames for a conditional 5499/10^9 > 2^-18 bound", "created_at": "2026-10-08T10:24:48Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 22, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/22", "title": "Refine translated parameters to conditional \u03ba = 5.7114918e-6", "created_at": "2026-10-08T10:34:55Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 23, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/23", "title": "Semantic precision and bulk resampling for a conditional 1099/10^8 > 2^-17 bound", "created_at": "2026-10-08T10:43:55Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 25, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/25", "title": "Expose an A5 block for conditional \u03ba = 1.1447067e-5 > 2^-17", "created_at": "2026-10-08T10:52:00Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 27, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/27", "title": "Compose endpoint bit and semantic bulk interfaces for conditional \u03ba = 1.19720853e-5", "created_at": "2026-10-08T10:57:34Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 28, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/28", "title": "Rectangular geometry for conditional \u03ba = 1.2260937e-5 > 2^-17", "created_at": "2026-10-08T11:09:59Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 29, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/29", "title": "Two-stage controlled corners for a conditional 15536/10^9 > 2^-16 bound", "created_at": "2026-10-08T11:20:11Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 31, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/31", "title": "Exact data-corner certificates for conditional \u03ba = 1.5878574e-5 > 2^-16", "created_at": "2026-10-08T11:29:25Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 33, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/33", "title": "Compose smaller two-stage dimensions and data blocks for conditional \u03ba = 1.638103206e-5", "created_at": "2026-10-08T11:35:56Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 34, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/34", "title": "Reversed two-stage basis and balanced assembly for conditional \u03ba = 1.639226629e-5", "created_at": "2026-10-08T12:10:06Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 35, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/35", "title": "Fixed local bases in two stages for conditional \u03ba = 1.6631776e-5", "created_at": "2026-10-08T12:27:24Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 38, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/38", "title": "Copied centers with fixed local bases for conditional \u03ba = 3.886224e-5", "created_at": "2026-10-08T12:49:21Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 40, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/40", "title": "Both fixed bases and copied reversed corners: conditional \u03ba = 3.918734894e-5 > 2^-15", "created_at": "2026-10-08T13:15:57Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 41, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/41", "title": "Alternating pair-block networks for conditional \u03ba = 4.034168124 \u00d7 10\u207b\u2075 > 2\u207b\u00b9\u2075", "created_at": "2026-10-08T13:33:05Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 42, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/42", "title": "RaD producers with fixed reversed geometry: conditional \u03ba = 4.099494519e-5 > 2^-15", "created_at": "2026-10-08T13:51:36Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 44, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/44", "title": "Weighted carrier matching: conditional \u03ba = 4.100629254e-5 > 2^-15", "created_at": "2026-10-08T14:24:20Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 47, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/47", "title": "Hill-climbed producers for a conditional \u03ba = 4.105106623e-5 bound", "created_at": "2026-10-08T14:56:35Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 63, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/63", "title": "Rank-first pair assembly: conditional \u03ba = 5.102757e-5", "created_at": "2026-10-08T18:05:25Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 65, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/65", "title": "Reordered rank-pair regions: conditional \u03ba = 5.1028985071975e-5", "created_at": "2026-10-08T18:24:54Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 67, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/67", "title": "Cost-aware retired-slot selection: conditional \u03ba = 5.1033760584215e-5", "created_at": "2026-10-08T18:39:26Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 68, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/68", "title": "Cost-aware live controls: conditional \u03ba = 5.103512721785e-5", "created_at": "2026-10-08T18:40:15Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 69, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/69", "title": "Balanced coarse sums: conditional \u03ba = 5.136837484e-5", "created_at": "2026-10-08T19:01:51Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 71, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/71", "title": "Anchored split frames with profile-cost live reclamation: \u03ba = 5.1414646104039e-5", "created_at": "2026-10-08T19:06:56Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 74, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/74", "title": "Stopped pair-star trees: conditional \u03ba = 7.808981744031e-5", "created_at": "2026-10-08T19:26:36Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 75, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/75", "title": "Zero-circuit live clearing: conditional kappa = 5.14154245470094e-5 above #71", "created_at": "2026-10-08T19:34:43Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 76, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/76", "title": "Envelope-ordered carry exchanges: conditional \u03ba = 5.1738676045141e-5", "created_at": "2026-10-08T19:44:13Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 79, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/79", "title": "Balanced coarse split frames: conditional \u03ba = 5.1745625472866e-5", "created_at": "2026-10-08T19:51:47Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 80, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/80", "title": "Combined envelope/balanced axes and geometric flags: conditional \u03ba = 5.1778825456819e-5", "created_at": "2026-10-08T19:57:30Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 81, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/81", "title": "Balanced-column carry exchanges: conditional \u03ba = 5.1915547765237e-5", "created_at": "2026-10-08T20:13:01Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 82, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/82", "title": "Envelope ordering on balanced frames with geometric pricing: conditional \u03ba = 5.203279888519e-5", "created_at": "2026-10-08T20:14:13Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 84, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/84", "title": "Indexed carry two-cycles and coordinate flags: conditional \u03ba = 5.22712890914e-5", "created_at": "2026-10-08T20:32:42Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 85, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/85", "title": "Coordinate refinement of indexed two-cycles: conditional \u03ba = 5.2272192668365e-5", "created_at": "2026-10-08T20:47:52Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 86, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/86", "title": "Coordinate-aware indexed compilation: conditional \u03ba = 5.2275423755251e-5", "created_at": "2026-10-08T20:55:27Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 91, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/91", "title": "Aligned frame composition: \u03ba=5.2789616935221e-5 with Lean arithmetic certificate", "created_at": "2026-10-08T21:36:57Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 93, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/93", "title": "Coordinate refinement of aligned composition: conditional \u03ba = 5.2790906739644e-5", "created_at": "2026-10-08T21:53:34Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 94, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/94", "title": "Adjacent coordinate refinement beyond PR93: conditional \u03ba = 5.2790937858556e-5", "created_at": "2026-10-08T22:00:47Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 95, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/95", "title": "Coordinate descent beyond PR94: conditional \u03ba = 5.279109590448e-5", "created_at": "2026-10-08T22:07:02Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 96, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/96", "title": "Merged auxiliary exteriors: conditional \u03ba = 5.5354656014473e-5", "created_at": "2026-10-08T22:13:58Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 97, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/97", "title": "Deferred endpoints and signed phase correction for a conditional 63965813/10^12 > 2^-14 bound", "created_at": "2026-10-08T22:39:54Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 100, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/100", "title": "Balanced transfer of deferred signed networks: conditional \u03ba = 6.3978919675787e-5", "created_at": "2026-10-08T22:57:24Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 103, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/103", "title": "Saturated readouts with complete signed/balanced integration: conditional \u03ba = 6.398282083297e-5", "created_at": "2026-10-08T23:10:11Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 107, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/107", "title": "Reversed rational-center orders: conditional \u03ba = 7.798412662809e-5", "created_at": "2026-10-08T23:24:30Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 108, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/108", "title": "Dual-suffix pair stars in the rational-center producer: conditional \u03ba = 7.988289348441e-5", "created_at": "2026-10-08T23:54:10Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 109, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/109", "title": "Weighted dual-suffix carriers: conditional \u03ba = 7.9961717358e-5", "created_at": "2026-10-08T23:59:38Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 110, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/110", "title": "Deferred readouts on both stopped networks: conditional \u03ba = 8.58478e-5", "created_at": "2026-10-09T00:02:51Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 113, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/113", "title": "Deferred readouts on the cyclic-strip complex network: conditional \u03ba = 9.39074e-5", "created_at": "2026-10-09T00:13:34Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 114, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/114", "title": "Shared completed cores and physical frames: conditional \u03ba = 1.23988197806e-4", "created_at": "2026-10-09T00:23:37Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 116, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/116", "title": "Cube recurrence with balanced deferred frames: conditional \u03ba = 9.8699350338e-5", "created_at": "2026-10-09T00:34:00Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 117, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/117", "title": "Deferred bit word and a 28,705-role complex producer under stopped-product accounting: conditional \u03ba = 1.044939e-4", "created_at": "2026-10-09T00:39:23Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 118, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/118", "title": "Deferred readouts on PR117\u2019s complex producer: conditional \u03ba = 1.085428e-4", "created_at": "2026-10-09T00:46:49Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 120, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/120", "title": "Deferred readouts on the replayed h24 complex network: conditional \u03ba = 1.0911630664e-4", "created_at": "2026-10-09T00:56:35Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 122, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/122", "title": "Terminal accumulator elimination with exact majorization audit", "created_at": "2026-10-09T01:11:36Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 124, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/124", "title": "Birth-read slot recycling: conditional kappa 1.1038332094346e-4", "created_at": "2026-10-09T01:19:02Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 125, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/125", "title": "Shrunk lifted frames with saturated deferral: conditional \u03ba = 1.10591581647e-4", "created_at": "2026-10-09T01:20:13Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 127, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/127", "title": "Birth-read reuse on shrunk saturated frames: conditional \u03ba = 1.1239534209971e-4", "created_at": "2026-10-09T01:34:34Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 128, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/128", "title": "Completed-core sharing: conditional kappa > 2^-13", "created_at": "2026-10-09T01:35:20Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 129, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/129", "title": "Shared bit cores and gauged scratch reuse: conditional \u03ba = 1.29186205798e-4", "created_at": "2026-10-09T02:07:28Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 131, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/131", "title": "Physical frames and scratch reuse on Cayley covers: conditional \u03ba = 3.32205398986e-4", "created_at": "2026-10-09T02:41:54Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 132, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/132", "title": "Paired lockstep first-stage vertices on three-stage covers: conditional \u03ba = 3.416202e-4", "created_at": "2026-10-09T02:46:41Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 134, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/134", "title": "Shrunk frames under paired lockstep covers: conditional \u03ba = 3.48102e-4", "created_at": "2026-10-09T02:52:00Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 135, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/135", "title": "Paired physical scratch reuse: candidate conditional \u03ba = 3.62108222954e-4 (+4.02% vs #134)", "created_at": "2026-10-09T02:58:07Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 136, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/136", "title": "Tightened slack constants on the conservative paired scratch-reuse candidate: conditional \u03ba = 3.6210858481e-4", "created_at": "2026-10-09T03:13:24Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 137, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/137", "title": "Padded triple covers with sequential dirty reuse: conditional \u03ba = 4.13596233702e-4", "created_at": "2026-10-09T03:18:33Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 138, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/138", "title": "Tightened slack constants on paid padded triple covers: conditional \u03ba = 4.13596659368e-4", "created_at": "2026-10-09T03:24:38Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 142, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/142", "title": "Restricted h22 padded triple covers: conditional \u03ba = 4.20151003347e-4", "created_at": "2026-10-09T03:47:19Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 143, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/143", "title": "Late compensation and joint frame refinement: conditional \u03ba = 4.24830828577e-4", "created_at": "2026-10-09T04:09:31Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 146, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/146", "title": "Use exact telescoping min-cut bit subset on paired-cube shared cores for kappa = 4.61028508707e-4 (4.61239827139e-4 at atom=1/2000)", "created_at": "2026-10-09T04:45:27Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 148, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/148", "title": "Raise conditional kappa to 4.611281e-4 with tightened adapter toll", "created_at": "2026-10-09T04:49:51Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 152, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/152", "title": "Paired cubes at p = 11 with an h = 21 bit word: conditional \u03ba = 5.108289e-4", "created_at": "2026-10-09T06:05:07Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 153, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/153", "title": "Re-instantiated phase-stop on the p = 11 paired cubes: conditional \u03ba = 5.108294e-4", "created_at": "2026-10-09T06:11:37Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 155, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/155", "title": "Paired cubes at p = 11 with physical frames and a paired-cube bit word: conditional \u03ba = 5.508074e-4", "created_at": "2026-10-09T06:40:26Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 157, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/157", "title": "Paired cubes at p = 11 with a searched pair module, physical frames and a paired-cube bit word: conditional \u03ba = 5.555021e-4", "created_at": "2026-10-09T06:54:05Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 158, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/158", "title": "Re-instantiated atom exponent at the toll edge on the searched pair module: conditional \u03ba = 5.557315e-4", "created_at": "2026-10-09T07:07:00Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 160, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/160", "title": "Searched pair module in the paired-cube bit word at p = 11: conditional \u03ba = 5.616446e-4", "created_at": "2026-10-09T07:12:17Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 161, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/161", "title": "Merged complex outputs and an annealed bit pair module on paired cubes: conditional \u03ba = 5.878747e-4", "created_at": "2026-10-09T07:23:37Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 162, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/162", "title": "Extended carrier matching on #161's complex word: conditional \u03ba = 5.901881e-4", "created_at": "2026-10-09T07:38:03Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 163, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/163", "title": "Fused paired cubes and paid balanced transfer: conditional \u03ba = 5.93970203079492e-4", "created_at": "2026-10-09T07:44:15Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 164, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/164", "title": "Connected bit-frame descents on #163: conditional \u03ba = 5.94035602295411e-4", "created_at": "2026-10-09T08:04:53Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 165, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/165", "title": "Certify extended paired cubes and bit frames (\u03ba=5.94272360424954e-4)", "created_at": "2026-10-09T08:08:21Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 168, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/168", "title": "Annealed modules, terminal sinks and physical bit words on paired cubes: conditional \u03ba = 6.558894e-4", "created_at": "2026-10-09T08:22:16Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 169, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/169", "title": "Bit operation-frame descent on #168's bit word: conditional \u03ba = 6.105562e-4", "created_at": "2026-10-09T08:36:30Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 170, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/170", "title": "Paired bit-output fusion and verified lifetime reuse: conditional \u03ba = 5.96818007e-4", "created_at": "2026-10-09T08:47:18Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 171, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/171", "title": "Causal bit-frame refinement of #169: conditional kappa = 6.11068410271618e-4", "created_at": "2026-10-09T08:57:39Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 176, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/176", "title": "Refine terminal paired cubes (\u03ba = 6.48942003256776e-4)", "created_at": "2026-10-09T09:55:12Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 178, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/178", "title": "Refine PR168 operation frames: conditional \u03ba = 0.00065591780345", "created_at": "2026-10-09T10:28:58Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 179, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/179", "title": "Refine paired-cube frames on PR168 v4 with retained terminal sinks (\u03ba = 6.55920176686219e-4)", "created_at": "2026-10-09T10:41:01Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 180, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/180", "title": "Independently audit PR #186 and refine its conditional exponent", "created_at": "2026-10-09T11:10:49Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 181, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/181", "title": "Shared-edge local circuit on PR168 v4 paired cubes (\u03ba = 6.59180578557293e-4)", "created_at": "2026-10-09T11:10:57Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 182, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/182", "title": "Shared-edge local circuit, refined bit frames and bit terminal sinks on PR168 v4 (\u03ba = 6.60216552061722e-4)", "created_at": "2026-10-09T11:27:40Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 185, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/185", "title": "Finite leaf bootstrap above PR182: conditional kappa = 0.000660627334074291", "created_at": "2026-10-09T11:41:08Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 186, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/186", "title": "Shared-edge supplier, coordinated frames and entrance banks: conditional kappa = 6.61885549259598e-4", "created_at": "2026-10-09T11:54:01Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 191, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/191", "title": "Source-assisted complex word on PR168 v4 modules: conditional \u03ba = 6.626307e-4", "created_at": "2026-10-09T12:16:23Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 193, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/193", "title": "Pair donors to avoid parity erasure on the source-assisted v4 word: conditional \u03ba = 6.647872e-4", "created_at": "2026-10-09T12:36:35Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 194, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/194", "title": "Source-assisted v4 complex word with PR189's bit supplier: conditional \u03ba = 6.674324e-4", "created_at": "2026-10-09T12:43:44Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 197, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/197", "title": "Pack #187's bit residuals: conditional \u03ba = 0.000676080316519385", "created_at": "2026-10-09T13:27:16Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 199, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/199", "title": "Bit leaf bootstrap: queue standing + the deferred #200 composition at conditional \u03ba = 6.773148e-4", "created_at": "2026-10-09T14:08:35Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 202, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/202", "title": "Compose the v4 source-assisted complex word with the PR200 bit supplier: conditional \u03ba = 6.768823e-4", "created_at": "2026-10-09T14:39:29Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 205, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/205", "title": "Pack PR200 diagonal bit residuals into completed banks (conditional \u03ba = 0.000683061299399923)", "created_at": "2026-10-09T15:46:40Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 207, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/207", "title": "Conditional kappa 6.831904550365e-4: coordinated frame optimization and completed entrance banks", "created_at": "2026-10-09T16:00:16Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 210, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/210", "title": "\u03ba = 7.10069340338651e-4: five-stage banks and F\u2082 movement fusion", "created_at": "2026-10-09T16:58:57Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 211, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/211", "title": "Conditional kappa 6.838479e-4: cascade-optimized frames on PR200's banked bit word", "created_at": "2026-10-09T17:14:57Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 213, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/213", "title": "Conditional \u03ba = 6.83847872497761e-4: five-level bootstrap on PR211 cascade frames", "created_at": "2026-10-09T17:33:01Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 217, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/217", "title": "Conditional \u03ba = 6.84696826673891e-4: paid XOR butterflies with cascade-optimized frames", "created_at": "2026-10-09T18:38:12Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 230, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/230", "title": "\u03ba = 6.94787513005285e-4: plateau retiming on PR210's 471-source word", "created_at": "2026-10-09T20:49:52Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 234, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/234", "title": "Conditional \u03ba \u2248 7.037017435 \u00d7 10\u207b\u2074 > 2\u207b\u00b9\u00b9: five-stage bit and complex suppliers", "created_at": "2026-10-09T22:05:48Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 235, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/235", "title": "Conditional \u03ba = 7.08582414684555347682e-4: fixed prime and finite leaves on PR237 banks", "created_at": "2026-10-09T22:07:45Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 237, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/237", "title": "Conditional \u03ba = 7.08582410781108e-4: completed width-120 entrance banks on #234's five-stage bit supplier", "created_at": "2026-10-09T22:20:18Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 244, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/244", "title": "\u03ba = 7.10346589668175e-4: retime source-pair additions to their delivery frames", "created_at": "2026-10-09T23:43:37Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 247, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/247", "title": "Conditional \u03ba = 7.10346593569665e-4: fixed-prime refinement on PR244", "created_at": "2026-10-10T00:00:30Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 248, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/248", "title": "Conditional \u03ba = 7.10346593569666e-4: fixed prime, seven finite levels and \u03b7 = 10\u207b\u00b2\u2074 on #244's retimed source527 banks", "created_at": "2026-10-10T00:05:19Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 249, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/249", "title": "\u03ba = 7.10392186446856e-4: transport dirty compensations to 21 entrance frames", "created_at": "2026-10-10T00:06:20Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 251, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/251", "title": "\u03ba = 7.10433687047883e-4: expand transported entrances with shared frame intersections", "created_at": "2026-10-10T00:27:52Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 253, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/253", "title": "Conditional \u03ba = 0.000710433690953069816941696: fixed-prime refinement on PR251", "created_at": "2026-10-10T01:01:24Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 254, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/254", "title": "Response-kernel entrance gauges: 132 helper-pair rewrites, \u03ba = 7.1046520063283e-4", "created_at": "2026-10-10T01:14:01Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 255, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/255", "title": "Conditional \u03ba = 7.10465204542247e-4: fixed prime, seven finite levels and \u03b7 = 10\u207b\u00b2\u2074 on #254", "created_at": "2026-10-10T01:35:33Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 257, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/257", "title": "Conditional \u03ba=710465204542247142217249/10^27: eight-level refinement of #254", "created_at": "2026-10-10T01:42:41Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 258, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/258", "title": "Compose 25 exact frame retimings with PR254 (conditional \u03ba = 7.1046804825911e-4)", "created_at": "2026-10-10T01:51:57Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 260, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/260", "title": "Draft: Conditional \u03ba = 7.10436534421701e-4: concave-descent frame retiming of 25 gates on #251's source527 banks", "created_at": "2026-10-10T02:01:41Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 261, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/261", "title": "Fixed-prime refinement of PR259 (kappa = 0.000711029389987426878345881)", "created_at": "2026-10-10T02:15:46Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 263, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/263", "title": "Conditional \u03ba = 7.11032238200698e-4: concave-descent frame retiming of 25 gates on #259's multi-cut condensation", "created_at": "2026-10-10T02:28:07Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 265, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/265", "title": "Conditional \u03ba = 7.11032242134072e-4: fixed prime, eight finite levels and \u03b7 = 10\u207b\u00b2\u2074 on #263's descent-retimed multicut word", "created_at": "2026-10-10T02:40:32Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 266, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/266", "title": "Conditional \u03ba = 7.14026746429965\u00b710\u207b\u2074 on #249's word: 890 kernel families, #263/#270 retimings, #273's target-prefix squares and 126 cleanup sandwiches (#271), composed (+0.42% over #259; above #271/#275)", "created_at": "2026-10-10T03:00:32Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 270, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/270", "title": "Conditional \u03ba = 0.000711457853376510: 887 entrances and connected-block retiming", "created_at": "2026-10-10T03:25:42Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 271, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/271", "title": "Cancel cleanup sandwiches of 99 helpers on #272: conditional \u03ba = 7.1366215638961e-4", "created_at": "2026-10-10T03:41:48Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 272, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/272", "title": "Frame-filtered collective kernels + target-prefix sharing: kappa = 0.000712074434532274423885827", "created_at": "2026-10-10T03:42:02Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 279, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/279", "title": "Conditional \u03ba = 7.24098741932703e-4: 880-gate concave-descent retiming and 220 target-prefix squares on #276's gen4 five-stage banks", "created_at": "2026-10-10T04:41:19Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 280, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/280", "title": "Conditional \u03ba = 0.000724189082265949: gen4 retiming, 440 early restorations and 60 dirty entrances", "created_at": "2026-10-10T04:54:10Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 281, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/281", "title": "Conditional \u03ba = 7.25113717934416e-4: target-prefix compression (280 groups) composed with #280's gen4 retiming, early restorations and dirty entrances", "created_at": "2026-10-10T05:12:49Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 284, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/284", "title": "Conditional \u03ba = 7.26291692225845\u00b710\u207b\u2074: 91 collective response-kernel families on helpers untouched by #283, at its own cut (+0.0248% over #283)", "created_at": "2026-10-10T06:37:26Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 285, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/285", "title": "Conditional \u03ba = 7.42785663120535e-4: gen5 \u2014 compile-cost-annealed pair and all-but-one modules on #276's gen4 bit word, five-stage completed banks", "created_at": "2026-10-10T07:10:08Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 287, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/287", "title": "Conditional \u03ba = 7.44136146100942e-4: two concave-descent retimings (904 + 111 gates) and 220 target-prefix squares on #285's gen5 five-stage banks", "created_at": "2026-10-10T07:46:25Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 289, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/289", "title": "Extreme-meet frame retiming (87 gates) on target-compressed gen5 word: kappa = 7.44127392470948e-4", "created_at": "2026-10-10T08:37:44Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 290, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/290", "title": "Conditional \u03ba = 7.44714499357628\u00b710\u207b\u2074: 450 collective response-kernel entries on #285's gen5 word, after #287's descent and target squares (+0.080% over #287)", "created_at": "2026-10-10T08:39:53Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 291, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/291", "title": "Conditional \u03ba = 7.44728650221677e-4: second concave-descent retiming (89 gates, constructed frames) after #290's kernel entries on the gen5 word", "created_at": "2026-10-10T09:15:52Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 295, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/295", "title": "Conditional \u03ba = 7.45513573133379\u00b710\u207b\u2074: early restorations and terminal sinks on the gen5 kernel word, with #233's complex word as supplier (+0.107% over #290)", "created_at": "2026-10-10T09:40:32Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 296, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/296", "title": "Conditional \u03ba = 7.46709720962478\u00b710\u207b\u2074: gen5b \u2014 exactly optimal local design and a debt-10 all-but-one module on #285's word, #287's stages re-derived, #233's complex supplier (+0.348% over #287)", "created_at": "2026-10-10T09:47:14Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 299, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/299", "title": "Conditional \u03ba = 7.50237961741364\u00b710\u207b\u2074: kernels, early restorations, terminal sinks, a post-sink retiming and addition reordering on the gen5b word (+0.473% over #296)", "created_at": "2026-10-10T10:12:42Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 300, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/300", "title": "Conditional \u03ba = 7.49982567267028e-4: 1,734 kernel entries (restart-packed), second descent, 440 restorations and 8 sinks on #296's gen5b word", "created_at": "2026-10-10T10:40:28Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 301, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/301", "title": "Verify a 12-helper co-retiming improvement on pinned PR #299", "created_at": "2026-10-10T11:14:19Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 302, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/302", "title": "Verify shared-donor kernel improvements on pinned weighted and reordered words", "created_at": "2026-10-10T11:55:41Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 305, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/305", "title": "\u03ba = 7.51140529238897e-4: restart-packed kernels on weighted gen5b matching", "created_at": "2026-10-10T12:17:44Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 306, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/306", "title": "Conditional \u03ba = 7.51458925311258\u00b710\u207b\u2074: addition reordering on #305's weighted gen5b composition (+0.0424% over #305)", "created_at": "2026-10-10T13:00:46Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 308, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/308", "title": "Conditional \u03ba = 7.51472114011902e-4: #307's fresh selections on the weighted gen5b word with #306's reorder stages", "created_at": "2026-10-10T13:25:50Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 310, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/310", "title": "Conditional \u03ba = 0.000752893499605334868002344: source-bound w3 word and complete finite admission (+0.1855% over #309)", "created_at": "2026-10-10T14:13:47Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 311, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/311", "title": "Conditional \u03ba = 7.53508664880762e-4: 209 exact F\u2082 target-prefix squares on #310's w3 word (+0.082% over #310)", "created_at": "2026-10-10T14:51:43Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 312, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/312", "title": "Conditional \u03ba = 7.54549816771013\u00b710\u207b\u2074: kernel, target-prefix, plateau and reorder stages on #310's w3 word, priced against #304's complex supplier (+0.138% over #311)", "created_at": "2026-10-10T15:33:00Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 314, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/314", "title": "Conditional \u03ba = 7.55120411314104e-4: 438 early restorations after #312's kernel/target/plateau/reorder stages on the w3 word (+0.0756% over #312)", "created_at": "2026-10-10T15:52:23Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 315, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/315", "title": "Conditional \u03ba = 7.64230861320245e-4: the paired-cube bit word at cube size p = 10 (h = 20, m = 100), with a new centre-sharing complex supplier (+1.21% over #314)", "created_at": "2026-10-10T15:55:14Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 316, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/316", "title": "Conditional \u03ba = 7.65146115390441e-4: 480-gate concave-descent retiming on #315's p = 10 word (+0.120% over #315)", "created_at": "2026-10-10T16:14:55Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 317, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/317", "title": "\u03ba = 7.6817007781759e-4: composed p10 stages with full source-bound admission", "created_at": "2026-10-10T16:26:45Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 319, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/319", "title": "\u03ba = 7.68257328708259e-4: shared-donor kernels after frozen PR317", "created_at": "2026-10-10T16:43:10Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 320, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/320", "title": "Conditional \u03ba = 7.69553898621543\u00b710\u207b\u2074: the full transcript stage stack on #315's p = 10 word, with a shared-donor closure kernel (+0.697% over #315)", "created_at": "2026-10-10T16:51:00Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 322, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/322", "title": "\u03ba = 7.69556690340075e-4: four frame retimings after PR320 restoration", "created_at": "2026-10-10T18:05:01Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 323, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/323", "title": "\u03ba = 7.69557449978832e-4: three rank-two kernels after frozen PR322", "created_at": "2026-10-10T18:10:24Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 325, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/325", "title": "Conditional \u03ba = 7.696840393833340e-4: a stronger p = 10 bit word \u2014 re-annealed pair module, p = 10 local design, balanced cube orientation, tiered reuse matching (+0.71% over #315's word)", "created_at": "2026-10-10T18:26:33Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 328, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/328", "title": "\u03ba = 7.72285110892838493685197e-4: source-bound p10b stages and retimed complex supplier", "created_at": "2026-10-10T19:11:14Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 329, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/329", "title": "Conditional \u03ba = 7.76518649004426\u00b710\u207b\u2074: the full transcript stage stack on #325's p10b word, priced against #327's p = 10 complex supplier (+0.888% over #325)", "created_at": "2026-10-10T19:17:41Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 330, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/330", "title": "\u03ba = 7.7652200910342944936985e-4: cross-entrance retiming and operational PR327 supplier", "created_at": "2026-10-10T19:39:14Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 331, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/331", "title": "\u03ba = 7.76523967665819025774905e-4: nested donor entrances on the p10b word", "created_at": "2026-10-10T19:56:21Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 332, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/332", "title": "\u03ba = 7.77268259042371640048112e-4: oriented p10b source and 42 constructed-frame retimings", "created_at": "2026-10-10T20:17:54Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 334, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/334", "title": "\u03ba = 7.77596191161693861459874e-4: all-rank donor flow and 52 final retimings", "created_at": "2026-10-10T21:15:26Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 335, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/335", "title": "\u03ba = 7.77607473791708458474546e-4: refreshed donors and 54 final retimings", "created_at": "2026-10-10T21:34:52Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 336, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/336", "title": "\u03ba = 7.776299656948249002253e-4: exact-subspace grouping and sixteen carrier switches", "created_at": "2026-10-10T22:14:48Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 337, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/337", "title": "\u03ba = 7.77646134698096194171091e-4: source orientations preserving fifteen sinks", "created_at": "2026-10-10T22:19:08Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 338, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/338", "title": "\u03ba = 7.77667758368047375562422e-4: three source orientations preserve fifteen sinks", "created_at": "2026-10-10T22:41:23Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 339, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/339", "title": "\u03ba = 7.77699286748588506644032e-4: combine sink-preserving orientations and carrier switches", "created_at": "2026-10-10T22:42:41Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 340, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/340", "title": "Conditional \u03ba \u2248 7.7766181e-4: exact-objective free-form final retiming (490 gates, \u03c6 \u221285.9) replacing #337's 52-gate descent on the same word", "created_at": "2026-10-10T22:52:59Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 341, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/341", "title": "\u03ba = 7.77709755852032951391533e-4: selected carrier switches preserve fifteen sinks", "created_at": "2026-10-10T23:04:27Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 342, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/342", "title": "\u03ba = 7.77733996775530073717409e-4: selected carriers preserve sixteen sinks", "created_at": "2026-10-10T23:13:00Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 343, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/343", "title": "\u03ba = 7.77751087387777005145646e-4: refreshed sixteen-sink carriers", "created_at": "2026-10-10T23:20:18Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 344, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/344", "title": "\u03ba = 7.77947425336102317479703e-4: restore ten terminal caches in original registers", "created_at": "2026-10-10T23:28:33Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 345, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/345", "title": "\u03ba = 7.7809154371141892133459e-4: transfer compatible PR340 frame components", "created_at": "2026-10-10T23:43:59Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 346, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/346", "title": "\u03ba = 7.92580093369946e-4: w3 cube layer on #325's p10b word with a stronger p = 10 complex supplier", "created_at": "2026-10-10T23:45:40Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 348, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/348", "title": "Conditional \u03ba = 7.93392809291691\u00b710\u207b\u2074: #346's w3 bit word with a per-point p = 10 complex supplier (+0.1025 % over #346)", "created_at": "2026-10-11T00:17:42Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 350, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/350", "title": "\u03ba = 7.93469326753735e-4: #348 with a frame-retimed complex program (+7.65e-8)", "created_at": "2026-10-11T00:38:20Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 352, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/352", "title": "\u03ba = 8.01083628465007e-4: #346's w3 bit word with Sussman's Lean-checked E8 unit as the complex supplier (+0.96 % over #350)", "created_at": "2026-10-11T01:03:47Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 353, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/353", "title": "\u03ba = 8.01598358635541e-4: #352 with Design T + twins on a reordered-design p10b base word (+0.064%)", "created_at": "2026-10-11T01:25:23Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 354, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/354", "title": "Conditional \u03ba = 8.03137165163490\u00b710\u207b\u2074: w3 Design T + twins on #329's transcript-staged p10b word with Sussman's E8 complex unit (+0.256 % over #352)", "created_at": "2026-10-11T01:33:04Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 356, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/356", "title": "\u03ba = 8.03161884970454053300282e-4: staged signed twins with complete native admission", "created_at": "2026-10-11T01:57:54Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 357, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/357", "title": "\u03ba = 8.03654539036015e-4: #354's staged Design T + twins on a reordered-design p10b base word (+0.064%)", "created_at": "2026-10-11T02:06:59Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 358, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/358", "title": "\u03ba = 8.0367971186626189473809e-4: reordered stages with 471 twins and signed18", "created_at": "2026-10-11T02:14:43Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 359, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/359", "title": "Conditional \u03ba = 8.04303459176812\u00b710\u207b\u2074: kernel, retiming and reorders re-derived on #354's Design T word (+0.0776 % over #358)", "created_at": "2026-10-11T02:22:25Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 361, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/361", "title": "Conditional \u03ba = 8.04849251275843\u00b710\u207b\u2074: post-Design-T kernel, retiming and reorders on #357's reordered base word with all 471 twins (+0.0679 % over #359)", "created_at": "2026-10-11T02:55:01Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 364, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/364", "title": "\u03ba = 8.04879370798932e-4: #362 with \u03ba-exact min-cost carrier matching in the base producer (+3.0e-8)", "created_at": "2026-10-11T03:36:29Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 366, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/366", "title": "Conditional \u03ba = 8.04939789231485e-4: 123 coupled frame changes after #364 (+0.00751%)", "created_at": "2026-10-11T04:23:13Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 369, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/369", "title": "Conditional \u03ba = 8.049462195041506e-4: two kernels and 15 extra retimings after #366", "created_at": "2026-10-11T04:45:56Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 370, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/370", "title": "\u03ba = 8.75481145306751e-4: first E8 bit word (complex-bound; +9.29% over #352)", "created_at": "2026-10-11T05:05:44Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 373, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/373", "title": "\u03ba = 9.3191395651209e-4: #370's E8 bit word and Sussman's E8 complex unit in the seven-stage bridged word (+6.45 % over #370)", "created_at": "2026-10-11T05:26:18Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 374, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/374", "title": "Conditional \u03ba = 9.54395132518163e-4: coupled complex retiming after #375 (+0.01588%)", "created_at": "2026-10-11T05:40:40Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 375, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/375", "title": "\u03ba = 9.5424356568133e-4: seven-stage E8 suppliers with the complex idle climbs at halving degree two (+2.40 % over #373)", "created_at": "2026-10-11T05:43:05Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 376, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/376", "title": "Conditional \u03ba=0.0011208649522582786: split centres with complete signed admission", "created_at": "2026-10-11T05:44:01Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 377, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/377", "title": "\u03ba = 9.98243154231047e-4: nine-stage complex E8 (\u22482^-9.9683; complex +14.036%, bit side pending)", "created_at": "2026-10-11T05:50:35Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 378, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/378", "title": "Conditional \u03ba = 9.5464544449649\u00b710\u207b\u2074: Sussman's E8 complex unit re-timed by far piece relocation, in #375's unsplit B\u2083 (+0.042 % over #375)", "created_at": "2026-10-11T05:54:38Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 382, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/382", "title": "Conditional \u03ba = 9.98243154231047\u00b710\u207b\u2074: our retimed + kernel E8 bit word in B\u2083 (unsplit) with #377's nine-stage complex component (+0.26 % over #381)", "created_at": "2026-10-11T06:18:39Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 384, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/384", "title": "Conditional \u03ba = 9.98634656132003\u00b710\u207b\u2074: #377's nine-stage E8 complex component with our #378 re-timed E8 unit, paired with our #382 bit word (+0.039 % over #382)", "created_at": "2026-10-11T06:27:31Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 387, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/387", "title": "Conditional kappa 0.000998634658090835: finite bootstrap and exact coarse precision", "created_at": "2026-10-11T06:45:48Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 389, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/389", "title": "Complete far-retimed E8 replay and coupled bit frames; conditional kappa 0.000998634658090835", "created_at": "2026-10-11T07:00:30Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 390, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/390", "title": "E8 prefix restoration and heterogeneous helper banks: conditional kappa = 1.000220222889528e-3", "created_at": "2026-10-11T07:09:46Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 392, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/392", "title": "Conditional kappa 0.001000220224856110: six fixed levels on #390", "created_at": "2026-10-11T07:17:34Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 394, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/394", "title": "Conditional \u03ba = 1.000385913854264\u00b710\u207b\u00b3: bank padding fused into three new free sink helpers on #390's E8 complex program (+0.0166 % over #390)", "created_at": "2026-10-11T07:38:00Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 395, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/395", "title": "Conditional kappa 0.001001256225581264: signed prefixes and padding fusion", "created_at": "2026-10-11T07:41:32Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 396, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/396", "title": "Conditional kappa 0.001001098432210898: signed-prefix donor gauges", "created_at": "2026-10-11T07:52:46Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 398, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/398", "title": "Title: Signed target-prefix cancellation on R781: conditional kappa = 0.001002494659629864", "created_at": "2026-10-11T07:58:05Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 399, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/399", "title": "Conditional \u03ba = 1.002661106042177\u00b710\u207b\u00b3: our #394 padding fusion on #398's R781 signed-prefix E8 complex program (+0.0166 % over #398)", "created_at": "2026-10-11T08:10:47Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 400, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/400", "title": "Conditional kappa 0.001002683712533373: R781 heterogeneous banks and padding fusion", "created_at": "2026-10-11T08:26:49Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 401, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/401", "title": "research: response-subspace gauges and two-sided normalization, kappa = 1.013310887459710e-3", "created_at": "2026-10-11T08:44:39Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 402, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/402", "title": "Conditional \u03ba = 1.013357935292321\u00b710\u207b\u00b3: exact value-level re-synthesis of two targets on #401's response-subspace R781 E8 complex program (+4.70\u00b710\u207b\u2078 over #401)", "created_at": "2026-10-11T09:05:22Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 403, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/403", "title": "Conditional kappa 0.001013370540420331: 64-replica response-subspace banks", "created_at": "2026-10-11T09:08:49Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 404, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/404", "title": "research: shared-donor chains and overlapping target recovery, conditional kappa = 1.016422320428301e-3", "created_at": "2026-10-11T09:16:42Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 405, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/405", "title": "Conditional kappa 0.001013417593791468: target re-synthesis with 64-replica banks", "created_at": "2026-10-11T09:18:07Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 406, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/406", "title": "Conditional kappa 0.001016469657190768: shared-donor chains with target re-synthesis", "created_at": "2026-10-11T09:26:31Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 407, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/407", "title": "Conditional \u03ba = 1.016526770666368\u00b710\u207b\u00b3: response-gauge re-pivoting (checker-clean) and padding fusion on #404's shared-donor R781 E8 complex program (+5.71\u00b710\u207b\u2078 over #406)", "created_at": "2026-10-11T09:34:29Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 408, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/408", "title": "\u03ba = 1.017022657082799e-3: 205 shared-donor gauges with 64-replica banks", "created_at": "2026-10-11T09:40:25Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 409, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/409", "title": "Conditional kappa 0.001017250500928266: ordered sequential entrance gauges", "created_at": "2026-10-11T09:41:27Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 410, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/410", "title": "\u03ba = 1.017562145187818e-3: enlarged entrance spaces with sequential donor promotion", "created_at": "2026-10-11T09:57:46Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 411, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/411", "title": "\u03ba = 1.017629458064773e-3: exact target-prefix resynthesis on sequential206", "created_at": "2026-10-11T10:02:50Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 412, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/412", "title": "Conditional \u03ba = 1.017776060460931\u00b710\u207b\u00b3: checker-clean composition of sequential and enlarged entrance gauges with re-pivoting and padding fusion (+1.47\u00b710\u207b\u2077 over #411; #406/#408\u2013#410 fail gx E4)", "created_at": "2026-10-11T10:11:42Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 413, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/413", "title": "Candidate conditional kappa 0.001017671197486403: enlarged entrance spaces", "created_at": "2026-10-11T10:12:36Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 415, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/415", "title": "Candidate conditional kappa 0.001017786140030308: enlarged entrances and target prefixes", "created_at": "2026-10-11T10:21:10Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 416, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/416", "title": "\u03ba = 1.017798035290733e-3: propagated frames admit 214 entrance gauges", "created_at": "2026-10-11T10:24:33Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 418, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/418", "title": "Candidate conditional kappa 0.001017923290728024: propagated entrance frames", "created_at": "2026-10-11T10:37:42Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 419, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/419", "title": "Conditional \u03ba = 1.017962405296845\u00b710\u207b\u00b3: checker-clean grouped and frame-closure entrance promotions with a target-124 helper prefix on our #412 word (+3.9\u00b710\u207b\u2078 over #418; #414\u2013#416 fail gx E4/gxcore E5)", "created_at": "2026-10-11T10:40:06Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 422, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/422", "title": "Candidate conditional kappa 0.001018475695250068: grouped entrance capacity and shared-frame enlargement", "created_at": "2026-10-11T10:51:54Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 423, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/423", "title": "\u03ba = 1.018335129864748e-3: fourteen entrance enlargements with shared frame costs", "created_at": "2026-10-11T10:56:01Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 424, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/424", "title": "Conditional \u03ba = 1.018509848057013\u00b710\u207b\u00b3: checker-clean entrance enlargements, closure and rank-two gauges with a target-125 helper prefix on our #419 word (+1.75\u00b710\u207b\u2077 over #423)", "created_at": "2026-10-11T11:10:12Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 425, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/425", "title": "\u03ba = 1.048005508028206e-3: mutable-basis Hamming packets (\u22482^-9.89814; conditional; complex +4.97%)", "created_at": "2026-10-11T11:13:41Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 426, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/426", "title": "Conditional kappa 0.001018766833114736: checker-clean chronological gauges and R767 reuse", "created_at": "2026-10-11T11:17:05Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 429, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/429", "title": "Candidate conditional kappa 0.001019646575559504: R779 gauged helper inlining", "created_at": "2026-10-11T11:28:01Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 431, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/431", "title": "Candidate conditional kappa 0.001056975315151441: Hamming complex and retimed bit composition", "created_at": "2026-10-11T11:38:19Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 433, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/433", "title": "Split centres and source-basis reuse for conditional \u03ba = 0.001120864952258278", "created_at": "2026-10-11T11:54:58Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 434, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/434", "title": "Conditional kappa 0.001249035299298004: hosting-selected rank147 kernel", "created_at": "2026-10-11T12:20:44Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 435, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/435", "title": "\u03ba = 0.001128832830332521: #417's shared-donor kernel on #433's R758 bit word (+0.71%)", "created_at": "2026-10-11T12:21:21Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 436, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/436", "title": "Conditional \u03ba = 1.128983115440183e-3: an E8 bit word with 740 helpers under #433's complex supplier", "created_at": "2026-10-11T12:21:51Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 439, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/439", "title": "Conditional \u03ba = 0.001133928043872860: R740 shared-donor kernel with explicit residual bank routes", "created_at": "2026-10-11T12:46:32Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 440, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/440", "title": "\u03ba = 1.136403735815528e-3: R740 shared-donor kernel with 57 primitive frame changes", "created_at": "2026-10-11T13:04:16Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 441, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/441", "title": "\u03ba = 1.138798055343319e-3: R740 block retiming after shared-donor kernel", "created_at": "2026-10-11T13:17:26Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 445, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/445", "title": "Conditional \u03ba = 0.001263365464781156: eleven-stage R740 hosting with complete row bound", "created_at": "2026-10-11T14:15:35Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 447, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/447", "title": "Conditional \u03ba = 0.001265848755025709: rank147 kernel with eleven-stage hosting", "created_at": "2026-10-11T14:26:32Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 448, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/448", "title": "Under review (split-residual interface): cross-copy idle-axis hosting, one residual on two copies of one idle child; computed \u03ba = 0.001330733966732373 not established", "created_at": "2026-10-11T14:51:42Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 450, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/450", "title": "Conditional \u03ba = 0.001347744547714835: eleven-stage cross-copy hosting with target mixing (+1.278% over #448)", "created_at": "2026-10-11T15:02:31Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 451, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/451", "title": "Conditional \u03ba = 0.001265931727546219: dual eleven-stage whole-residual hosting", "created_at": "2026-10-11T15:06:55Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 453, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/453", "title": "Under review: rank137 cross-copy candidate; inherited operator obstruction", "created_at": "2026-10-11T15:13:36Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 454, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/454", "title": "Conditional \u03ba = 0.001266536148630310: target mixing with whole-residual hosting", "created_at": "2026-10-11T15:43:24Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 456, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/456", "title": "Conditional \u03ba = 0.001266564732900111: seven-replica whole-residual hosting", "created_at": "2026-10-11T16:11:58Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 458, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/458", "title": "Conditional \u03ba = 0.001274032589159993: complex kernel with paid residual adapters", "created_at": "2026-10-11T16:31:37Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 460, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/460", "title": "Conditional \u03ba = 0.001274415506145115: paid complex kernel + rank151 target mixing", "created_at": "2026-10-11T16:42:30Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 461, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/461", "title": "Conditional kappa = 0.001274032592088050: sharper bit bad-class charge on #458", "created_at": "2026-10-11T16:50:06Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 462, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/462", "title": "Conditional \u03ba = 0.001274494971185576: four-replica whole bit hosting", "created_at": "2026-10-11T16:57:22Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 463, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/463", "title": "Conditional \u03ba = 0.001283479303751122: E8 bit word R715 (carrier lower bound + F2 overlap cancellation) with #458's complex supplier (+0.711% over #460)", "created_at": "2026-10-11T16:59:33Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 464, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/464", "title": "Conditional \u03ba = 0.001347744550711765: sharper bit bad-class charge on #450's word", "created_at": "2026-10-11T17:01:11Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 465, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/465", "title": "Conditional kappa = 0.001283479306671789: certified R715 assembly with sharp bit charge", "created_at": "2026-10-11T17:08:50Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 467, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/467", "title": "Conditional \u03ba = 0.001289283116193775: R715 shared kernel, retiming and whole pooling", "created_at": "2026-10-11T17:17:25Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 469, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/469", "title": "Conditional \u03ba = 0.001350580884553120: gate-frame retiming of #450's eleven-stage cross-copy word (+0.2105%)", "created_at": "2026-10-11T17:32:48Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 470, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/470", "title": "Conditional \u03ba = 0.001291474845253222: retimed kernel and reordered R715 deliveries", "created_at": "2026-10-11T17:35:13Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 473, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/473", "title": "Conditional kappa 0.001467289440740487: rank-sector factory on 112 ports", "created_at": "2026-10-11T18:02:57Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 490, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/490", "title": "Conditional \u03ba = 0.001295625678120464: whole-owner GL cover with sharp fallback", "created_at": "2026-10-11T19:58:25Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 496, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/496", "title": "Conditional \u03ba = 0.001332077359286333: pooled whole-owner complex supply", "created_at": "2026-10-11T20:57:04Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 499, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/499", "title": "Retimed complex word (#495) on cross-copy hosting with #493's bit word: conditional \u03ba 1.452948511251494e-3 (stacked on #494)", "created_at": "2026-10-11T21:32:10Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 529, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/529", "title": "Conditional \u03ba = 0.001469603966017302: rank-sector102 on112 ports, fully rebuilt", "created_at": "2026-10-12T01:20:07Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 627, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/627", "title": "Conditional \u03ba = 0.001635749838057164: two factored cold ends on the K492 supplier", "created_at": "2026-10-12T22:38:57Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 629, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/629", "title": "Conditional \u03ba = 0.001635768210079684: four dim-8 hyperplane cold ends per word (h4a) on the K-triangle witness", "created_at": "2026-10-12T23:05:54Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 632, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/632", "title": "Conditional \u03ba = 0.001635877117861902: owner repair on PR627 factored ends", "created_at": "2026-10-12T23:15:58Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 635, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/635", "title": "Conditional \u03ba = 0.001636241501576388: h4a plus PR627's two factored jp8 cold ends", "created_at": "2026-10-12T23:41:56Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 637, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/637", "title": "Conditional \u03ba = 0.001636448463297071: four premix-only dim-8 cold ends (u4) on PR635", "created_at": "2026-10-12T23:56:53Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 641, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/641", "title": "Conditional \u03ba = 0.001636523543003976: cost-neutral pivot swaps with four entering ends (s4) on PR635", "created_at": "2026-10-13T00:36:30Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 643, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/643", "title": "Conditional \u03ba = 0.001636542223442109: second jp8-family supplier replaces the CK call (twin dispatch) on PR637", "created_at": "2026-10-13T00:58:08Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 645, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/645", "title": "Gauge44 factory and whole-family assignment for conditional \u03ba = 0.001649483702558979", "created_at": "2026-10-13T01:13:08Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 648, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/648", "title": "Conditional \u03ba = 0.001651096360425895: repacked owner map on PR645's gauge44 construction", "created_at": "2026-10-13T01:27:30Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 649, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/649", "title": "Conditional \u03ba = 0.001652528731617094: PR589 bit supplier and dissolved owner map on PR645's gauge44 construction", "created_at": "2026-10-13T01:36:57Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 652, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/652", "title": "Conditional \u03ba = 0.001652760598550299: alternating dissolve/gap-merge owner map on the PR649 gauge44 + PR589 package", "created_at": "2026-10-13T01:41:39Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 655, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/655", "title": "Conditional \u03ba = 0.00165395497190225: pivot swaps, entering ends and cold dim-8 ends layered on PR645's gauge44 with PR589", "created_at": "2026-10-13T02:13:00Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 656, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/656", "title": "Conditional \u03ba = 0.001654108529511355: joint two-call owner map on the PR655 gauge44-layered word", "created_at": "2026-10-13T02:15:12Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 658, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/658", "title": "Conditional \u03ba = 0.001654192296855146: joint three- and four-call owners on PR656", "created_at": "2026-10-13T02:34:59Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 659, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/659", "title": "Conditional \u03ba = 0.001656193765416678: gauge44 without K-triangles (56 cold ends), with layered ends", "created_at": "2026-10-13T02:56:07Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 664, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/664", "title": "Conditional \u03ba = 0.00165861362787227: three entrance-promotion groups on the PR659 no-triangle word", "created_at": "2026-10-13T03:17:28Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 858, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/858", "title": "Research: T16 owner concentration raises conditional \u03ba to 0.001661642255531641", "created_at": "2026-10-13T08:00:07Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 1193, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1193", "title": "Conditional \u03ba = 0.001675809683500501: mixed T37 allocation with X54 and fusions", "created_at": "2026-10-13T19:55:47Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 1268, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1268", "title": "Conditional \u03ba = 0.001676021619355108: #1252's idle pair exchanges on #1218's global mixed X54 + fusions construction", "created_at": "2026-10-13T21:27:52Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 1280, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1280", "title": "Conditional \u03ba = 0.001676377648122875: pivot-531 helper-donor cold kernel composed with multi-donor idle 48+48 to 45+51 exchanges on the global mixed X54 fusions word", "created_at": "2026-10-13T21:39:42Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 1305, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1305", "title": "Conditional \u03ba = 0.001677162029073474: four helper-donor cold kernels (pivots 531, 543, 555, 567) composed with multi-donor idle exchanges toward rank 51", "created_at": "2026-10-13T22:14:48Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 1324, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1324", "title": "Conditional \u03ba = 0.001677380107853623: idle rank-48 axis reassignments with simultaneous swaps toward rank 51 on #1305's four cold kernels", "created_at": "2026-10-13T22:40:16Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 1681, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1681", "title": "Conditional \u03ba = 0.001677201606748643: capped phase-cell fusion outer (PR1673) on the pivot-566+554 T74 supplier", "created_at": "2026-10-14T06:35:01Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 1683, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1683", "title": "Conditional \u03ba = 0.001677201747396342: capped phase-cell fusion outer (PR1673) on the pivot-566+554 T74 supplier", "created_at": "2026-10-14T06:47:13Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 1688, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1688", "title": "Conditional \u03ba = 0.001677255458915620: capped phase-cell fusion outer (PR1673) on the pivot-566+554 T74 supplier", "created_at": "2026-10-14T07:04:29Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 1699, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1699", "title": "Conditional \u03ba = 0.001677641731343354: classical matrix boundary with signed554 T74", "created_at": "2026-10-14T07:21:49Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 1712, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1712", "title": "Conditional \u03ba = 0.0016776417313433545: classical-matrix capped phase-cell fusion outer (PR1673 + PR1699's Le Gall tau=12/5) on the pivot-566+554 T74 supplier", "created_at": "2026-10-14T07:31:55Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 1721, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1721", "title": "Conditional \u03ba = 0.001677819902314436: radix-distributed sparse-union schedule on PR1673's capped phase-cell fusion outer (Le Gall tau=2.372864, PR1699) on the pivot-566+554 T74 supplier", "created_at": "2026-10-14T07:52:08Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 1725, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1725", "title": "Conditional \u03ba = 0.001677992607205282: rectangular boundary batching and radix-distributed sparse-union schedule on PR1673's capped phase-cell fusion outer, pivot-566+554 T74 supplier", "created_at": "2026-10-14T08:00:30Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 1731, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1731", "title": "Conditional \u03ba = 0.001678123830633547: rectangular (k=5) boundary batching and radix-distributed sparse-union schedule on PR1673's capped phase-cell fusion outer, pivot-566+554 T74 supplier", "created_at": "2026-10-14T08:06:36Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 1754, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1754", "title": "Conditional \u03ba = 0.001678344171736538: structured (displacement-rank) boundary solves and radix-distributed sparse-union schedule on PR1673's capped phase-cell fusion outer, pivot-566+554 T74 supplier", "created_at": "2026-10-14T08:44:31Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 1758, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1758", "title": "Conditional \u03ba = 0.001679745508802299: gauge-free (fractional-shift) interiors, structured boundary solves and radix-distributed sparse-union schedule on PR1673's capped phase-cell fusion outer, pivot-566+554 T74 supplier", "created_at": "2026-10-14T08:57:20Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 1786, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1786", "title": "Conditional \u03ba = 0.001679754788150048 from fine source-prime padding", "created_at": "2026-10-14T09:58:18Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 1800, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1800", "title": "Conditional \u03ba = 0.001679754956125544: fine source-prime padding (PR1786) at the free epsilon -> 1 point, with gauge-free interiors and the radix-distributed union schedule on PR1673's capped phase-cell 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0.00167975495612554452133567099392070257699831143850258029546032752016286454826032563882630565613: recertified 1e-1000 supplier endpoint and 1e-1010 slacks (kappa +8.11857e-401 over PR1876): fine source-prime padding (PR1786) at the free epsilon -> 1 point, with gauge-free interiors and the radix-distributed union schedule on PR1673's capped phase-cell fusion outer, pivot-566+554 T74 supplier", "created_at": "2026-10-14T13:38:26Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 1905, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1905", "title": "Conditional \u03ba = 0.001679754956125544521335670993920702576998311438502580295460327520162864548260325638826305656132: recertified 1e-3000 supplier endpoint and 1e-3010 slacks (kappa +2.00336e-500 over PR1897): fine source-prime padding (PR1786) at the free epsilon -> 1 point, with gauge-free interiors and the radix-distributed union schedule on PR1673's 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bound: four aliases + 24 entrance raises give \u03ba = 0.001699160892139825", "created_at": "2026-10-15T09:45:22Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 2447, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2447", "title": "Conditional \u03ba = 0.001698511924002761: optimal owner fill on #2435's entrance-raised words", "created_at": "2026-10-15T10:46:40Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 2462, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2462", "title": "Conditional \u03ba = 0.001703552312979594: optimal owner fill for #2436's aliases on the entrance-raised T74 words", "created_at": "2026-10-15T11:25:27Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 2474, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2474", "title": "Conditional \u03ba = 0.001703676387993676: a fifth #2436 alias on the entrance-raised T74 words", "created_at": "2026-10-15T12:00:00Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 2526, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2526", "title": "Conditional \u03ba = 0.001703713039257905: a sixth #2436-type alias (helper 656 borrows lender 88) on the entrance-raised T74 words", "created_at": "2026-10-15T13:36:35Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 2575, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2575", "title": "Conditional \u03ba = 0.001713879320009017: owner evacuation on #2530's source-partner words", "created_at": "2026-10-15T15:03:49Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 2588, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2588", "title": "Conditional \u03ba = 0.001714252039260245: swapped helper labels for lenders 80 and 88 on #2530's source-partner words, with an evacuated owner fill", "created_at": "2026-10-15T15:32:24Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 2673, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2673", "title": "Conditional \u03ba = 0.001714600409398252: priority-ordered window-optimal owner fill on #2588's words", "created_at": "2026-10-15T16:58:17Z", "accepted_at": null, "reason_not_on_acceptance_plot": "No GitHub merge timestamp in the frozen snapshot" }, { "pr": 2679, "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2679", "title": "Conditional \u03ba = 0.0017148565406944334: pre-life hosting and a frame-refit alias on the #2588 T74 words", "created_at": "2026-10-15T17:01:34Z", "accepted_at": null, 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Finite scalar/binary-frame checks alone do not prove the universal operator claim.", "Own common-label/all-column/whole-call/all-size compiler and normalized completed Gaussian endpoint identities.", "New fixed-wiring complete-row realization, complete native scalar/basis/phase/clear work and once-only row padding; only public-size address routing is free.", "Exact dyadic augmented-grid native arithmetic and nonlinear source path guard; completed Gaussian-integer H returns discard only proven-zero fractional guard bits.", "The separately closed nonlinear whole proof pays exact incoming-grid arithmetic, proven-zero guard-bit discard only at complete Gaussian-integer H returns, disjoint complete coefficient-block direct sums and full C0*d^C1 transient height,33p stored words/66p exact products.", "Concrete normalized Gaussian accretivity, bounded scale-aware Schur/finite-LDU, convolution/rounding/boundary/recovery and repaired optimized-reference correctness/halting remain explicit; no false arbitrary-scale theorem or historical BIT expense is used." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "recovered_literal_highwater", "stream_row": 8, "source_index": null, "at": "2026-10-08T08:26:23Z", "until": null, "date_basis": "body-version", "fraction": "6149999/50000000000000", "value_decimal": "1.2299998E-7", "dashboard_float_text": null, "expression": "(6149999)/(50000000000000)", "historical_title": "Batch recursive networks for a conditional kappa > 2^-23 bound", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/10", "evidence_excerpt": "pports the conditional integer-multiplication bound\r\n\r\n\r\nT(n)=O\\left(n(\\log n)^(1-\u03ba)\\right),\\qquad\r\n\u03ba=(6149999)/(50000000000000)>2^(-23).\r\n\r\n\r\n- Batch contiguous rational projector blocks using a simultaneous controlled basis.\r\n- Apply whole complex residuals as recursive calls, with mixed-width row handlin", "automated_comparable": true, "body_sha256": "6b6e9deaf5d2239cf2ccb237d0af81c457a4384fc6a67a3256b546375a0253ac" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/10000000", "own_source_scope": [ "Own selected full all-role physical input/output Gaussian operator identities, required absolute phases and arbitrary dirty auxiliaries restored. Finite scalar/binary-frame checks alone do not prove the universal operator claim.", "Own common-label/all-column/whole-call/all-size compiler and normalized completed Gaussian endpoint identities.", "New fixed-wiring complete-row realization, complete native scalar/basis/phase/clear work and once-only row padding; only public-size address routing is free.", "Exact dyadic augmented-grid native arithmetic and nonlinear source path guard; completed Gaussian-integer H returns discard only proven-zero fractional guard bits.", "The separately closed nonlinear whole proof pays exact incoming-grid arithmetic, proven-zero guard-bit discard only at complete Gaussian-integer H returns, disjoint complete coefficient-block direct sums and full C0*d^C1 transient height,33p stored words/66p exact products.", "Concrete normalized Gaussian accretivity, bounded scale-aware Schur/finite-LDU, convolution/rounding/boundary/recovery and repaired optimized-reference correctness/halting remain explicit; no false arbitrary-scale theorem or historical BIT expense is used." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr10-earliest-selected-gaussian-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 7, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/10-manifest.json", "sha256": "7fe69e279250a23ab573eeed7c89d42acaa64d905f1f358f15f909d06ff3dff1" }, { "file": "remaining-record-audit/artifacts/10/priority-manifest.json", "sha256": "c6748a4319013af26e2cc99a0dd3dd0a53aa801ca7ef50273e67053abd24ea1a" } ], "source_head": "62691e395a0458ce089a1c7b5d89e74291e95e29" } }, { "pr": 24, "title": "Endpoint gauges for a conditional kappa = 5.98615e-6 bound", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/24", "author": "icekylinx", "created_at": "2026-10-08T10:46:30Z", "accepted_at": "2026-10-08T15:18:18Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00000598615", "kappa_fraction": "119723/20000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^2361183242025118417206705651704)", "log2log2_input_bits": "2361183242025118417206705651704", "plot_triple_log": { "exact_log2log2_integer": "2361183242025118417206705651704" }, "source": "data/operation-audit/pr24-nonlinear-native-gaussian-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own complete all-role native circuit, physical entry/output frames and absolute phases on arbitrary dirty data.", "Own nondegenerate binary residual normal forms, normalized completed Gaussian endpoint and all-column/common-label/whole-helper restoration.", "Source complete-row volume and spectator identity, with once-only padding; fixed nonuniform routing replaces compact address descriptors only.", "Named Gaussian analytic/boundary/recovery interfaces and separate nonlinear C1>1 global precision/count proof; no whole-integer upper admitted by this component.", "Concrete normalized Gaussian shifted-kernel accretivity/finite-LDU, narrow/cyclic boundary recovery and complete integer convolution/carry interfaces from the closed direct Gaussian construction remain explicit. The false arbitrary-scale accretive theorem is not used.", "The nonlinear source height C0*d^C1, not completed norm1, is paid in full at every native invocation, including the synchronized factors and outer-transform normalization.", "This new direct Gaussian/Fermat coefficient circuit does not execute the historical source BIT supplier or compact address-descriptor routing. Full native operator/absolute-phase/common-label/owned/complete-row identities remain premises.", "The repaired unlimited optimized-GMP source model and finite-kernel halting are retained; numerical bounds concern this declared source-derived family, not every implementation." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 7, "source_index": null, "at": "2026-10-08T15:18:19Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00000598615", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/24", "evidence_excerpt": "\\kappa=\\frac{119723}{20000000000}=5.98615\\times10^{-6}.", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/10000000", "own_source_scope": [ "Own complete all-role native circuit, physical entry/output frames and absolute phases on arbitrary dirty data.", "Own nondegenerate binary residual normal forms, normalized completed Gaussian endpoint and all-column/common-label/whole-helper restoration.", "Source complete-row volume and spectator identity, with once-only padding; fixed nonuniform routing replaces compact address descriptors only.", "Named Gaussian analytic/boundary/recovery interfaces and separate nonlinear C1>1 global precision/count proof; no whole-integer upper admitted by this component.", "Concrete normalized Gaussian shifted-kernel accretivity/finite-LDU, narrow/cyclic boundary recovery and complete integer convolution/carry interfaces from the closed direct Gaussian construction remain explicit. The false arbitrary-scale accretive theorem is not used.", "The nonlinear source height C0*d^C1, not completed norm1, is paid in full at every native invocation, including the synchronized factors and outer-transform normalization.", "This new direct Gaussian/Fermat coefficient circuit does not execute the historical source BIT supplier or compact address-descriptor routing. Full native operator/absolute-phase/common-label/owned/complete-row identities remain premises.", "The repaired unlimited optimized-GMP source model and finite-kernel halting are retained; numerical bounds concern this declared source-derived family, not every implementation." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr24-nonlinear-native-gaussian-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 12, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/24-manifest.json", "sha256": "02e67df6db8093569e3561dbf904b2587f408701cd1a1847979077dcb13f6e6b" }, { "file": "remaining-record-audit/artifacts/24/priority-manifest.json", "sha256": "59ebb1e916c75ffbe5bc7552b889ba7efaf9a75a45bacf6506e7c7cab16b53c7" } ], "source_head": "ed90fd940279c336ebc45968631bdebfb087b505" } }, { "pr": 32, "title": "Structured projector blocks and bulk assembly for conditional kappa = 1.2523415e-5", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/32", "author": "icekylinx", "created_at": "2026-10-08T11:33:32Z", "accepted_at": "2026-10-08T15:18:18Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.000012523415", "kappa_fraction": "2504683/200000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^2882303833574711477927928)", "log2log2_input_bits": "2882303833574711477927928", "plot_triple_log": { "exact_log2log2_integer": "2882303833574711477927928" }, "source": "data/operation-audit/pr32-structured-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own h30/h40 matched native absolute-phase, simultaneous physical bases, scalar/normalized-wrapper and full public input/output/owned/spectator contracts; original C++ matching and fixed-basis BIT CRT profiler not rerun.", "Own all-size complete common-label Gaussian-dyadic supplier, full three-axis physical profile, C1=1 and sequential full row stock.", "Same Gaussian/fine-prime/finite-section/boundary/recovery analytic and fixed repaired optimized-GMP correctness/halting contracts.", "Preserving original record asymptotic additionally requires own original-record same-XAG realization; no quantified original-tail threshold." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 8, "source_index": null, "at": "2026-10-08T15:18:19Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.000012523415", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/32", "evidence_excerpt": "\\kappa=\\frac{2504683}{200000000000}=1.2523415\\times10^{-5}.", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/1000000", "own_source_scope": [ "Own h30/h40 matched native absolute-phase, simultaneous physical bases, scalar/normalized-wrapper and full public input/output/owned/spectator contracts; original C++ matching and fixed-basis BIT CRT profiler not rerun.", "Own all-size complete common-label Gaussian-dyadic supplier, full three-axis physical profile, C1=1 and sequential full row stock.", "Same Gaussian/fine-prime/finite-section/boundary/recovery analytic and fixed repaired optimized-GMP correctness/halting contracts.", "Preserving original record asymptotic additionally requires own original-record same-XAG realization; no quantified original-tail threshold." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr32-structured-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 56, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "finite-bridge-source-expansion/32-manifest.json", "sha256": "a983ef1544185cf50c2d4c61268a81d4d8ec7febe8fc95923d8a66a6b0864d78" } ], "source_head": "0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52" } }, { "pr": 36, "title": "Copied retained centers and two-stage assembly for conditional kappa = 3.84569e-5", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/36", "author": "icekylinx", "created_at": "2026-10-08T12:27:27Z", "accepted_at": "2026-10-08T15:18:18Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0000384569", "kappa_fraction": "384569/10000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^281475047079400177656)", "log2log2_input_bits": "281475047079400177656", "plot_triple_log": { "exact_log2log2_integer": "281475047079400177656" }, "source": "data/operation-audit/pr36-copied-center-extension-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 9, "source_index": null, "at": "2026-10-08T15:18:19Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.0000384569", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/36", "evidence_excerpt": "\\kappa=\\frac{384569}{10000000000}=3.84569\\times10^{-5}.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 28, "source_index": null, "at": "2026-10-08T12:27:27Z", "until": null, "date_basis": "body-version", "fraction": "384569/10000000000", "value_decimal": "0.0000384569", "dashboard_float_text": null, "expression": "(384569)/(10000000000)", "historical_title": "Copied retained centers and two-stage assembly for conditional kappa = 3.84569e-5", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/36", "evidence_excerpt": "ation framework and those analytic/tape interfaces,\r\n\r\n\r\nT(n)=O\\left(n(\\log n)^(1-\u03ba)\\right),\\qquad\r\n\u03ba=(384569)/(10000000000)=3.84569*10^(-5).\r\n\r\n\r\n## Construction\r\n\r\nThe copied retained-center schedule supplies each scatter from a transformed copy while the original role proceeds directly to cleanup. In", "automated_comparable": true, "body_sha256": "f7e6917818d9eea9816d8a166a7a6b460e02f281062515d81e85c252bc19e0fe" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/100000", "own_source_scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr36-copied-center-extension-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 38, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "copied-center-finite-source/36-invoice-extra-manifest.json", "sha256": "103d5cc7a51cd65443b4d3eb55063eccfab8cb9e293ee62c30c74b0487284289" }, { "file": "copied-center-finite-source/36-manifest.json", "sha256": "c880b69fbac385a33ec20cd42dcf2c6133d7f5861d5b43941e4758357337e0a5" }, { "file": "finite-bridge-source-expansion/36-manifest.json", "sha256": "6157ae37747e9ce4ea6d513a5f60a55762f2935c628eca493e33b87a0f2bf8a4" } ], "source_head": "11817ccacb564bb7f98789c20dc11d3fece207e3" } }, { "pr": 37, "title": "Copied centers and reversed corners for conditional \u03ba = 3.850771033e-5 > 2^-15", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/37", "author": "rohanarun", "created_at": "2026-10-08T12:39:52Z", "accepted_at": "2026-10-08T15:18:18Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00003850771033", "kappa_fraction": "3850771033/100000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^281475047079400177656)", "log2log2_input_bits": "281475047079400177656", "plot_triple_log": { "exact_log2log2_integer": "281475047079400177656" }, "source": "data/operation-audit/pr37-copied-center-reversed-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 10, "source_index": null, "at": "2026-10-08T15:18:19Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00003850771033", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/37", "evidence_excerpt": "**T(n) = O(n (log n)^(1 \u2212 \u03ba)), with \u03ba = 3850771033/10^14 = 3.850771033 \u00d7 10\u207b\u2075 > 2\u207b\u00b9\u2075.**", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 29, "source_index": null, "at": "2026-10-08T12:39:52Z", "until": null, "date_basis": "body-version", "fraction": "3850771033/100000000000000", "value_decimal": "0.00003850771033", "dashboard_float_text": null, "expression": "3850771033/10^14", "historical_title": "Copied centers and reversed corners for conditional \u03ba = 3.850771033e-5 > 2^-15", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/37", "evidence_excerpt": "etained analytic and fixed finite-alphabet multitape hypotheses,\n\nT(n) = O(n (log n)^(1 - \u03ba)), with \u03ba = 3850771033/10^14 = 3.850771033 * 10^-5 > 2^-15.\n\nThis composes icekylinx's copied-center schedule (#36, 11817cc) with James Chang's reversed boundary family (#34, 7fecbe3) at dimensions (23,25) an", "automated_comparable": true, "body_sha256": "acc83fc55d53bf318f1a63b5cab7cfc749a3f63d04a4733aff040de5a51d4bdc" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/100000", "own_source_scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr37-copied-center-reversed-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 23, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "copied-center-finite-source/37-invoice-extra-manifest.json", "sha256": "5065650bb59de282ccd0d9c591922a769bcf797c3666cb84fd21fdfc022ee406" }, { "file": "copied-center-finite-source/37-manifest.json", "sha256": "7140ea6b1a007cfe607f90a76f8bb111916da45838a77e7853f793812efac111" }, { "file": "finite-bridge-source-expansion/37-manifest.json", "sha256": "0deb23ffdf4b335013bfcafff4b188cccfbd62ad30a55dc5358f8b2b8f689d51" }, { "file": "remaining-record-audit/artifacts/37/priority-manifest.json", "sha256": "c1f3988a9705b875b71503b4417a64ede1defd6641b954a0acc6e49f5a4c9c7d" } ], "source_head": "2f7578affce416ad4b6c41f3438ebb734f66a899" } }, { "pr": 39, "title": "Fixed middle basis and copied reversed corners: conditional \u03ba = 3.886675852e-5 > 2^-15", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/39", "author": "rohanarun", "created_at": "2026-10-08T12:58:44Z", "accepted_at": "2026-10-08T15:18:18Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00003886675852", "kappa_fraction": "971668963/25000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^281475047079400177656)", "log2log2_input_bits": "281475047079400177656", "plot_triple_log": { "exact_log2log2_integer": "281475047079400177656" }, "source": "data/operation-audit/pr39-copied-center-reversed-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 6, "source_index": 6, "at": "2026-10-08T15:18:19Z", "until": "2026-10-08T16:19:03Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.00003886675852", "dashboard_float_text": "3.886675852e-05", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/39", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 11, "source_index": null, "at": "2026-10-08T15:18:19Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00003886675852", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/39", "evidence_excerpt": "**T(n) = O(n (log n)^(1 \u2212 \u03ba)), with \u03ba = 971668963/25000000000000 = 3.886675852 \u00d7 10\u207b\u2075 > 2\u207b\u00b9\u2075.**", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 31, "source_index": null, "at": "2026-10-08T12:58:44Z", "until": null, "date_basis": "body-version", "fraction": "971668963/25000000000000", "value_decimal": "0.00003886675852", "dashboard_float_text": null, "expression": "971668963/25000000000000", "historical_title": "Fixed middle basis and copied reversed corners: conditional \u03ba = 3.886675852e-5 > 2^-15", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/39", "evidence_excerpt": "etained analytic and fixed finite-alphabet multitape hypotheses,\n\nT(n) = O(n (log n)^(1 - \u03ba)), with \u03ba = 971668963/25000000000000 = 3.886675852 * 10^-5 > 2^-15.\n\nThis fixes only the middle basis in PR #37's copied reversed (23,25) construction: L25=I+J, with one common generic rational L23. The complete orig", "automated_comparable": true, "body_sha256": "4b30fb8ddc18871d2506a5464994161cf2aa45ff1491aa6c142247f1d83dbb1f" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/100000", "own_source_scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr39-copied-center-reversed-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 23, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "copied-center-finite-source/39-invoice-extra-manifest.json", "sha256": "e6c6b5b307ba5ed646551bed17fe693c701db7eaccbe84df7a5d291dba1e598d" }, { "file": "copied-center-finite-source/39-manifest.json", "sha256": "236a7fb7ee6b2007f30d9b8621834b0a96a52cca11eda72f97ff114869a8d035" }, { "file": "finite-bridge-source-expansion/39-manifest.json", "sha256": "1d685bc5b546c1463f3d9ec7cf6523d8e61652349073b7a87359b7c4c685ada6" }, { "file": "remaining-record-audit/artifacts/39/priority-manifest.json", "sha256": "671ad9a97e6ac2b8d700dc47f241d66b50ef928ee2256d5a1011c8db60cb019b" } ], "source_head": "70ae24129649f6d6d4ec6360962a80c3c42a38f1" } }, { "pr": 18, "title": "Partial-swap networks for a conditional kappa = 1.884586e-6 bound", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/18", "author": "icekylinx", "created_at": "2026-10-08T10:01:42Z", "accepted_at": "2026-10-08T15:18:19Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.000001884586", "kappa_fraction": "942293/500000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^2361183242025118417206705651704)", "log2log2_input_bits": "2361183242025118417206705651704", "plot_triple_log": { "exact_log2log2_integer": "2361183242025118417206705651704" }, "source": "data/operation-audit/pr18-nonlinear-native-gaussian-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own complete all-role native circuit, physical entry/output frames and absolute phases on arbitrary dirty data.", "Own nondegenerate binary residual normal forms, normalized completed Gaussian endpoint and all-column/common-label/whole-helper restoration.", "Source complete-row volume and spectator identity, with once-only padding; fixed nonuniform routing replaces compact address descriptors only.", "Named Gaussian analytic/boundary/recovery interfaces and separate nonlinear C1>1 global precision/count proof; no whole-integer upper admitted by this component.", "Concrete normalized Gaussian shifted-kernel accretivity/finite-LDU, narrow/cyclic boundary recovery and complete integer convolution/carry interfaces from the closed direct Gaussian construction remain explicit. The false arbitrary-scale accretive theorem is not used.", "The nonlinear source height C0*d^C1, not completed norm1, is paid in full at every native invocation, including the synchronized factors and outer-transform normalization.", "This new direct Gaussian/Fermat coefficient circuit does not execute the historical source BIT supplier or compact address-descriptor routing. Full native operator/absolute-phase/common-label/owned/complete-row identities remain premises.", "The repaired unlimited optimized-GMP source model and finite-kernel halting are retained; numerical bounds concern this declared source-derived family, not every implementation." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_chronology": { "own_head": "f2ab41aebad47861caf6316282c1793e5513845e", "created_at": "2026-10-08T10:01:42Z", "merged_at": "2026-10-08T15:18:19Z", "merge_commit_sha": "f2ab41aebad47861caf6316282c1793e5513845e", "merge_parents": [ "62691e395a0458ce089a1c7b5d89e74291e95e29" ], "source_committed_at": "2026-10-08T09:59:58Z", "source_authored_at": "2026-10-08T09:59:58Z", "source_committed_before_or_at_merge": true, "historical_merged_source_chronology_anchored": true, "source_date_chart_policy": "May use actual merged_at for this exact source-head-derived construction; no creation-date backdating.", "source": "data/operation-audit/early-native-source-chronology/primary-chronology.json", "scope": "Primary date/source anchors only; no new mathematical or record-truth claim." }, "historical_streams": [ "current_chart_frontier", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 6, "source_index": null, "at": "2026-10-08T15:18:19Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.000001884586", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/18", "evidence_excerpt": "\\kappa=\\frac{942293}{500000000000}=1.884586\\times10^{-6}.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 14, "source_index": null, "at": "2026-10-08T10:01:42Z", "until": null, "date_basis": "body-version", "fraction": "942293/500000000000", "value_decimal": "0.000001884586", "dashboard_float_text": null, "expression": "(942293)/(500000000000)", "historical_title": "Partial-swap networks for a conditional kappa = 1.884586e-6 bound", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/18", "evidence_excerpt": "er the retained analytic and fixed-tape interfaces,\r\n\r\n\r\nT(n)=O\\left(n(\\log n)^(1-\u03ba)\\right),\\qquad\r\n\u03ba=(942293)/(500000000000)=1.884586*10^(-6).\r\n\r\n\r\nPartial-swap frames remove the source rank penalty, giving s = Wm - 2N + 2L. The binary retained-total triple producer uses dimensions (25,23,57), compatibl", "automated_comparable": true, "body_sha256": "f11762581019ff4e1a76233482c265d7c65b0b2f285515c0e12b494ed913a73a" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/10000000", "own_source_scope": [ "Own complete all-role native circuit, physical entry/output frames and absolute phases on arbitrary dirty data.", "Own nondegenerate binary residual normal forms, normalized completed Gaussian endpoint and all-column/common-label/whole-helper restoration.", "Source complete-row volume and spectator identity, with once-only padding; fixed nonuniform routing replaces compact address descriptors only.", "Named Gaussian analytic/boundary/recovery interfaces and separate nonlinear C1>1 global precision/count proof; no whole-integer upper admitted by this component.", "Concrete normalized Gaussian shifted-kernel accretivity/finite-LDU, narrow/cyclic boundary recovery and complete integer convolution/carry interfaces from the closed direct Gaussian construction remain explicit. The false arbitrary-scale accretive theorem is not used.", "The nonlinear source height C0*d^C1, not completed norm1, is paid in full at every native invocation, including the synchronized factors and outer-transform normalization.", "This new direct Gaussian/Fermat coefficient circuit does not execute the historical source BIT supplier or compact address-descriptor routing. Full native operator/absolute-phase/common-label/owned/complete-row identities remain premises.", "The repaired unlimited optimized-GMP source model and finite-kernel halting are retained; numerical bounds concern this declared source-derived family, not every implementation." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr18-nonlinear-native-gaussian-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 9, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/18-manifest.json", "sha256": "59a5c5683a34b15a59bcaa1c6379d728264816d02cf825849034937438ab3727" }, { "file": "remaining-record-audit/artifacts/18/priority-manifest.json", "sha256": "7648c2239a911f90e49c3f12923d6f5541d0e2583f38a4833becdf1104ab4795" } ], "source_head": "f2ab41aebad47861caf6316282c1793e5513845e" } }, { "pr": 26, "title": "Lean certificate check", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/26", "author": "princezuda", "created_at": "2026-10-08T10:54:03Z", "accepted_at": "2026-10-08T16:46:58Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "8.3E-11", "kappa_fraction": "83/1000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain the exact stated lemma, finite-audit scope, correction or provenance with its actual selected target. A numerical runtime bound requires an actual source-selected full native/owner/recursive invoice/precision/outer realization and exact own commitments. No cutoff follows from unchanged kappa, a scalar lemma or an audit pass." ], "source_manifest": [ { "file": "individual-primary-interface-source/26-manifest.json", "sha256": "d12fa300924bcd99b23826f3ba2106694a77a437b4aa2c8cdb20886ec0d8ae89" }, { "file": "remaining-record-audit/artifacts/26/priority-manifest.json", "sha256": "7ff3a868c71c251be1c8e092eebd8654d7132dc3b8b0970d8b229a4051b14b4a" } ], "source_head": "f764fb98208506354730f6f108a8c87fb679432e" } }, { "pr": 43, "title": "Changed graphs and fixed bases: conditional \u03ba = 4.09953e-5 > 2^-15", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/43", "author": "chafreaky", "created_at": "2026-10-08T13:55:52Z", "accepted_at": "2026-10-08T16:46:58Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0000409953", "kappa_fraction": "409953/10000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^281475047079400177656)", "log2log2_input_bits": "281475047079400177656", "plot_triple_log": { "exact_log2log2_integer": "281475047079400177656" }, "source": "data/operation-audit/pr43-copied-center-extension-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "recovered_literal_highwater", "stream_row": 36, "source_index": null, "at": "2026-10-08T13:55:52Z", "until": null, "date_basis": "body-version", "fraction": "409953/10000000000", "value_decimal": "0.0000409953", "dashboard_float_text": null, "expression": "409953/10000000000", "historical_title": "Changed graphs and fixed bases: conditional \u03ba = 4.09953e-5 > 2^-15", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/43", "evidence_excerpt": " base theorem and the retained analytic and fixed finite-alphabet multitape interfaces, this gives\n\n\u03ba = 409953/10000000000 = 4.09953 * 10^-5 > 2^-15, for T(n) = O(n (log n)^(1-\u03ba)).\n\nThe exponent saving is 6.6006360% above #36 and 1.6202070% above #41 (\u03ba=4.034168124e-5). During final verification, Roha", "automated_comparable": true, "body_sha256": "aa7a31f6684da7795c62c4f60eb10a6108e46f25f65ceff293c7a6ac92173082" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/100000", "own_source_scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr43-copied-center-extension-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 23, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "copied-center-finite-source/43-invoice-extra-manifest.json", "sha256": "0e38725e3eff68a0cfdb51d89efe032b33e270db5f80e79d0d23920492ec3ffe" }, { "file": "copied-center-finite-source/43-manifest.json", "sha256": "5edc98ad09caea1d9c353ad9f0cad49b4a86ded703e83c33ff335a206896d8ef" }, { "file": "finite-bridge-source-expansion/43-manifest.json", "sha256": "4ef3fd57d913e1ede72b25a58af772633376d249a345a77df6783afa365648c2" }, { "file": "remaining-record-audit/artifacts/43/priority-manifest.json", "sha256": "97c704cada9d1a7ed98875fe6ea0d673bbc1c1a81c074a745e7987e46a644090" } ], "source_head": "c0fbfd3cc4fd6e95cef54ab307dfb50c69dd96f6" } }, { "pr": 46, "title": "Weighted matching and exact data recovery: conditional \u03ba = 4.10062945e-5", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/46", "author": "chafreaky", "created_at": "2026-10-08T14:44:04Z", "accepted_at": "2026-10-08T16:46:58Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0000410062945", "kappa_fraction": "82012589/2000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^281475047079400177656)", "log2log2_input_bits": "281475047079400177656", "plot_triple_log": { "exact_log2log2_integer": "281475047079400177656" }, "source": "data/operation-audit/pr46-copied-center-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 7, "source_index": 8, "at": "2026-10-08T16:46:58Z", "until": "2026-10-08T16:46:59Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.0000410062945", "dashboard_float_text": "4.10062945e-05", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/46", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 12, "source_index": null, "at": "2026-10-08T16:46:58Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.0000410062945", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/46", "evidence_excerpt": "**\u03ba = 82012589/2000000000000 = 0.0000410062945 > 2^-15**, with bit saving **410079761/10000000000000**.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 38, "source_index": null, "at": "2026-10-08T14:44:04Z", "until": null, "date_basis": "body-version", "fraction": "82012589/2000000000000", "value_decimal": "0.0000410062945", "dashboard_float_text": null, "expression": "82012589/2000000000000", "historical_title": "Weighted matching and exact data recovery: conditional \u03ba = 4.10062945e-5", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/46", "evidence_excerpt": "44 with exact rational recovery of all ten data-corner fallbacks. It gives the conditional witness\n\n\u03ba = 82012589/2000000000000 = 0.0000410062945 > 2^-15, with bit saving 410079761/10000000000000.\n\nThis is 6.6292252% above #36, 0.0268189% above #43, and 0.00000477975% above #44 (an absolute increment of 1.", "automated_comparable": true, "body_sha256": "b4a5046250f2a3d2f02ceeaa469a001047bfcc7d4306abbeb59cb3d10def5d95" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/100000", "own_source_scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; 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acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^281475047079400177656)", "log2log2_input_bits": "281475047079400177656", "plot_triple_log": { "exact_log2log2_integer": "281475047079400177656" }, "source": "data/operation-audit/pr48-copied-center-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 13, "source_index": null, "at": "2026-10-08T16:46:59Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.0000411862541", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/48", "evidence_excerpt": "**\u03ba = 411862541/10000000000000 = 4.11862541e-5 > 2^-15**,", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 40, "source_index": null, "at": "2026-10-08T15:14:53Z", "until": null, "date_basis": "body-version", "fraction": "411862541/10000000000000", "value_decimal": "0.0000411862541", "dashboard_float_text": null, "expression": "411862541/10000000000000", "historical_title": "Reordered exclusion sums: conditional \u03ba = 4.11862541e-5", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/48", "evidence_excerpt": "77,530,859. Under the inherited OpenAI base theorem and analytic/fixed-tape interfaces, this gives\n\n\u03ba = 411862541/10000000000000 = 4.11862541e-5 > 2^-15,\nwith bit saving 82375901/2000000000000.\n\nThis is 7.0971766% above #36, 0.4388585% above our previous #46, and 0.3293163% above Rohan Arun's contemporaneou", "automated_comparable": true, "body_sha256": "399eb88ea6b3a5099ee1eb43ee7df27e1e4096c6dddf437d2d1ec90a55cf7c4e" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/100000", "own_source_scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; 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C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr49-copied-center-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 14, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "copied-center-finite-source/49-invoice-extra-manifest.json", "sha256": "4cc79cc81bd462e88ff020c90a2d281bda2f36c9f88cef8433bcac64a92930c3" }, { "file": "copied-center-finite-source/49-manifest.json", "sha256": "543fccdc65f773e149a2628c4bd841239d05e261c838e87d017c72a263b71404" }, { "file": "finite-bridge-source-expansion/49-manifest.json", "sha256": "8ac78886cca3350cbf358d7f4e30eacd771986ce9fd73e5ba79181ac35615e59" } ], "source_head": "f95d2910e027495983b53cae1693cf535abf2569" } }, { "pr": 55, "title": "Dual suffix-skip strips: conditional \u03ba = 4541011/10^11 > 2^-15", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/55", "author": "gupt1156", "created_at": "2026-10-08T17:05:20Z", "accepted_at": "2026-10-08T18:35:33Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00004541011", "kappa_fraction": "4541011/100000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; 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no numeric original-record tail cutoff." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 16, "source_index": null, "at": "2026-10-08T18:35:34Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00004136014808", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/52", "evidence_excerpt": "$$T(n)=O(n(\\log n)^{1-\\kappa}),\\qquad\\kappa=\\frac{4136014808}{10^{14}}=4.136014808\\times10^{-5}>2^{-15}.$$", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/100000", "own_source_scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr52-copied-center-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 14, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "copied-center-finite-source/52-invoice-extra-manifest.json", "sha256": "ce80975435088bc397ce36f1ec330f40685737230e90d9c38887ce21c5032c82" }, { "file": "copied-center-finite-source/52-manifest.json", "sha256": "285783d2f3bda876edae98164149e02c176558c725cb310dd454bb171bf66fa6" }, { "file": "finite-bridge-source-expansion/52-manifest.json", "sha256": "3ef4e9e645c58dffaef894d4d1560e0285f63cfea9762d675162dbea98280ad8" } ], "source_head": "5b58921c9757ffc48663ae010322c0f2a679b2ce" } }, { "pr": 53, "title": "Skip-prefix strips: conditional \u03ba = 4498144/10^11 > 2^-15", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/53", "author": "ikeboy", "created_at": "2026-10-08T16:31:14Z", "accepted_at": "2026-10-08T18:35:34Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00004498144", "kappa_fraction": "140567/3125000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^281475047079400177656)", "log2log2_input_bits": "281475047079400177656", "plot_triple_log": { "exact_log2log2_integer": "281475047079400177656" }, "source": "data/operation-audit/pr53-copied-center-extension-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 17, "source_index": null, "at": "2026-10-08T18:35:34Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00004498144", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/53", "evidence_excerpt": "**\u03ba = 4498144/10^11 \u2248 4.498144\u00d710\u207b\u2075 > 2\u207b\u00b9\u2075**, conditional on OpenAI's base theorem and the retained analytic and fixed-tape interfaces. That is **9.2146906% above #48** (411862541/10^13), which it builds on. It is also 7.8378235% above the highest open claim at the time of writing, #51 (4171211781/10^14); #49 and #50 claim 4.123863984e-5 and 4.129418696e-5. The exact bit saving is 4498347/10^11.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 44, "source_index": null, "at": "2026-10-08T16:31:14Z", "until": null, "date_basis": "body-version", "fraction": "140567/3125000000", "value_decimal": "0.00004498144", "dashboard_float_text": null, "expression": "4498144/10^11", "historical_title": "Skip-prefix strips: conditional \u03ba = 4498144/10^11 > 2^-15", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/53", "evidence_excerpt": "\u03ba = 4498144/10^11 \u2248 4.498144*10^-5 > 2^-15, conditional on OpenAI's base theorem and the retained analytic and fixed-tape interfaces. That is 9.2146906% above #48 (411862541/10^13), which it builds", "automated_comparable": true, "body_sha256": "52169a5368c894c6e58c60eb2dbb8af2f0a5d8e87c67bf6d60bad27acf188b72" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/100000", "own_source_scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr53-copied-center-extension-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 14, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "copied-center-finite-source/53-invoice-extra-manifest.json", "sha256": "e18bf0df2ab6497cce1d4075ac1d82f8aebca536ede9dacc49c0b9b5bba956f1" }, { "file": "copied-center-finite-source/53-manifest.json", "sha256": "225f65fe24b9a10dceb1b43a361b763a3594dba7ce8f65d3ee7494ca95d72a5f" }, { "file": "finite-bridge-source-expansion/53-manifest.json", "sha256": "7d515e72f82b21f09544a67787fae6398ddff24dfea6e0460c8ca50bd963c4dd" }, { "file": "remaining-record-audit/artifacts/53/priority-manifest.json", "sha256": "e7302e563d0560a12b1340d2082db654d6a0be01ac032a083964208309aa863d" } ], "source_head": "3ffd4021995c959ac02d12920e0279ae97dd03c7" } }, { "pr": 54, "title": "Paid clones on skip-prefix strips: conditional \u03ba = 4.529040672e-5", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/54", "author": "chafreaky", "created_at": "2026-10-08T16:41:24Z", "accepted_at": "2026-10-08T18:35:34Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00004529040672", "kappa_fraction": "141532521/3125000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^281475047079400177656)", "log2log2_input_bits": "281475047079400177656", "plot_triple_log": { "exact_log2log2_integer": "281475047079400177656" }, "source": "data/operation-audit/pr54-copied-center-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 18, "source_index": null, "at": "2026-10-08T18:35:34Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00004529040672", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/54", "evidence_excerpt": "\\kappa=\\frac{141532521}{3125000000000}=4.529040672\\times10^{-5}>2^{-15}.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 45, "source_index": null, "at": "2026-10-08T16:41:24Z", "until": null, "date_basis": "body-version", "fraction": "141532521/3125000000000", "value_decimal": "0.00004529040672", "dashboard_float_text": null, "expression": "(141532521)/(3125000000000)", "historical_title": "Paid clones on skip-prefix strips: conditional \u03ba = 4.529040672e-5", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/54", "evidence_excerpt": "e/cover envelopes. The resulting conditional bound is\n\n\\[\nT(n)=O\\left(n(\\log n)^(1-\u03ba)\\right),\\qquad\n\u03ba=(141532521)/(3125000000000)=4.529040672*10^(-5)>2^(-15).\n\\]\n\nThis is 0.686876% above #53 and 17.769260% above #36. The exact bit saving is 1132311451/25000000000000. This branch builds on #53 (3ffd4021995c95", "automated_comparable": true, "body_sha256": "853ee44b0ff1b2a49fb332db095fc79d604be76f2abe384743df2beab9d3a7f3" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/100000", "own_source_scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr54-copied-center-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 35, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "copied-center-finite-source/54-invoice-extra-manifest.json", "sha256": "7134005d07dca6ac47952c99d69b13fc6d27562069f6161cb9071aff72f1a6f7" }, { "file": "copied-center-finite-source/54-manifest.json", "sha256": "0869a5a7bb84ce1ad2b651fb35e0728206d42e3e14521d58814e6371fdca0b3c" }, { "file": "finite-bridge-source-expansion/54-manifest.json", "sha256": "608b2ca172d3448490eea736b95d72b6a453cdac5c4b9f78e78bfcff5434cdcb" }, { "file": "remaining-record-audit/artifacts/54/priority-manifest.json", "sha256": "a6ed0977fea68a6ab080382fd13261d9d44d66cf5bce4cb93ca2ea4e52015e4c" } ], "source_head": "1d1bb12d4ded9986c7fc064d1e805d856a6d35e6" } }, { "pr": 56, "title": "Positive frames and paid clones on skip-prefix graphs for a conditional \u03ba = 4.548671376e-5 bound", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/56", "author": "rohanarun", "created_at": "2026-10-08T17:06:10Z", "accepted_at": "2026-10-08T18:35:34Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00004548671376", "kappa_fraction": "284291961/6250000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^281475047079400177656)", "log2log2_input_bits": "281475047079400177656", "plot_triple_log": { "exact_log2log2_integer": "281475047079400177656" }, "source": "data/operation-audit/pr56-copied-center-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 20, "source_index": null, "at": "2026-10-08T18:35:34Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00004548671376", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/56", "evidence_excerpt": "$$T(n)=O(n(\\log n)^{1-\\kappa}),\\qquad\\kappa=\\frac{4548671376}{10^{14}}=4.548671376\\times10^{-5}.$$", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 47, "source_index": null, "at": "2026-10-08T17:06:10Z", "until": null, "date_basis": "opening-title", "fraction": "284291961/6250000000000", "value_decimal": "0.00004548671376", "dashboard_float_text": null, "expression": "4.548671376e-5", "historical_title": "Positive frames and paid clones on skip-prefix graphs for a conditional \u03ba = 4.548671376e-5 bound", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/56", "evidence_excerpt": "Positive frames and paid clones on skip-prefix graphs for a conditional \u03ba = 4.548671376e-5 bound", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/100000", "own_source_scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr56-copied-center-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 14, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "copied-center-finite-source/56-invoice-extra-manifest.json", "sha256": "8747ab3e27e2cefea914bb172290085d26c90522aaf4238000e704996e3d1d8f" }, { "file": "copied-center-finite-source/56-manifest.json", "sha256": "0b50c91285a23d1bb4400eb4e5c2360243591eb8ec3ece81492e87697faa53b0" }, { "file": "finite-bridge-source-expansion/56-manifest.json", "sha256": "af2eea650f08958022a4e7b9db729a9c4e5ff888fdd796eb022c530cf6ceea3f" } ], "source_head": "f2b10023c2309b11a77d67dcea7da97ad735ed7e" } }, { "pr": 57, "title": "Joint frame compiler: conditional \u03ba = 4.669442391e-5", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/57", "author": "eumemic", "created_at": "2026-10-08T17:07:21Z", "accepted_at": "2026-10-08T18:35:34Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00004669442391", "kappa_fraction": "4669442391/100000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^281475047079400177656)", "log2log2_input_bits": "281475047079400177656", "plot_triple_log": { "exact_log2log2_integer": "281475047079400177656" }, "source": "data/operation-audit/pr57-copied-center-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "recovered_literal_highwater", "stream_row": 48, "source_index": null, "at": "2026-10-08T17:07:21Z", "until": null, "date_basis": "body-version", "fraction": "4669442391/100000000000000", "value_decimal": "0.00004669442391", "dashboard_float_text": null, "expression": "4669442391/10^14", "historical_title": "Joint frame compiler: \u03ba \u2248 4669442391/10\u00b9\u2074 > 2\u207b\u00b9\u2075 (conditional)", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/57", "evidence_excerpt": "ible binary map and retired signal components are reclaimed. The resulting conditional witness is:\n\n\u03ba \u2248 4669442391/10^14 > 2^-15 (exactly 4669442391/100000000000000).\n\nThis is 2.8283% above the newly opened #55, 3.1000% above #54, and 3.8082% above #53, comparing their stated conditional exponent sa", "automated_comparable": true, "body_sha256": "e340a6840bda9972924cdd2062930a8c7ec2b0ebf33c9095d08081509ae0f077" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/100000", "own_source_scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr57-copied-center-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 18, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "copied-center-finite-source/57-invoice-extra-manifest.json", "sha256": "a2666632e40b7c7af1cc4f37e894bae3183e6144581c9d9c741de7ca39bb6f96" }, { "file": "copied-center-finite-source/57-manifest.json", "sha256": "86d0eb2f5cb0295d583011746e4dccd8799ebe9ecddcf901da775eb9abcfe095" }, { "file": "finite-bridge-source-expansion/57-manifest.json", "sha256": "43b63a931c1d54096056b49dc49f39f59846065d846b2b65477c55dc37503199" }, { "file": "remaining-record-audit/artifacts/57/priority-manifest.json", "sha256": "80e8e4378745c1516298abd31f1287f740fa4df6b7af04fae9490ba492811249" } ], "source_head": "47916b3bf2895c117f8b53ffff4732f67178a132" } }, { "pr": 58, "title": "Joint frames on dual-suffix strips: conditional \u03ba = 4.75073569e-5", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/58", "author": "chafreaky", "created_at": "2026-10-08T17:24:40Z", "accepted_at": "2026-10-08T18:35:34Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0000475073569", "kappa_fraction": "475073569/10000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^281475047079400177656)", "log2log2_input_bits": "281475047079400177656", "plot_triple_log": { "exact_log2log2_integer": "281475047079400177656" }, "source": "data/operation-audit/pr58-copied-center-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 21, "source_index": null, "at": "2026-10-08T18:35:34Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.0000475073569", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/58", "evidence_excerpt": "\\kappa=\\frac{475073569}{10^{13}}=4.75073569\\times10^{-5}>2^{-15}.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 49, "source_index": null, "at": "2026-10-08T17:24:40Z", "until": null, "date_basis": "opening-title", "fraction": "475073569/10000000000000", "value_decimal": "0.0000475073569", "dashboard_float_text": null, "expression": "4.75073569e-5", "historical_title": "Joint frames on dual-suffix strips: conditional \u03ba = 4.75073569e-5", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/58", "evidence_excerpt": "Joint frames on dual-suffix strips: conditional \u03ba = 4.75073569e-5", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/100000", "own_source_scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr58-copied-center-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 29, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "copied-center-finite-source/58-invoice-extra-manifest.json", "sha256": "071865f02ad06be918efc61622ee57a9f304a25ed74a25ad9a6045aafe1875a8" }, { "file": "copied-center-finite-source/58-manifest.json", "sha256": "eac55a693fc8cbd8af5d6bd42518f1cb9b94a8a9f77e1376000aa940e5518777" }, { "file": "finite-bridge-source-expansion/58-manifest.json", "sha256": "4d23b6fbb4f87096187cec8d1b2893621405b00f193c60ea6fbbe84310cad228" }, { "file": "remaining-record-audit/artifacts/58/priority-manifest.json", "sha256": "584770958257104c71d4e184d569b5409f564dff6588d896836eee9169618af4" } ], "source_head": "be5d3e6e39ad9a11372f168e37466af412e51e53" } }, { "pr": 60, "title": "Ranked slot reclamation: conditional \u03ba = 4.764513337e-5", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/60", "author": "chafreaky", "created_at": "2026-10-08T17:40:30Z", "accepted_at": "2026-10-08T18:36:42Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00004764513337", "kappa_fraction": "4764513337/100000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^281475047079400177656)", "log2log2_input_bits": "281475047079400177656", "plot_triple_log": { "exact_log2log2_integer": "281475047079400177656" }, "source": "data/operation-audit/pr60-copied-center-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "recovered_literal_highwater", "stream_row": 50, "source_index": null, "at": "2026-10-08T17:40:30Z", "until": null, "date_basis": "opening-title", "fraction": "4764513337/100000000000000", "value_decimal": "0.00004764513337", "dashboard_float_text": null, "expression": "4.764513337e-5", "historical_title": "Ranked slot reclamation: conditional \u03ba = 4.764513337e-5", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/60", "evidence_excerpt": "Ranked slot reclamation: conditional \u03ba = 4.764513337e-5", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/100000", "own_source_scope": [ "Own matched physical scalar/frame/absolute-phase and copied-stream scheduling correctness, simultaneous bases and owned/spectator interface; C++ matching not freshly replayed.", "Own all-size exact common-label dyadic supplier realization with C1=1 and full sequential row-stock/guard semantics.", "Gaussian/fine-prime/finite-section/boundary/exact-recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires own original-record same-XAG realization; no numeric original-record tail cutoff." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr60-copied-center-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 32, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "copied-center-finite-source/60-invoice-extra-manifest.json", "sha256": "c7e3c06364440e97b74e08fe288921deb2403fb31d56b0c190593a4009fb9fd3" }, { "file": "copied-center-finite-source/60-manifest.json", "sha256": "42553a5a5cbe834828281dca84e5efc3060fff38d8f72f72796c49ddf0138613" }, { "file": "finite-bridge-source-expansion/60-manifest.json", "sha256": "14a02876e78f9beed3de929960eabe1fc57b5ba69423f88d9e17a98f679b4220" }, { "file": "remaining-record-audit/artifacts/60/priority-manifest.json", "sha256": "e6f8ec8e7f786ed40ee3cd57a3e4eb94f473893a8a31b4077a48278d372e99d7" } ], "source_head": "21a121960644b8c6fdf9c06fe39dea1944dd2231" } }, { "pr": 149, "title": "Integrate reviewed PR144: conditional kappa = 0.0004609169", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/149", "author": "Mister-Meeseeks", "created_at": "2026-10-09T04:53:53Z", "accepted_at": "2026-10-09T05:06:00Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0004609169", "kappa_fraction": "4609169/10000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr149-finite-controller-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own native/full-group/arbitrary-column scalar and absolute-phase identities, sharing and complete spectator/owned restoration.", "Own source unequal-child batching, once-only padding, fixed odd-grid and completed-child semantic C1=1 interfaces.", "Parameterized Gaussian/fine-prime/finite-section/boundary/recovery analytic branch.", "Exact fixed small-rational and odd-grid fixed-divisor conversion conditions, including endpoint divisibility and stored-width guards.", "Unchanged optimized-GMP finite-native correctness/halting and model contracts.", "Optional original-record asymptotic preservation requires own original-record same-XAG realization; original-record numerical tail remains unquantified." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own native/full-group/arbitrary-column scalar and absolute-phase identities, sharing and complete spectator/owned restoration.", "Own source unequal-child batching, once-only padding, fixed odd-grid and completed-child semantic C1=1 interfaces.", "Parameterized Gaussian/fine-prime/finite-section/boundary/recovery analytic branch.", "Exact fixed small-rational and odd-grid fixed-divisor conversion conditions, including endpoint divisibility and stored-width guards.", "Unchanged optimized-GMP finite-native correctness/halting and model contracts.", "Optional original-record asymptotic preservation requires own original-record same-XAG realization; original-record numerical tail remains unquantified." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr149-finite-controller-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 56, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "early-native-producer-source/149-manifest.json", "sha256": "cf8f723f8f15406b756f00bf20dc4e0d23829b0763cdb5443258d98566584bb0" }, { "file": "finite-bridge-source-expansion/149-manifest.json", "sha256": "e73da0eb482e63534b370bcb9ff60682f58110f7c0fe415a98d96b12c0df1ee2" }, { "file": "remaining-record-audit/artifacts/149/priority-manifest.json", "sha256": "f83525dca81733be65880d93959e8598bfc6d044c95522f14cbf7e55523ca969" } ], "source_head": "6aed8701e3e3102898c66b5dcfc28d3cfc264edc" } }, { "pr": 104, "title": "Stopped product-ring interchange and rational centers for conditional kappa = 7.79476e-5", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/104", "author": "icekylinx", "created_at": "2026-10-08T23:12:03Z", "accepted_at": "2026-10-09T05:06:02Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0000779476", "kappa_fraction": "194869/2500000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^281475047079400177656)", "log2log2_input_bits": "281475047079400177656", "plot_triple_log": { "exact_log2log2_integer": "281475047079400177656" }, "source": "data/operation-audit/pr104-odd21-finite-controller-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own original C++ scalar/frame/matching producer, absolute phase, normalized-wrapper, whole-job and owned/spectator correctness; not freshly replayed here.", "Own exact common21-odd grid, completed Gaussian-dyadic endpoint/new-child odd divisibility, C1=1 and all-size/common-label realization.", "Gaussian/fine-prime/finite-section/boundary/recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility requires an extra same-XAG realization contract; no numerical original-tail bound." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "recovered_literal_highwater", "stream_row": 79, "source_index": null, "at": "2026-10-08T23:12:03Z", "until": null, "date_basis": "body-version", "fraction": "194869/2500000000", "value_decimal": "0.0000779476", "dashboard_float_text": null, "expression": "(194869)/(2500000000)", "historical_title": "Stopped product-ring interchange and rational centers for conditional kappa = 7.79476e-5", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/104", "evidence_excerpt": "plication framework and those analytic/tape interfaces,\n\n\nT(n)=O\\left(n(\\log n)^(1-\u03ba)\\right),\\qquad\n\u03ba=(194869)/(2500000000)=7.79476*10^(-5).\n\n\n## Construction\n\nThe bit network uses (23,23). A common generic rational basis and opposite bank orders reduce each rank-r projector residual to one contiguous ", "automated_comparable": true, "body_sha256": "d9b59b73df8fa603b64d4f7c8d6e24ce4448531da0277e09a7a464d2e6fdf10c" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/100000", "own_source_scope": [ "Own original C++ scalar/frame/matching producer, absolute phase, normalized-wrapper, whole-job and owned/spectator correctness; not freshly replayed here.", "Own exact common21-odd grid, completed Gaussian-dyadic endpoint/new-child odd divisibility, C1=1 and all-size/common-label realization.", "Gaussian/fine-prime/finite-section/boundary/recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility requires an extra same-XAG realization contract; no numerical original-tail bound." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr104-odd21-finite-controller-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 46, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "early-native-producer-source/104-manifest.json", "sha256": "b88afc1a1e3440f44632d895ab014c611d24b9485175bfbc92e02a09372f0872" }, { "file": "remaining-record-audit/artifacts/104/priority-manifest.json", "sha256": "5e5424bec05ae052db8b901e435e8697f7e86a9e50c28e44656cbf7e565ed081" } ], "source_head": "948ce1510df750f4c18b96bdaef436a86f8bf834" } }, { "pr": 115, "title": "Partial source gauges and cube producers for conditional kappa = 9.26336e-5", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/115", "author": "icekylinx", "created_at": "2026-10-09T00:26:56Z", "accepted_at": "2026-10-09T05:06:02Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0000926336", "kappa_fraction": "7237/78125000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^281475047079400177656)", "log2log2_input_bits": "281475047079400177656", "plot_triple_log": { "exact_log2log2_integer": "281475047079400177656" }, "source": "data/operation-audit/pr115-odd21-partial-gauge-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own original C++ scalar/frame/matching producer, absolute phase, normalized-wrapper, whole-job and owned/spectator correctness; not freshly replayed here.", "Own exact common21-odd grid, completed Gaussian-dyadic endpoint/new-child odd divisibility, C1=1 and all-size/common-label realization.", "Gaussian/fine-prime/finite-section/boundary/recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires an own same-XAG realization contract; numerical original-record tail remains unquantified." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/100000", "own_source_scope": [ "Own original C++ scalar/frame/matching producer, absolute phase, normalized-wrapper, whole-job and owned/spectator correctness; not freshly replayed here.", "Own exact common21-odd grid, completed Gaussian-dyadic endpoint/new-child odd divisibility, C1=1 and all-size/common-label realization.", "Gaussian/fine-prime/finite-section/boundary/recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility additionally requires an own same-XAG realization contract; numerical original-record tail remains unquantified." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr115-odd21-partial-gauge-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 77, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "early-native-producer-source/115-manifest.json", "sha256": "266dd8513cb76b3804c966fbd9ee0737a15c34d9bbefb812452101d43cae7dd4" }, { "file": "finite-bridge-source-expansion/115-manifest.json", "sha256": "83f29f615a8ebbc7c6ff01fe199c4e86762862fa81c3e8d4def2a2099eeb5928" } ], "source_head": "cf60442983c153a3a0f5272ea4713f99eba13c86" } }, { "pr": 130, "title": "Three-stage Cayley covers for conditional kappa = 3.146011e-4 > 2^-12", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/130", "author": "icekylinx", "created_at": "2026-10-09T02:29:02Z", "accepted_at": "2026-10-09T05:06:02Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0003146011", "kappa_fraction": "3146011/10000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^281475047079400177656)", "log2log2_input_bits": "281475047079400177656", "plot_triple_log": { "exact_log2log2_integer": "281475047079400177656" }, "source": "data/operation-audit/pr130-odd21-finite-controller-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own original C++ scalar/frame/matching producer, absolute phase, normalized-wrapper, whole-job and owned/spectator correctness; not freshly replayed here.", "Own exact common21-odd grid, completed Gaussian-dyadic endpoint/new-child odd divisibility, C1=1 and all-size/common-label realization.", "Gaussian/fine-prime/finite-section/boundary/recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility requires an extra same-XAG realization contract; no numerical original-tail bound." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "recovered_literal_highwater", "stream_row": 99, "source_index": null, "at": "2026-10-09T02:29:02Z", "until": null, "date_basis": "body-version", "fraction": "3146011/10000000000", "value_decimal": "0.0003146011", "dashboard_float_text": null, "expression": "(3146011)/(10000000000)", "historical_title": "Three-stage Cayley covers for conditional kappa = 3.146011e-4 > 2^-12", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/130", "evidence_excerpt": "plication framework and those analytic/tape interfaces,\n\n\nT(n)=O\\left(n(\\log n)^(1-\u03ba)\\right),\\qquad\n\u03ba=(3146011)/(10000000000)=3.146011*10^(-4).\n\n\n## Construction\n\nThe global architecture uses three invocation banks on a regular Cayley cover in dimension 3h-2. Each local port retains its source line while", "automated_comparable": true, "body_sha256": "908bdb229b4c9ece1a71dccedb084cdade92b268233b1e92cdb463b695776f4b" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/100000", "own_source_scope": [ "Own original C++ scalar/frame/matching producer, absolute phase, normalized-wrapper, whole-job and owned/spectator correctness; not freshly replayed here.", "Own exact common21-odd grid, completed Gaussian-dyadic endpoint/new-child odd divisibility, C1=1 and all-size/common-label realization.", "Gaussian/fine-prime/finite-section/boundary/recovery analytic branch and fixed comparator correctness/halting interfaces.", "Original-record asymptotic compatibility requires an extra same-XAG realization contract; no numerical original-tail bound." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr130-odd21-finite-controller-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 63, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "early-native-producer-source/130-manifest.json", "sha256": "a776fe24a579a278ce83c350814d122f728ac8ee993149dc4c889475c53fd7c6" }, { "file": "remaining-record-audit/artifacts/130/priority-manifest.json", "sha256": "b79ebf6abb7a552b605206da9b9a935cb787fe0b0bd48e2de9f8cf1dd4bde509" } ], "source_head": "6a9970a530119174507904e23592fd59ede19a5d" } }, { "pr": 144, "title": "Paired cubes and shared completed cores for conditional kappa = 4.609169e-4", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/144", "author": "icekylinx", "created_at": "2026-10-09T04:19:35Z", "accepted_at": "2026-10-09T05:06:02Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0004609169", "kappa_fraction": "4609169/10000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr144-finite-controller-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": "['Own native/full-group/arbitrary-column scalar and absolute-phase identities, sharing and complete spectator/owned restoration.', 'Own source unequal-child batching, once-only padding, fixed odd-grid and completed-child semantic C1=1 interfaces.', 'Parameterized Gaussian/fine-prime/finite-section/boundary/recovery analytic branch.', 'Exact fixed small-rational and odd-grid fixed-divisor conversion conditions, including endpoint divisibility and stored-width guards.', 'Unchanged optimized-GMP finite-native correctness/halting and model contracts.', 'Original-record asymptotic compatibility requires an extra retained same-XAG realization contract; no numerical original-tail bound is supplied.'] Supplemental75-guard replay corrects the earlier extracted-function argument-order evidence; every guard passes and the cutoff is unchanged." }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "recovered_literal_highwater", "stream_row": 110, "source_index": null, "at": "2026-10-09T04:19:35Z", "until": null, "date_basis": "body-version", "fraction": "4609169/10000000000", "value_decimal": "0.0004609169", "dashboard_float_text": null, "expression": "(4609169)/(10000000000)", "historical_title": "Paired cubes and shared completed cores for conditional kappa = 4.609169e-4", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/144", "evidence_excerpt": "plication framework and those analytic/tape interfaces,\n\n\nT(n)=O\\left(n(\\log n)^(1-\u03ba)\\right),\\qquad\n\u03ba=(4609169)/(10000000000)=4.609169*10^(-4).\n\n\n## Construction\n\nThe new complex local motif uses twelve coordinate pairs and 1,760 ports grouped into eight-port cubes. Its scalar identity is I=K+H+B: signed", "automated_comparable": true, "body_sha256": "16fe6a46a36664411dbfbd2a395f9a00dcfb439c45838f883febe76232d10081" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "90446448750933/125000000000000000", "status": "Published on main: maintainer-reviewed conditional construction", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/gen4-pr279.json", "path": "certificates/checkpoints/gen4-pr279.json", "commit": null, "at": null, "scope": "Conditional on retained all-size compiler, weighted/common-ancestor chart, restored rows, selectors/routing, prime supply, precision/recovery, complex symbolic correctness and analytic transfer; finite replay and written review, not a full formal multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "90446448750933/125000000000000000", "status": "Published on main: maintainer-reviewed conditional construction", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/91e29e7bbb7eab7d9ef8a4adc5d6971cd06bda51/certificates/selected-result.json", "path": null, "commit": "91e29e7bbb7eab7d9ef8a4adc5d6971cd06bda51", "at": "2026-10-10T14:08:14Z", "scope": "Conditional on retained all-size compiler, weighted/common-ancestor chart, restored rows, selectors/routing, prime supply, precision/recovery, complex symbolic correctness and analytic transfer; finite replay and written review, not a full formal multiplication theorem." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": "['Own native/full-group/arbitrary-column scalar and absolute-phase identities, sharing and complete spectator/owned restoration.', 'Own source unequal-child batching, once-only padding, fixed odd-grid and completed-child semantic C1=1 interfaces.', 'Parameterized Gaussian/fine-prime/finite-section/boundary/recovery analytic branch.', 'Exact fixed small-rational and odd-grid fixed-divisor conversion conditions, including endpoint divisibility and stored-width guards.', 'Unchanged optimized-GMP finite-native correctness/halting and model contracts.', 'Original-record asymptotic compatibility requires an extra retained same-XAG realization contract; no numerical original-tail bound is supplied.'] Supplemental75-guard replay corrects the earlier extracted-function argument-order evidence; every guard passes and the cutoff is unchanged.", "own_source_record_tail_quantified": false, "own_source_certificate": "pr144-finite-controller-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 43, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "early-native-producer-source/144-manifest.json", "sha256": "15b2e390ad2c963844a33fed21876153f666afb09eb3f0909766083c1f4d0253" }, { "file": "remaining-record-audit/artifacts/144/priority-manifest.json", "sha256": "1522de4670de727f0d63a272f52c38988ae51a1eed046d1159538036d91002a8" } ], "source_head": "c8b22bc5c10dba497ac25804e27d9647d818e2ff" } }, { "pr": 64, "title": "Verify finite profiles and formalize multiplication transfer interfaces", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/64", "author": "rfu08", "created_at": "2026-10-08T18:20:24Z", "accepted_at": "2026-10-09T12:57:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.000051738676045141", "kappa_fraction": "51738676045141/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "finite_symbolic_bridge", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (README.md, research/machine-transfer-verification/selected-certificate.json, research/machine-transfer-verification/stream-transfer/audit/pr76-arithmetic.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/machine-transfer-verification/stream-transfer/audit/pr76-arithmetic.json#/profile_reconstruction and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "Bind/recompute the source finite work, scalar coefficient grammar, denominator/precision/guard and all-size row-stock from research/machine-transfer-verification/selected-certificate.json#/ before using the stopped recurrence or compiled uniform supplier.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/machine-transfer-verification/selected-certificate.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "finite-bridge-source-expansion/64-manifest.json", "sha256": "024ce882e0db4fa12382ab4e94e8ef998402b3f92515f6a79c1e71e6c6a1bb13" } ], "source_head": "2d970ab3ca0271cfb2b609dc9aae1b7073b7774d" } }, { "pr": 147, "title": "Terminal elimination on #144's shared bit cores: conditional \u03ba = 4.646633e-4", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/147", "author": "hpst3r", "created_at": "2026-10-09T04:49:26Z", "accepted_at": "2026-10-09T12:57:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0004646633", "kappa_fraction": "4646633/10000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews. The upper costs this own-source finite-controller branch. Original-record compatibility requires an additional same-XAG realization contract; the original tail is not quantified.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 85, "input_bits": "2^85", "plot_triple_log": { "exact_log2_integer": 85, "expression": "log2(log2(85))" }, "scope": "Declared explicit EARLY Gaussian unreduced complete finite-cover literal enhancement family: every active native word retains every group vertex and full field coordinate with paid ADD lowering and no pruning/aggregation/bypass; if no native word is used the output branch is exactly the same optimized GMP reference. All switching policies are included. The optional original-record/min-total hybrid and every other implementation are excluded; the early effective exponent is1/5000.", "source": "data/operation-audit/pr147-finite-full-cover-lower.json", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source_explanation": "Own PR147 mandatory complete O(72,2) cover and actual producer binary additions, compared with the independently closed same-reference compact upper." }, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr147-finite-full-cover-range.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Original scalar/frame identities, completed-core sharing, ambient O(72,2) realization, uniform recursion, analytic precision/recovery and fixed-tape contracts remain original source assumptions. No full native replay or Lean proof is claimed.", "Declared explicit EARLY Gaussian unreduced complete finite-cover literal enhancement family: every active native word retains every group vertex and full field coordinate with paid ADD lowering and no pruning/aggregation/bypass; if no native word is used the output branch is exactly the same optimized GMP reference. All switching policies are included. The optional original-record/min-total hybrid and every other implementation are excluded; the early effective exponent is1/5000.", "Fixed real ADD word width at least two and the stipulated unreduced truncated addition subnetworks; full word and every physical coordinate remain present.", "Declared explicit EARLY Gaussian unreduced complete finite-cover literal enhancement family: every active native word retains every group vertex and full field coordinate with paid ADD lowering and no pruning/aggregation/bypass; if no native word is used the output branch is exactly the same optimized GMP reference. All switching policies are included. The optional original-record/min-total hybrid and every other implementation are excluded; the early effective exponent is1/5000.", "The explicit full-cover early circuit only. Its full source elementary charge is retained without dividing byW; corrected/refined rows fund the same full producer and complete field coefficient volume. Original-record/min-total hybrid branch is not in this lower family." ] }, "cost_status": "conditional_own_source_range", "historical_streams": [ "recovered_literal_highwater" ], "historical_status": "historical_selected_or_reviewed_conditional_checkpoint_source", "historical_events": [ { "stream": "recovered_literal_highwater", "stream_row": 112, "source_index": null, "at": "2026-10-09T04:49:26Z", "until": null, "date_basis": "body-version", "fraction": "4646633/10000000000", "value_decimal": "0.0004646633", "dashboard_float_text": null, "expression": "4646633/10^10", "historical_title": "Terminal elimination on #144's shared bit cores: conditional \u03ba = 4.646633e-4", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/147", "evidence_excerpt": "file changes.\n\nUnder #144's retained interfaces, this certifies\n\n T(n) = O(n (log n)^(1 - \u03ba)), \u03ba = 4646633/10^10 = 4.646633e-4\n\nThat is +0.813% over #144 (4609169/10^10). #144 is bit-limited, so a bit-side change moves \u03ba directly.\n\n## What changes\n\nOnly the bit word changes. #144's bit branc", "automated_comparable": true, "body_sha256": "f0defabe7cea087ff48d237d85d3a12cac44f9fdb43120d8f860fd47978f1dcd" } ], "reviewed_checkpoint_associations": [ { "stream": "all_selected_result_history", "record_kappa": "472154791/1000000000000", "status": "Selected maintainer-reviewed conditional composition; publication is a separate step", "role": "first_listed_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/86b30e035fcdffb72db93f759b4fda6a41b24de5/certificates/selected-result.json", "path": null, "commit": "86b30e035fcdffb72db93f759b4fda6a41b24de5", "at": "2026-10-09T06:01:09Z", "scope": "Conditional on retained analytic, uniform-recursion and fixed-tape interfaces; finite certificates and written review, not a formal proof of multiplication" }, { "stream": "all_selected_result_history", "record_kappa": "94428617/200000000000", "status": "Selected maintainer-reviewed conditional composition; publication is a separate step", "role": "first_listed_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/e2a02cac14dccf1279b3cfe673ce59ef0ba702d0/certificates/selected-result.json", "path": null, "commit": "e2a02cac14dccf1279b3cfe673ce59ef0ba702d0", "at": "2026-10-09T05:55:01Z", "scope": "Conditional on retained analytic, uniform-recursion and fixed-tape interfaces; finite certificates and written review, not a formal proof of multiplication" } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "upper_only_finite_source": true, "native_coordinate_rank": 72, "early_effective_kappa": "1/5000", "own_source_cost_extension": true, "own_source_scope": [ "Original scalar/frame identities, completed-core sharing, ambient O(72,2) realization, uniform recursion, analytic precision/recovery and fixed-tape contracts remain original source assumptions. No full native replay or Lean proof is claimed.", "Declared explicit EARLY Gaussian unreduced complete finite-cover literal enhancement family: every active native word retains every group vertex and full field coordinate with paid ADD lowering and no pruning/aggregation/bypass; if no native word is used the output branch is exactly the same optimized GMP reference. All switching policies are included. The optional original-record/min-total hybrid and every other implementation are excluded; the early effective exponent is1/5000.", "Fixed real ADD word width at least two and the stipulated unreduced truncated addition subnetworks; full word and every physical coordinate remain present.", "Declared explicit EARLY Gaussian unreduced complete finite-cover literal enhancement family: every active native word retains every group vertex and full field coordinate with paid ADD lowering and no pruning/aggregation/bypass; if no native word is used the output branch is exactly the same optimized GMP reference. All switching policies are included. The optional original-record/min-total hybrid and every other implementation are excluded; the early effective exponent is1/5000.", "The explicit full-cover early circuit only. Its full source elementary charge is retained without dividing byW; corrected/refined rows fund the same full producer and complete field coefficient volume. Original-record/min-total hybrid branch is not in this lower family." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr147-finite-full-cover-range.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 0, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [], "source_head": "29383a28d96b9880edbe59ed930f1da1dd6fdfa6" } }, { "pr": 150, "title": "Recycled bit registers on #147's reduced word: conditional \u03ba = 4.71809569e-4", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/150", "author": "DaysSky", "created_at": "2026-10-09T05:25:46Z", "accepted_at": "2026-10-09T12:57:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.000471809569", "kappa_fraction": "471809569/1000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr150-retained-complex-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own native/full-group/arbitrary-column scalar and absolute-phase identities, sharing and complete spectator/owned restoration.", "Own source unequal-child batching, once-only padding, fixed odd-grid and completed-child semantic C1=1 interfaces.", "Parameterized Gaussian/fine-prime/finite-section/boundary/recovery analytic branch.", "Exact fixed small-rational and odd-grid fixed-divisor conversion conditions, including endpoint divisibility and stored-width guards.", "Unchanged optimized-GMP finite-native correctness/halting and model contracts.", "New source-equivalent direct Gaussian/Fermat early and own-record circuits. No original changed bit producer/geometry replay or timing claim; exact own original bit-row pricing only binds each historical claim." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "recovered_literal_highwater", "stream_row": 113, "source_index": null, "at": "2026-10-09T05:25:46Z", "until": null, "date_basis": "body-version", "fraction": "471809569/1000000000000", "value_decimal": "0.000471809569", "dashboard_float_text": null, "expression": "471809569/10^12", "historical_title": "Recycled bit registers on #147's reduced word: conditional \u03ba = 4.71809569e-4", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/150", "evidence_excerpt": "ain directly.\n\nUnder #144's retained interfaces, this certifies\n\n T(n) = O(n (log n)^(1 - \u03ba)), \u03ba = 471809569/10^12 = 4.71809569e-4\n\nThat is +1.54% over #147 (4646633/10^10) and +2.36% over the merged #144 (4609169/10^10). #144 is bit-limited, so a bit-side change moves \u03ba directly.\n\n## What cha", "automated_comparable": true, "body_sha256": "77daca29d496b7297a05f2faa13a0baa5aaa42dbeab51ebcd66bb791c22aada9" } ], "reviewed_checkpoint_associations": [ { "stream": "all_selected_result_history", "record_kappa": "472154791/1000000000000", "status": "Selected maintainer-reviewed conditional composition; publication is a separate step", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/86b30e035fcdffb72db93f759b4fda6a41b24de5/certificates/selected-result.json", "path": null, "commit": "86b30e035fcdffb72db93f759b4fda6a41b24de5", "at": "2026-10-09T06:01:09Z", "scope": "Conditional on retained analytic, uniform-recursion and fixed-tape interfaces; finite certificates and written review, not a formal proof of multiplication" }, { "stream": "all_selected_result_history", "record_kappa": "94428617/200000000000", "status": "Selected maintainer-reviewed conditional composition; publication is a separate step", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/e2a02cac14dccf1279b3cfe673ce59ef0ba702d0/certificates/selected-result.json", "path": null, "commit": "e2a02cac14dccf1279b3cfe673ce59ef0ba702d0", "at": "2026-10-09T05:55:01Z", "scope": "Conditional on retained analytic, uniform-recursion and fixed-tape interfaces; finite certificates and written review, not a formal proof of multiplication" } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own native/full-group/arbitrary-column scalar and absolute-phase identities, sharing and complete spectator/owned restoration.", "Own source unequal-child batching, once-only padding, fixed odd-grid and completed-child semantic C1=1 interfaces.", "Parameterized Gaussian/fine-prime/finite-section/boundary/recovery analytic branch.", "Exact fixed small-rational and odd-grid fixed-divisor conversion conditions, including endpoint divisibility and stored-width guards.", "Unchanged optimized-GMP finite-native correctness/halting and model contracts.", "New source-equivalent direct Gaussian/Fermat early and own-record circuits. No original changed bit producer/geometry replay or timing claim; exact own original bit-row pricing only binds each historical claim." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr150-retained-complex-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 5, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/150-manifest.json", "sha256": "23e64a8bd1cbf97bd8fac6357646756e7d93e7f5fe99bce393ca78e7e1b21417" }, { "file": "remaining-record-audit/artifacts/150/priority-manifest.json", "sha256": "6173f3257e6a9a05f6a28e03026ccfbfb990fb820f1570577e1918025e5b5369" } ], "source_head": "40d4038760ebb6d6d3d702ce88fa3645de29f0c1" } }, { "pr": 151, "title": "Compose gauge refinement with PR150 recycling: conditional \u03ba = 0.000472154791", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/151", "author": "SovereignSteak", "created_at": "2026-10-09T05:45:33Z", "accepted_at": "2026-10-09T12:57:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.000472154791", "kappa_fraction": "472154791/1000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr151-retained-complex-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own native/full-group/arbitrary-column scalar and absolute-phase identities, sharing and complete spectator/owned restoration.", "Own source unequal-child batching, once-only padding, fixed odd-grid and completed-child semantic C1=1 interfaces.", "Parameterized Gaussian/fine-prime/finite-section/boundary/recovery analytic branch.", "Exact fixed small-rational and odd-grid fixed-divisor conversion conditions, including endpoint divisibility and stored-width guards.", "Unchanged optimized-GMP finite-native correctness/halting and model contracts.", "New source-equivalent direct Gaussian/Fermat early and own-record circuits. No original changed bit producer/geometry replay or timing claim; exact own original bit-row pricing only binds each historical claim." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "recovered_literal_highwater", "stream_row": 114, "source_index": null, "at": "2026-10-09T05:45:33Z", "until": null, "date_basis": "body-version", "fraction": "472154791/1000000000000", "value_decimal": "0.000472154791", "dashboard_float_text": null, "expression": "472154791/10^12", "historical_title": "Compose gauge refinement with PR150 recycling: conditional \u03ba = 0.000472154791", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/151", "evidence_excerpt": "## Result\n\nConditional kappa = 472154791/10^12 = 0.000472154791, versus #150's best reported .000472026274: approximately +0.0272%.\n\nStacked on #150 at 40d4038760ebb6d6d3d702ce88fa3645de29f0c1; please review/merge that depende", "automated_comparable": true, "body_sha256": "bdae040b4f752c78788e6dac4012bca9a79bc2f7f70002808f3efb104fbc531b" } ], "reviewed_checkpoint_associations": [ { "stream": "all_selected_result_history", "record_kappa": "472154791/1000000000000", "status": "Selected maintainer-reviewed conditional composition; publication is a separate step", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/86b30e035fcdffb72db93f759b4fda6a41b24de5/certificates/selected-result.json", "path": null, "commit": "86b30e035fcdffb72db93f759b4fda6a41b24de5", "at": "2026-10-09T06:01:09Z", "scope": "Conditional on retained analytic, uniform-recursion and fixed-tape interfaces; finite certificates and written review, not a formal proof of multiplication" } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own native/full-group/arbitrary-column scalar and absolute-phase identities, sharing and complete spectator/owned restoration.", "Own source unequal-child batching, once-only padding, fixed odd-grid and completed-child semantic C1=1 interfaces.", "Parameterized Gaussian/fine-prime/finite-section/boundary/recovery analytic branch.", "Exact fixed small-rational and odd-grid fixed-divisor conversion conditions, including endpoint divisibility and stored-width guards.", "Unchanged optimized-GMP finite-native correctness/halting and model contracts.", "New source-equivalent direct Gaussian/Fermat early and own-record circuits. No original changed bit producer/geometry replay or timing claim; exact own original bit-row pricing only binds each historical claim." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr151-retained-complex-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/151-manifest.json", "sha256": "79b9a00e796afe4b0a94ac2a9b1f20ba380272feddac60a1e8a2ae4e9e0d6bcf" }, { "file": "remaining-record-audit/artifacts/151/priority-manifest.json", "sha256": "1b16adeee298dd67f38ce19f59ac38c77bb3a495cd2d670483ee0087cc6fbaaf" } ], "source_head": "5a46ac37ae2e2f8f75637cb2cf6b9d0b36afc436" } }, { "pr": 276, "title": "Conditional \u03ba = 7.22869827347495e-4: a new paired-cube bit word (arc-aware local circuit, centre-sharing pair module) in the five-stage completed banks", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/276", "author": "DreamingOfClouds", "created_at": "2026-10-10T04:17:57Z", "accepted_at": "2026-10-10T14:08:25Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.000722869827347495", "kappa_fraction": "144573965469499/200000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "recovered_literal_highwater", "stream_row": 192, "source_index": null, "at": "2026-10-10T04:17:57Z", "until": null, "date_basis": "opening-title", "fraction": "144573965469499/200000000000000000", "value_decimal": "0.000722869827347495", "dashboard_float_text": null, "expression": "7.22869827347495e-4", "historical_title": "Conditional \u03ba = 7.22869827347495e-4: a new paired-cube bit word (arc-aware local circuit, centre-sharing pair module) in the five-stage completed banks", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/276", "evidence_excerpt": "Conditional \u03ba = 7.22869827347495e-4: a new paired-cube bit word (arc-aware local circuit, centre-sharing pair module) in the five-stage completed banks", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "90446448750933/125000000000000000", "status": "Published on main: maintainer-reviewed conditional construction", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/gen4-pr279.json", "path": "certificates/checkpoints/gen4-pr279.json", "commit": null, "at": null, "scope": "Conditional on retained all-size compiler, weighted/common-ancestor chart, restored rows, selectors/routing, prime supply, precision/recovery, complex symbolic correctness and analytic transfer; finite replay and written review, not a full formal multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "90446448750933/125000000000000000", "status": "Published on main: maintainer-reviewed conditional construction", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/91e29e7bbb7eab7d9ef8a4adc5d6971cd06bda51/certificates/selected-result.json", "path": null, "commit": "91e29e7bbb7eab7d9ef8a4adc5d6971cd06bda51", "at": "2026-10-10T14:08:14Z", "scope": "Conditional on retained all-size compiler, weighted/common-ancestor chart, restored rows, selectors/routing, prime supply, precision/recovery, complex symbolic correctness and analytic transfer; finite replay and written review, not a full formal multiplication theorem." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/five-stage-gen4-banks/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/five-stage-gen4-banks/MANIFEST.json, research/five-stage-gen4-banks/PROOF.md, research/five-stage-gen4-banks/README.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/five-stage-gen4-banks/MANIFEST.json, research/five-stage-gen4-banks/PROOF.md, research/five-stage-gen4-banks/README.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/276-manifest.json", "sha256": "58302496cfeaf154790b7a01cac9aa68c432df31c39a1e80879be1eaead38a82" }, { "file": "remaining-record-audit/artifacts/276/priority-manifest.json", "sha256": "991ebda734d368a1371fe4cf8a2152f634ae5251902922b0ee9892f28a4bee18" } ], "source_head": "cf6cb4ebb55f0ee5f03918033e96a29209ff6798" } }, { "pr": 468, "title": "Prove nine calls are necessary for three abelian bit registers", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/468", "author": "aliromman", "created_at": "2026-10-11T17:29:22Z", "accepted_at": "2026-10-12T01:36:58Z", "acceptance_basis": "github_merged_at", "kappa_decimal": null, "kappa_fraction": null, "kappa_status": "no_selected_positive_source_kappa", "kappa_scope": "Documented projection, retraction, mechanism objection or scope exclusion; see flags.", "source_status": "scope-flagged", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "observed_highwater" ], "historical_status": "wrong_metric_not_an_exponent_record", "historical_events": [ { "stream": "observed_highwater", "stream_row": 57, "source_index": 113, "at": "2026-10-11T18:00:48.957721Z", "until": "2026-10-11T18:08:16.046514Z", "date_basis": "observed_dashboard_segment", "fraction": null, "value_decimal": "9.0", "dashboard_float_text": "9.0", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/468", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/468-manifest.json", "sha256": "843fbf471201194fcd82db50a526563e0ac1440a050c27791a7410e16ec2e4b6" }, { "file": "remaining-record-audit/artifacts/468/priority-manifest.json", "sha256": "1e145fc05f0e1c0f371212a1e2ddb1bfee8d188de5a44822c6006f6f3f88ec96" } ], "source_head": "07a78bf335b0b5039a1fecd7cd74a0fe1d1605ea" } }, { "pr": 477, "title": "Add categorized experiment log: 100 ideas, 300 trials, and recorded failures", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/477", "author": "rohanarun", "created_at": "2026-10-11T18:29:58Z", "accepted_at": "2026-10-12T01:36:58Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001388082565814657", "kappa_fraction": "1388082565814657/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "scope-flagged", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain the exact stated lemma, finite-audit scope, correction or provenance with its actual selected target. A numerical runtime bound requires an actual source-selected full native/owner/recursive invoice/precision/outer realization and exact own commitments. No cutoff follows from unchanged kappa, a scalar lemma or an audit pass." ], "source_manifest": [ { "file": "individual-primary-interface-source/477-manifest.json", "sha256": "8dfeb6afe43b57d93e819a987fb24dba2c3262de5f02102d8a18b1cc89811627" }, { "file": "remaining-record-audit/artifacts/477/priority-manifest.json", "sha256": "33b0d884d5e85d0d52981e18a23437325c142f3a739ca9114b8e17b6585aefce" } ], "source_head": "a5b588d7f16be383ec80e6c5adaa1a75049cb758" } }, { "pr": 493, "title": "Conditional \u03ba = 0.001303530097714685: an E8 bit word with 489 helpers, sources as carriers (0.001325 with #484's draft complex supplier)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/493", "author": "eumemic", "created_at": "2026-10-11T20:09:25Z", "accepted_at": "2026-10-12T01:55:39Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001303530097714685", "kappa_fraction": "260706019542937/200000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/e8-bit-carrier-skeleton/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/e8-bit-carrier-skeleton/EXPECTED.json, research/e8-bit-carrier-skeleton/data/complex/pr448/EXPECTED.json, research/e8-bit-carrier-skeleton/data/complex/pr458/EXPECTED.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/e8-bit-carrier-skeleton/EXPECTED.json#/controls/pr472 after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/493-manifest.json", "sha256": "0e82191c19b2f6be98ad9df813b7665e1d441e61d6a9d80d2bcd400058c743a2" }, { "file": "remaining-record-audit/artifacts/493/priority-manifest.json", "sha256": "a43084c954e11cfb7fa1343253ae063f07c8f9b796e9a2644df3727e77c67193" } ], "source_head": "c3a9a436b84fe44fdc223a5784d84736d1c2d3c7" } }, { "pr": 514, "title": "Conditional kappa 0.001391523459591829: partial-own factory, 92 pivots and asynchronous whole owners", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/514", "author": "Dugongue", "created_at": "2026-10-11T23:22:36Z", "accepted_at": "2026-10-12T01:55:39Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001391523459591829", "kappa_fraction": "1391523459591829/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr514-partial-own-gaussian-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own complete normalized800-column native invocation acts on arbitrary120 data and560 dirty helper inputs, with required input/output frames, absolute phases, restoration and paid adapters at every positive fiber width. Finite exact phase/scalar executions are evidence rather than a universal proof.", "Own full whole-owner/spectator/common-label73-axis realization and all-size unequal-child/compiler/restored-row interfaces; complete semantic Gaussian norm1 and source precision/recovery/analytic transfer remain retained.", "This binding reuses exact original514 source and its already executed unchanged13-stage replay nested in523. It does not substitute the later112-data/728-column native or any later numerical cutoff.", "The dimension-independent rank73 finite-interface proof in pr514-partial-own-gaussian-bounds.md is used with the actual120-data,560-helper,16-private-centre ledger. The later112/504/8 native theorem is not imported. Every own monomial/Clifford map is bounded73-axis binary affine/even-quadratic Z4 with exactly recorded absolute phase and full owed normalization/copy/clear work.", "The completed exact Gaussian endpoint has semantic norm1; this is a retained operator interface, not a new field inferred from scalar replay or a claim that transient prefix gains are1.", "Concrete normalized Gaussian accretivity, finite LDU/narrow row-gap/cyclic-border and fine-prime/rounding/recovery interfaces; repaired reference correctness and finite-kernel halting. No arbitrary-scale accretive theorem is used." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own complete normalized800-column native invocation acts on arbitrary120 data and560 dirty helper inputs, with required input/output frames, absolute phases, restoration and paid adapters at every positive fiber width. Finite exact phase/scalar executions are evidence rather than a universal proof.", "Own full whole-owner/spectator/common-label73-axis realization and all-size unequal-child/compiler/restored-row interfaces; complete semantic Gaussian norm1 and source precision/recovery/analytic transfer remain retained.", "This binding reuses exact original514 source and its already executed unchanged13-stage replay nested in523. It does not substitute the later112-data/728-column native or any later numerical cutoff.", "The dimension-independent rank73 finite-interface proof in pr514-partial-own-gaussian-bounds.md is used with the actual120-data,560-helper,16-private-centre ledger. The later112/504/8 native theorem is not imported. Every own monomial/Clifford map is bounded73-axis binary affine/even-quadratic Z4 with exactly recorded absolute phase and full owed normalization/copy/clear work.", "The completed exact Gaussian endpoint has semantic norm1; this is a retained operator interface, not a new field inferred from scalar replay or a claim that transient prefix gains are1.", "Concrete normalized Gaussian accretivity, finite LDU/narrow row-gap/cyclic-border and fine-prime/rounding/recovery interfaces; repaired reference correctness and finite-kernel halting. No arbitrary-scale accretive theorem is used." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr514-partial-own-gaussian-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 9, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/514-manifest.json", "sha256": "e21c472ab8c5992e513be04e5dc45542db1e33363fa6574054db529720ab5901" }, { "file": "remaining-record-audit/artifacts/514/priority-manifest.json", "sha256": "95ccb173adc9e7d6f14652ab360da3413281b3f0894799418592397d260c1170" } ], "source_head": "246bfacd4cb4072836ae3147099f548bb728229f" } }, { "pr": 523, "title": "Punctured Hamming ports for conditional \u03ba = 0.001457945761723368", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/523", "author": "icekylinx", "created_at": "2026-10-12T00:26:22Z", "accepted_at": "2026-10-12T01:55:39Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001457945761723368", "kappa_fraction": "182243220215421/125000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr523-punctured-gaussian-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own exact required-entry/output all-column native phase realizations, complete row covers/common-label mutable-basis interfaces, owned erasure and all-size compiler semantics. Fresh14-stage replay checks finite native/frame/phase/owner/invoice/outer source implementations; universal analytic/physical interfaces remain hypotheses.", "Concrete normalized Gaussian/finite-LDU/narrow-gap/cyclic-border/fine-prime/exact-recovery and fixed repaired optimized-GMP correctness/halting contracts.", "New direct Gaussian/Fermat circuit realization of the exact selected punctured112 source core. Original optional493ordinaryBIT construction is not consumed or asserted freshly replayed." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 49, "source_index": 77, "at": "2026-10-12T00:26:22Z", "until": "2026-10-12T00:54:12Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001457945761723368", "dashboard_float_text": "0.001457945761723368", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/523", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 66, "source_index": null, "at": "2026-10-12T00:26:22Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001457945761723368", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/523", "evidence_excerpt": "=0.001457945761723368.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 334, "source_index": null, "at": "2026-10-12T00:26:22Z", "until": null, "date_basis": "body-version", "fraction": "182243220215421/125000000000000000", "value_decimal": "0.001457945761723368", "dashboard_float_text": null, "expression": "(182243220215421)/(125000000000000000)", "historical_title": "Punctured Hamming ports for conditional \u03ba = 0.001457945761723368", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/523", "evidence_excerpt": "d-row, precision/tape and analytic-transfer interfaces,\n\n\nT(n)=O\\left(n(\\log n)^(1-\u03ba)\\right),\\qquad\n\u03ba=(182243220215421)/(125000000000000000)\n=0.001457945761723368.\n\n\nThe saving is 4.77335% above [#514](https://github.com/CrocSwap/integer-mult-bounds/pull/514) and 4.61251% above [#518](https://github.com/CrocSwap/intege", "automated_comparable": true, "body_sha256": "accff6c134b182cc62b156aa55cdae590b878737ab6e506b053b5c732a0ea446" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/cold617.json", "path": "certificates/checkpoints/cold617.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. 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Historical research ceilings are preserved, not independently certified by this integration." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "upper_only_finite_source": true, "native_coordinate_rank": 73, "early_effective_kappa": "1/5000", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 0, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [], "source_head": "e07a8a3f9f79c22113398a0c5dbbc7601f489b3e" } }, { "pr": 484, "title": "Complex supplier b \u2248 1.327\u00b710\u207b\u00b3 (+4.7%) on whole-residual hosting: shared-donor kernel and entrance gauges with paid residual wrappers (conditional on two lemmas)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/484", "author": "DreamingOfClouds", "created_at": "2026-10-11T19:37:10Z", "accepted_at": "2026-10-12T02:24:40Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001237552", "kappa_fraction": "77347/62500000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "scope-flagged", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/e8-complex-gauge-kernel/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/e8-complex-gauge-kernel/EXPECTED.json, research/e8-complex-gauge-kernel/MANIFEST.json, research/e8-complex-gauge-kernel/PROOF.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/e8-complex-gauge-kernel/EXPECTED.json, research/e8-complex-gauge-kernel/MANIFEST.json, research/e8-complex-gauge-kernel/PROOF.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/e8-complex-gauge-kernel/EXPECTED.json#/suppliers/R724 mixed, eleven stages, whole-residual hosting after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/484-manifest.json", "sha256": "cbfc06b9e67c17428329b2718260d44b6cdad6d2cf6c54c42c7a1aee146c6d7c" }, { "file": "remaining-record-audit/artifacts/484/priority-manifest.json", "sha256": "37abdea5f5fb117409826da344e45d127d1ac0e1ac13581583f7c052c4eb8517" } ], "source_head": "d30a05f90190dff6435e62ebed95aff9a0ddb610" } }, { "pr": 442, "title": "Conditional \u03ba \u2248 1.2375517e-3: idle-axis hosting of helper residuals (+9.2% over #434)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/442", "author": "DaysSky", "created_at": "2026-10-11T13:18:56Z", "accepted_at": "2026-10-12T02:24:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0012375517", "kappa_fraction": "12375517/10000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "observed_highwater", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 37, "source_index": 54, "at": "2026-10-11T13:18:56Z", "until": "2026-10-11T13:23:19Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001237551733247294", "dashboard_float_text": "0.001237551733247294", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/442", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "observed_highwater", "stream_row": 48, "source_index": 86, "at": "2026-10-11T13:19:13.093542Z", "until": "2026-10-11T13:49:50.740486Z", "date_basis": "observed_dashboard_segment", "fraction": null, "value_decimal": null, "dashboard_float_text": "0.0012375517", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/442", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 54, "source_index": null, "at": "2026-10-11T13:18:56Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001237551733247294", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/442", "evidence_excerpt": "Conditional **\u03ba = 618775866623647/(5\u00b710\u00b9\u2077) \u2248 1.237551733247294\u00b710\u207b\u00b3**, **+9.218% over #434** (1.133100552284434\u00b710\u207b\u00b3). The bit supplier binds. It is also +8.67% above the newest posted value, #441 (1.138798055343319\u00b710\u207b\u00b3). Hosting changes only the global template, so it should stack on #440/#441's R740 word as well.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 316, "source_index": null, "at": "2026-10-11T13:18:56Z", "until": null, "date_basis": "opening-title", "fraction": "12375517/10000000000", "value_decimal": "0.001237551733247294", "dashboard_float_text": null, "expression": "1.2375517e-3", "historical_title": "Conditional \u03ba \u2248 1.2375517e-3: idle-axis hosting of helper residuals (+9.2% over #434)", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/442", "evidence_excerpt": "Conditional \u03ba \u2248 1.2375517e-3: idle-axis hosting of helper residuals (+9.2% over #434)", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/cold617.json", "path": "certificates/checkpoints/cold617.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. 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Integration Linux CI status is separate." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier890.json", "path": "certificates/checkpoints/frontier890.json", "commit": null, "at": null, "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier942.json", "path": "certificates/checkpoints/frontier942.json", "commit": null, "at": null, "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "16127213726553/10000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/hyperplane596.json", "path": "certificates/checkpoints/hyperplane596.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "51110230636731/31250000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/k492626.json", "path": "certificates/checkpoints/k492626.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1584931111785787/1000000000000000000", "status": "Published on main: maintainer-reviewed conditional finite construction", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/post-center535.json", "path": "certificates/checkpoints/post-center535.json", "commit": null, "at": null, "scope": "Local finite and exact source/kernel checks, with inherited all-size/compiler/realization/analytic assumptions retained. No Linux CI success claimed. See review for replay reuse and unresolved formal-instance obligations." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/87db776d70ad1d28a27e9f7906237e5a279414f3/certificates/selected-result.json", "path": null, "commit": "87db776d70ad1d28a27e9f7906237e5a279414f3", "at": "2026-10-13T18:05:11Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3825dc0ea1317629864ebeb6929719cc4bbf525f/certificates/selected-result.json", "path": null, "commit": "3825dc0ea1317629864ebeb6929719cc4bbf525f", "at": "2026-10-13T15:06:01Z", "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3b83e4f14825ce1ae038a8c8159f130646991086/certificates/selected-result.json", "path": null, "commit": "3b83e4f14825ce1ae038a8c8159f130646991086", "at": "2026-10-13T13:30:30Z", "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d6dfd8f21b1e0b7e3f93b7e30e64639390e48504/certificates/selected-result.json", "path": null, "commit": "d6dfd8f21b1e0b7e3f93b7e30e64639390e48504", "at": "2026-10-13T06:44:14Z", "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. Not a full Lean multiplication theorem. Integration Linux CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/c290b7b919790300e14004a75d8d24b55ca3c5b5/certificates/selected-result.json", "path": null, "commit": "c290b7b919790300e14004a75d8d24b55ca3c5b5", "at": "2026-10-13T06:10:31Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/2cdd93d0250554e5160edbb8535c4500c4227349/certificates/selected-result.json", "path": null, "commit": "2cdd93d0250554e5160edbb8535c4500c4227349", "at": "2026-10-13T05:57:09Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "51110230636731/31250000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/5c5567d15bd019186519a4db267914257b5f1ac0/certificates/selected-result.json", "path": null, "commit": "5c5567d15bd019186519a4db267914257b5f1ac0", "at": "2026-10-12T22:36:34Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/2e9ed969d09570fbe949324b80da27a7f31d9399/certificates/selected-result.json", "path": null, "commit": "2e9ed969d09570fbe949324b80da27a7f31d9399", "at": "2026-10-12T21:01:12Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "16127213726553/10000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/1db1fbe68cb5186899cf1fd691bc92056a845e49/certificates/selected-result.json", "path": null, "commit": "1db1fbe68cb5186899cf1fd691bc92056a845e49", "at": "2026-10-12T16:59:30Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "400569730495803/250000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7f6ccd7ed1e5ee7fba9599f44f9a6fe08f582d62/certificates/selected-result.json", "path": null, "commit": "7f6ccd7ed1e5ee7fba9599f44f9a6fe08f582d62", "at": "2026-10-12T15:44:15Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "400569730495803/250000000000000000", "status": "Prepared locally for publication: maintainer-reviewed conditional finite construction; frozen-family integration still in progress", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/270c2458cf7f34fc252afe7c9d697f2cd6c93a59/certificates/selected-result.json", "path": null, "commit": "270c2458cf7f34fc252afe7c9d697f2cd6c93a59", "at": "2026-10-12T14:41:59Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "1584931111785787/1000000000000000000", "status": "Published on main: maintainer-reviewed conditional finite construction", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/1c1e42f0d87c605496b8de9b7a0504099a8360f1/certificates/selected-result.json", "path": null, "commit": "1c1e42f0d87c605496b8de9b7a0504099a8360f1", "at": "2026-10-12T13:10:36Z", "scope": "Local finite and exact source/kernel checks, with inherited all-size/compiler/realization/analytic assumptions retained. No Linux CI success claimed. See review for replay reuse and unresolved formal-instance obligations." }, { "stream": "all_selected_result_history", "record_kappa": "1517760977820331/1000000000000000000", "status": "Published on main: maintainer-reviewed conditional finite construction", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/a1e7d84866e73aa6f3355629ea31b24b8076b113/certificates/selected-result.json", "path": null, "commit": "a1e7d84866e73aa6f3355629ea31b24b8076b113", "at": "2026-10-12T01:55:19Z", "scope": "All three finite packages replayed; inherited all-size/compiler, common-label/mutable-basis, normalized residual realization, correlated whole-owner hosting, restored-row, precision/tape and analytic-transfer interfaces remain conditional. No new Lean proof. Historical research ceilings are preserved, not independently certified by this integration." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 9, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/idle-axis-hosting/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/e8-early-reset-kernel/EXPECTED.json, research/e8-early-reset-reuse/EXPECTED.json, research/idle-axis-hosting/EXPECTED.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/e8-early-reset-kernel/EXPECTED.json, research/e8-early-reset-reuse/EXPECTED.json, research/idle-axis-hosting/EXPECTED.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/e8-early-reset-kernel/EXPECTED.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/442-manifest.json", "sha256": "03f74f97934f867b89351a0bccae5d4331bfa7980c705203e760da00cf8cf3b1" }, { "file": "remaining-record-audit/artifacts/442/priority-manifest.json", "sha256": "d346c3e3f330df2e4872f4cb9b30c093da5208f3668794f390263cbb61f3d817" } ], "source_head": "4e16d001d505d4f21dd2bcfc44591f9be4c279bd" } }, { "pr": 503, "title": "Bit word R480: totals on dead registers, c = 0.001574753352953808650916 (+0.595% over #493)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/503", "author": "DreamingOfClouds", "created_at": "2026-10-11T21:55:59Z", "accepted_at": "2026-10-12T13:10:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001325031497415498", "kappa_fraction": "662515748707749/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "scope-flagged", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/e8-r480-dead-totals/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/e8-bit-carrier-skeleton/EXPECTED.json, research/e8-bit-carrier-skeleton/data/complex/pr448/EXPECTED.json, research/e8-bit-carrier-skeleton/data/complex/pr458/EXPECTED.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/e8-bit-carrier-skeleton/EXPECTED.json#/controls/pr472 after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/503/priority-manifest.json", "sha256": "693261ac3afd8504febe61ec6a9461636bc6bce6b2876bca512e192a6a428381" } ], "source_head": "3f27147013fdd4fa0aed825cb47bff3376c452eb" } }, { "pr": 510, "title": "Bit word R480 at nine stages: c = 0.001587447106092548137108 (+1.41% over #493)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/510", "author": "DreamingOfClouds", "created_at": "2026-10-11T22:46:45Z", "accepted_at": "2026-10-12T13:10:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001325031497415498", "kappa_fraction": "662515748707749/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "scope-flagged", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/e8-r480-nine-stage/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Recompute the complete own productive/paid histogram from research/e8-r480-nine-stage/EXPECTED.json#/nine and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/e8-bit-carrier-skeleton/EXPECTED.json#/controls/pr472 after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/510-manifest.json", "sha256": "3198dffc65721cc39a58d089601cffa27cbf4ed0df919fd5311311828718e120" }, { "file": "remaining-record-audit/artifacts/510/priority-manifest.json", "sha256": "c88bc3c1e8f91fbd05d7739a68a6a78467a891701944afed637a12a4c1d4d190" } ], "source_head": "64edee18af02aab0c1696b677a0287dd0146381b" } }, { "pr": 513, "title": "[Lean] Add sequential completed-bank source bindings", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/513", "author": "jamesyc", "created_at": "2026-10-11T23:10:56Z", "accepted_at": "2026-10-12T13:10:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.000723571590007464", "kappa_fraction": "90446448750933/125000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "supporting_formal_interface_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Bind the separately referenced complete integer construction and its actual physical/invoice/parameter changes before assigning a numerical cutoff; this source interface/tooling result creates no independent runtime point." ], "source_manifest": [ { "file": "individual-primary-interface-source/513-manifest.json", "sha256": "9243c0e2eeae16fe8d2723bc07bb2cad38b3cd9b7e793a976ff0f2eac393c968" }, { "file": "remaining-record-audit/artifacts/513/priority-manifest.json", "sha256": "7663d6f08dfe030e099503e071d475ab1a7062c3e7606350bea1f10115aedfb8" } ], "source_head": "d558ca6cbc23957163db81e23071d336ab761a12" } }, { "pr": 528, "title": "[Lean] Connect complete-bank endpoints to PR516 realization", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/528", "author": "jamesyc", "created_at": "2026-10-12T01:18:36Z", "accepted_at": "2026-10-12T13:10:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.000723571590007464", "kappa_fraction": "90446448750933/125000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "scope-flagged", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "supporting_formal_interface_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Bind the separately referenced complete integer construction and its actual physical/invoice/parameter changes before assigning a numerical cutoff; this source interface/tooling result creates no independent runtime point." ], "source_manifest": [ { "file": "individual-primary-interface-source/528-manifest.json", "sha256": "213e4bd7b09f967652e402410c81802b7fa9aae4968b8dba4d539f19da20a821" }, { "file": "remaining-record-audit/artifacts/528/priority-manifest.json", "sha256": "1ef985fbdcce7ef66094e23e7732089f6948e3cbd07e94243b159355cdc5e2e8" } ], "source_head": "df5bbdbf837df908ce2324ed880141918a19db5d" } }, { "pr": 533, "title": "Conditional \u03ba = 0.001524207950793244: 92-pivot direct504 supplier", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/533", "author": "chafreaky", "created_at": "2026-10-12T01:56:12Z", "accepted_at": "2026-10-12T13:10:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001524207950793244", "kappa_fraction": "381051987698311/250000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public switching policies for this own source-selected literal complete O(73,2) cover enhancement: keep one actual selected public real ADD at every cover vertex with guarded width>=2 and the stipulated ADD lowering; no pruning, CSE, compression, aggregation or native bypass. A branch without such a native invocation is the identical fixed GMP reference. This added inactive rule is a comparison-family definition, not an original source fact. No other implementation or original BIT composition is covered.", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source": "data/operation-audit/pr533-open-legacy-literal-cover-lower.json" }, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr533-legacy-kernel92-literal-cover-range.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "Own selected native all-input Gaussian/helper endpoints, exact physical entry/output frames and absolute phases, normalized residual wrappers and identity spectators remain substantive universal interfaces. Actual finite local phase/source checks strengthen the evidence but do not prove arbitrary all-size operator identities.", "Own common-label/mutable-basis owned restore, normalized completed-child semantic height, all-size compiler/occupied-row/stock/tape and analytic recovery remain conditional. The bounded73-axis binary-affine/even-quadratic-Z4 finite-phase grammar is required for the charged universal compiler tariff.", "Actual own constructor/kernel controls, native scalar/frame/wrapper and every finite local phase edge/endpoint, complete owner emitter plus seven mutations and fresh invoice with no retained prior allowance were executed. Original full global CLI, unchanged global data-phase replay and original BIT runtime are not claimed.", "This newly counted direct Gaussian/Fermat circuit uses the exact own selected source body and literal complete finite cover. No source equivalence, previous upper threshold, prior invoice or fabricated BIT saving is consumed. The fixed fallback density tax, per-coefficient40e fallback and full u^(1000000Q) stopped reserve remain paid in all seven operation rows.", "All valid public switching policies for this own source-selected literal complete O(73,2) cover enhancement: keep one actual selected public real ADD at every cover vertex with guarded width>=2 and the stipulated ADD lowering; no pruning, CSE, compression, aggregation or native bypass. A branch without such a native invocation is the identical fixed GMP reference. This added inactive rule is a comparison-family definition, not an original source fact. No other implementation or original BIT composition is covered.", "All valid public switching policies for this own source-selected literal complete O(73,2) cover enhancement: keep one actual selected public real ADD at every cover vertex with guarded width>=2 and the stipulated ADD lowering; no pruning, CSE, compression, aggregation or native bypass. A branch without such a native invocation is the identical fixed GMP reference. This added inactive rule is a comparison-family definition, not an original source fact. No other implementation or original BIT composition is covered.", "Exact same own literal selected programme and full-cover body; complete new group invoice pays it. Both early and record domains separately imply a nonempty native H row above the full1e6Q stopped base. Lower forall policies and constructive upper exists schedule remain distinct." ] }, "cost_status": "conditional_own_source_range", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 52, "source_index": 82, "at": "2026-10-12T01:56:12Z", "until": "2026-10-12T02:14:52Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001524207950793244", "dashboard_float_text": "0.001524207950793244", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/533", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 69, "source_index": null, "at": "2026-10-12T01:56:12Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001524207950793244", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/533", "evidence_excerpt": "Conditional \u03ba = 0.001524207950793244: 92-pivot direct504 supplier", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 338, "source_index": null, "at": "2026-10-12T01:56:12Z", "until": null, "date_basis": "body-version", "fraction": "381051987698311/250000000000000000", "value_decimal": "0.001524207950793244", "dashboard_float_text": null, "expression": "0.001524207950793244", "historical_title": "Conditional \u03ba = 0.001524207950793244: 92-pivot direct504 supplier", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/533", "evidence_excerpt": "ing from [#531](https://github.com/CrocSwap/integer-mult-bounds/pull/531)'s 0.001517760977820331 to \u03ba = 0.001524207950793244, exactly 381051987698311/250000000000000000: a 0.42477% improvement in exponent saving. The complex supplier still binds. This is a finite conditional witness under the retained a", "automated_comparable": true, "body_sha256": "798fab1d190ad68fa6e4aad7a7b5575ab9590e23f6a5653523f2532341c42fe5" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "Own selected native all-input Gaussian/helper endpoints, exact physical entry/output frames and absolute phases, normalized residual wrappers and identity spectators remain substantive universal interfaces. Actual finite local phase/source checks strengthen the evidence but do not prove arbitrary all-size operator identities.", "Own common-label/mutable-basis owned restore, normalized completed-child semantic height, all-size compiler/occupied-row/stock/tape and analytic recovery remain conditional. The bounded73-axis binary-affine/even-quadratic-Z4 finite-phase grammar is required for the charged universal compiler tariff.", "Actual own constructor/kernel controls, native scalar/frame/wrapper and every finite local phase edge/endpoint, complete owner emitter plus seven mutations and fresh invoice with no retained prior allowance were executed. Original full global CLI, unchanged global data-phase replay and original BIT runtime are not claimed.", "This newly counted direct Gaussian/Fermat circuit uses the exact own selected source body and literal complete finite cover. No source equivalence, previous upper threshold, prior invoice or fabricated BIT saving is consumed. The fixed fallback density tax, per-coefficient40e fallback and full u^(1000000Q) stopped reserve remain paid in all seven operation rows.", "All valid public switching policies for this own source-selected literal complete O(73,2) cover enhancement: keep one actual selected public real ADD at every cover vertex with guarded width>=2 and the stipulated ADD lowering; no pruning, CSE, compression, aggregation or native bypass. A branch without such a native invocation is the identical fixed GMP reference. This added inactive rule is a comparison-family definition, not an original source fact. No other implementation or original BIT composition is covered.", "All valid public switching policies for this own source-selected literal complete O(73,2) cover enhancement: keep one actual selected public real ADD at every cover vertex with guarded width>=2 and the stipulated ADD lowering; no pruning, CSE, compression, aggregation or native bypass. A branch without such a native invocation is the identical fixed GMP reference. This added inactive rule is a comparison-family definition, not an original source fact. No other implementation or original BIT composition is covered.", "Exact same own literal selected programme and full-cover body; complete new group invoice pays it. Both early and record domains separately imply a nonempty native H row above the full1e6Q stopped base. Lower forall policies and constructive upper exists schedule remain distinct." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr533-legacy-kernel92-literal-cover-range.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 10, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/533-manifest.json", "sha256": "e44701d136a32995a18eac71e532f19dfbe2c69e51aa8570dd364a12bca73e24" }, { "file": "remaining-record-audit/artifacts/533/priority-manifest.json", "sha256": "78eba794fd0951164c5dade245f360154347ea038536a0b498b76ce4d8a00b98" } ], "source_head": "6ad231bea07da57e94dbe4062bd045941db3287e" } }, { "pr": 534, "title": "Conditional \u03ba = 0.001526158885117467: frame-chain search on #531's 504-helper word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/534", "author": "rohanarun", "created_at": "2026-10-12T02:07:39Z", "accepted_at": "2026-10-12T13:10:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001526158885117467", "kappa_fraction": "1526158885117467/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr534-legacy-expected-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "Own534 completed native all-input Gaussian/helper endpoints, exact required entry/output frames and absolute phases, normalised residual wrappers and identity on spectators are substantive retained interfaces. Scalar-only specialization and finite frame checks do not prove these operator identities.", "The own all-size compiler, common-label/mutable-basis owned realisation, normalized completed-child height, restored-row/tape and analytic recovery contracts remain conditional exactly as qualified in the own README. The source bounded73-axis binary-affine/even-quadratic-Z4 finite phase grammar is required for the charged universal compiler tariff.", "The fresh original source preparation, complete owner/controller audit with seven mutations and no-prior-invoice full recount were actually executed. No full original global verifier, all-edge phase engine or predecessor cold replay is claimed.", "This is a newly counted direct Gaussian/Fermat XAG realization of the own selected complete complex construction. The original optional BIT supplier is neither consumed nor assigned an invented saving.", "The preserved finite fallback density tax is not adjustable. Full stopped-child reserve u^(1000000*Q), per-coordinate40e direct tensor fallback and all seven actual operation rows are included by the independently closed finite component." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "Own534 completed native all-input Gaussian/helper endpoints, exact required entry/output frames and absolute phases, normalised residual wrappers and identity on spectators are substantive retained interfaces. Scalar-only specialization and finite frame checks do not prove these operator identities.", "The own all-size compiler, common-label/mutable-basis owned realisation, normalized completed-child height, restored-row/tape and analytic recovery contracts remain conditional exactly as qualified in the own README. The source bounded73-axis binary-affine/even-quadratic-Z4 finite phase grammar is required for the charged universal compiler tariff.", "The fresh original source preparation, complete owner/controller audit with seven mutations and no-prior-invoice full recount were actually executed. No full original global verifier, all-edge phase engine or predecessor cold replay is claimed.", "This is a newly counted direct Gaussian/Fermat XAG realization of the own selected complete complex construction. The original optional BIT supplier is neither consumed nor assigned an invented saving.", "The preserved finite fallback density tax is not adjustable. Full stopped-child reserve u^(1000000*Q), per-coordinate40e direct tensor fallback and all seven actual operation rows are included by the independently closed finite component." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr534-legacy-expected-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 11, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/534-manifest.json", "sha256": "a8f0d2686d1d1437ddeddc13ac315def7f2ba6328d07bf35c86caa9750d9a37c" }, { "file": "remaining-record-audit/artifacts/534/priority-manifest.json", "sha256": "a47f53d600a30854ce2c8ba580184f6159fcfd3b52b49f2320493ca876acdc26" } ], "source_head": "3e148183cbf124fcaba4d3c2d609133ff2edd518" } }, { "pr": 535, "title": "Post-center rank-four kernels for conditional \u03ba = 0.001584931111785787", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/535", "author": "icekylinx", "created_at": "2026-10-12T02:14:52Z", "accepted_at": "2026-10-12T13:10:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001584931111785787", "kappa_fraction": "1584931111785787/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews. 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The current numerical upper additionally uses the independently checked integral gate refinement." }, "cost_status": "conditional_finite_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "historical_selected_or_reviewed_conditional_checkpoint_source", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 53, "source_index": 83, "at": "2026-10-12T02:14:52Z", "until": "2026-10-12T02:19:30Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001584931111785787", "dashboard_float_text": "0.001584931111785787", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/535", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 70, "source_index": null, "at": "2026-10-12T02:14:52Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001584931111785787", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/535", "evidence_excerpt": "=0.001584931111785787.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 339, "source_index": null, "at": "2026-10-12T02:14:52Z", "until": null, "date_basis": "opening-title", "fraction": "1584931111785787/1000000000000000000", "value_decimal": "0.001584931111785787", "dashboard_float_text": null, "expression": "0.001584931111785787", "historical_title": "Post-center rank-four kernels for conditional \u03ba = 0.001584931111785787", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/535", "evidence_excerpt": "Post-center rank-four kernels for conditional \u03ba = 0.001584931111785787", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/cold617.json", "path": "certificates/checkpoints/cold617.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. 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See review for replay reuse and unresolved formal-instance obligations." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "upper_only_finite_source": true, "native_coordinate_rank": 73, "early_effective_kappa": "1/5000", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 0, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [], "source_head": "8b758a103915179322766bed5798f9b6e7198011" } }, { "pr": 536, "title": "Conditional kappa 0.001530327580902932: kernel92 plus optimized delivery frames", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/536", "author": "rohanarun", "created_at": "2026-10-12T02:15:55Z", "accepted_at": "2026-10-12T13:10:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001530327580902932", "kappa_fraction": "382581895225733/250000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public switching policies of this exact own source-selected literal complete O(73,2) cover enhancement; at least one actual selected public-main unit real ADD per vertex survives at guarded width>=2. No pruning, CSE, aggregation, compression, cover quotienting or native bypass removes it. A branch without such a native invocation returns the identical fixed GMP reference. This inactive rule is an added comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source": "data/operation-audit/pr536-open-legacy-v2-literal-cover-lower.json" }, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr536-legacy-kernel92-literal-cover-range.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "Own selected native all-input Gaussian/helper endpoints, exact physical entry/output frames and absolute phases, normalized residual wrappers and identity spectators remain substantive universal interfaces. Actual finite local phase/source checks strengthen the evidence but do not prove arbitrary all-size operator identities.", "Own common-label/mutable-basis owned restore, normalized completed-child semantic height, all-size compiler/occupied-row/stock/tape and analytic recovery remain conditional. The bounded73-axis binary-affine/even-quadratic-Z4 finite-phase grammar is required for the charged universal compiler tariff.", "Actual own constructor/kernel controls, native scalar/frame/wrapper and every finite local phase edge/endpoint, complete owner emitter plus seven mutations and fresh invoice with no retained prior allowance were executed. Original full global CLI, unchanged global data-phase replay and original BIT runtime are not claimed.", "This newly counted direct Gaussian/Fermat circuit uses the exact own selected source body and literal complete finite cover. No source equivalence, previous upper threshold, prior invoice or fabricated BIT saving is consumed. The fixed fallback density tax, per-coefficient40e fallback and full u^(1000000Q) stopped reserve remain paid in all seven operation rows.", "All valid public switching policies of this exact own source-selected literal complete O(73,2) cover enhancement; at least one actual selected public-main unit real ADD per vertex survives at guarded width>=2. No pruning, CSE, aggregation, compression, cover quotienting or native bypass removes it. A branch without such a native invocation returns the identical fixed GMP reference. This inactive rule is an added comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "All valid public switching policies of this exact own source-selected literal complete O(73,2) cover enhancement; at least one actual selected public-main unit real ADD per vertex survives at guarded width>=2. No pruning, CSE, aggregation, compression, cover quotienting or native bypass removes it. A branch without such a native invocation returns the identical fixed GMP reference. This inactive rule is an added comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "Exact same own literal selected programme and full-cover body; complete new group invoice pays it. Both early and record domains separately imply a nonempty native H row above the full1e6Q stopped base. Lower forall policies and constructive upper exists schedule remain distinct." ] }, "cost_status": "conditional_own_source_range", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "Own selected native all-input Gaussian/helper endpoints, exact physical entry/output frames and absolute phases, normalized residual wrappers and identity spectators remain substantive universal interfaces. Actual finite local phase/source checks strengthen the evidence but do not prove arbitrary all-size operator identities.", "Own common-label/mutable-basis owned restore, normalized completed-child semantic height, all-size compiler/occupied-row/stock/tape and analytic recovery remain conditional. The bounded73-axis binary-affine/even-quadratic-Z4 finite-phase grammar is required for the charged universal compiler tariff.", "Actual own constructor/kernel controls, native scalar/frame/wrapper and every finite local phase edge/endpoint, complete owner emitter plus seven mutations and fresh invoice with no retained prior allowance were executed. Original full global CLI, unchanged global data-phase replay and original BIT runtime are not claimed.", "This newly counted direct Gaussian/Fermat circuit uses the exact own selected source body and literal complete finite cover. No source equivalence, previous upper threshold, prior invoice or fabricated BIT saving is consumed. The fixed fallback density tax, per-coefficient40e fallback and full u^(1000000Q) stopped reserve remain paid in all seven operation rows.", "All valid public switching policies of this exact own source-selected literal complete O(73,2) cover enhancement; at least one actual selected public-main unit real ADD per vertex survives at guarded width>=2. No pruning, CSE, aggregation, compression, cover quotienting or native bypass removes it. A branch without such a native invocation returns the identical fixed GMP reference. This inactive rule is an added comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "All valid public switching policies of this exact own source-selected literal complete O(73,2) cover enhancement; at least one actual selected public-main unit real ADD per vertex survives at guarded width>=2. No pruning, CSE, aggregation, compression, cover quotienting or native bypass removes it. A branch without such a native invocation returns the identical fixed GMP reference. This inactive rule is an added comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "Exact same own literal selected programme and full-cover body; complete new group invoice pays it. Both early and record domains separately imply a nonempty native H row above the full1e6Q stopped base. Lower forall policies and constructive upper exists schedule remain distinct." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr536-legacy-kernel92-literal-cover-range.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 10, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/536-manifest.json", "sha256": "1acde85ce95f32800da70a5cf67fc859b6eb353a344c722f267c709740fd820a" }, { "file": "remaining-record-audit/artifacts/536/priority-manifest.json", "sha256": "84489ebe6752265e858f27a6658a6bca6508025d89fef50582721e5c392482a0" } ], "source_head": "71a7ed7a95776810fede6f583885b7faf5d5ff2a" } }, { "pr": 537, "title": "Conditional kappa 0.001538356846647141: higher response spaces meet exact rank-32 saturation", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/537", "author": "Dugongue", "created_at": "2026-10-12T02:21:31Z", "accepted_at": "2026-10-12T13:10:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001538356846647141", "kappa_fraction": "1538356846647141/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public switching policies of this exact own source-selected literal complete O(73,2) cover enhancement; at least one actual selected public-main unit real ADD per vertex survives at guarded width>=2. No pruning, CSE, aggregation, compression, cover quotienting or native bypass removes it. A branch without such a native invocation returns the identical fixed GMP reference. This inactive rule is an added comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source": "data/operation-audit/pr537-open-legacy-v2-literal-cover-lower.json" }, "conditional_upper": null, "cost_status": "conditional_own_source_lower_only", "own_source_cost_extension": true, "early_effective_kappa": "1538356846647141/1000000000000000000", "own_source_scope": [ "Own native arbitrary-input full operator/required phase, dirty helpers, full columns/spectators, owned restoration and compiler/all-size correctness remain explicit hypotheses; finite scalar/byte checks do not discharge them.", "Narrow literal source-selected complete-cover family only; no superior alternative implementation, original BIT saving, sufficient upper, actual first crossing, formal or human proof is claimed.", "All valid public switching policies of this exact own source-selected literal complete O(73,2) cover enhancement; at least one actual selected public-main unit real ADD per vertex survives at guarded width>=2. No pruning, CSE, aggregation, compression, cover quotienting or native bypass removes it. A branch without such a native invocation returns the identical fixed GMP reference. This inactive rule is an added comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "Lower only. No upper, record saving, exact crossing, original full phase/owner replay or universal implementation bound is inferred." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr537-open-legacy-v2-literal-cover-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 12, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/537-manifest.json", "sha256": "722645dab34d8bde924a3ff79dac9643465b4531cc35b0f9097e540322ff0824" }, { "file": "remaining-record-audit/artifacts/537/priority-manifest.json", "sha256": "0ce821f01774ff7f9e509dcc0e29cdd2ada3eab67fbc4f968d0b6ef4dddc0baf" } ], "source_head": "39958faec4fd7e7958ca81f6cffcf70ce74c5e89" } }, { "pr": 584, "title": "Conditional \u03ba = 0.001602080856660739: PR583 frame coalescences on the PR582 three-provider witness", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/584", "author": "jeremykothe2", "created_at": "2026-10-12T12:09:48Z", "accepted_at": "2026-10-12T15:45:40Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001602080856660739", "kappa_fraction": "1602080856660739/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr584-early-frame-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": "Own explicitly selected finite source core, exact RAW and complete program commitments, full own PLAN/OWNERS and fresh complete physical invoice; newly counted direct Gaussian realization with retained operator, phase, owned, all-size and analytic contracts. No earlier invoice or cutoff transfer." }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 79, "source_index": 120, "at": "2026-10-12T12:09:48Z", "until": "2026-10-12T12:22:03Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001602080856660739", "dashboard_float_text": "0.001602080856660739", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/584", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 96, "source_index": null, "at": "2026-10-12T12:09:48Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001602080856660739", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/584", "evidence_excerpt": "Conditional \u03ba = 0.001602080856660739: PR583 frame coalescences on the PR582 three-provider witness", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 365, "source_index": null, "at": "2026-10-12T12:09:48Z", "until": null, "date_basis": "body-version", "fraction": "1602080856660739/1000000000000000000", "value_decimal": "0.001602080856660739", "dashboard_float_text": null, "expression": "0.001602080856660739", "historical_title": "Conditional \u03ba = 0.001602080856660739: PR583 frame coalescences on the PR582 three-provider witness", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/584", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001602080856660739. This is +4.19e-7 over PR583 (0.001601661522127798) and +5.94e-7 over our PR582. The conservative model gives 0.00160208085385131.\n\nThis PR applies chafreaky's PR583 six A-prefix ", "automated_comparable": true, "body_sha256": "cdd792c1441dd61d1f0a594a68a42c9b4c0686bb8af9b0007982a5ed50b657ce" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/cold617.json", "path": "certificates/checkpoints/cold617.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "400569730495803/250000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/family588.json", "path": "certificates/checkpoints/family588.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier741.json", "path": "certificates/checkpoints/frontier741.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier799.json", "path": "certificates/checkpoints/frontier799.json", "commit": null, "at": null, "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. Not a full Lean multiplication theorem. Integration Linux CI status is separate." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier890.json", "path": "certificates/checkpoints/frontier890.json", "commit": null, "at": null, "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier942.json", "path": "certificates/checkpoints/frontier942.json", "commit": null, "at": null, "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "16127213726553/10000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/hyperplane596.json", "path": "certificates/checkpoints/hyperplane596.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "51110230636731/31250000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/k492626.json", "path": "certificates/checkpoints/k492626.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/87db776d70ad1d28a27e9f7906237e5a279414f3/certificates/selected-result.json", "path": null, "commit": "87db776d70ad1d28a27e9f7906237e5a279414f3", "at": "2026-10-13T18:05:11Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3825dc0ea1317629864ebeb6929719cc4bbf525f/certificates/selected-result.json", "path": null, "commit": "3825dc0ea1317629864ebeb6929719cc4bbf525f", "at": "2026-10-13T15:06:01Z", "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3b83e4f14825ce1ae038a8c8159f130646991086/certificates/selected-result.json", "path": null, "commit": "3b83e4f14825ce1ae038a8c8159f130646991086", "at": "2026-10-13T13:30:30Z", "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d6dfd8f21b1e0b7e3f93b7e30e64639390e48504/certificates/selected-result.json", "path": null, "commit": "d6dfd8f21b1e0b7e3f93b7e30e64639390e48504", "at": "2026-10-13T06:44:14Z", "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. Not a full Lean multiplication theorem. Integration Linux CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/c290b7b919790300e14004a75d8d24b55ca3c5b5/certificates/selected-result.json", "path": null, "commit": "c290b7b919790300e14004a75d8d24b55ca3c5b5", "at": "2026-10-13T06:10:31Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/2cdd93d0250554e5160edbb8535c4500c4227349/certificates/selected-result.json", "path": null, "commit": "2cdd93d0250554e5160edbb8535c4500c4227349", "at": "2026-10-13T05:57:09Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "51110230636731/31250000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/5c5567d15bd019186519a4db267914257b5f1ac0/certificates/selected-result.json", "path": null, "commit": "5c5567d15bd019186519a4db267914257b5f1ac0", "at": "2026-10-12T22:36:34Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/2e9ed969d09570fbe949324b80da27a7f31d9399/certificates/selected-result.json", "path": null, "commit": "2e9ed969d09570fbe949324b80da27a7f31d9399", "at": "2026-10-12T21:01:12Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "16127213726553/10000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/1db1fbe68cb5186899cf1fd691bc92056a845e49/certificates/selected-result.json", "path": null, "commit": "1db1fbe68cb5186899cf1fd691bc92056a845e49", "at": "2026-10-12T16:59:30Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "400569730495803/250000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7f6ccd7ed1e5ee7fba9599f44f9a6fe08f582d62/certificates/selected-result.json", "path": null, "commit": "7f6ccd7ed1e5ee7fba9599f44f9a6fe08f582d62", "at": "2026-10-12T15:44:15Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "400569730495803/250000000000000000", "status": "Prepared locally for publication: maintainer-reviewed conditional finite construction; frozen-family integration still in progress", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/270c2458cf7f34fc252afe7c9d697f2cd6c93a59/certificates/selected-result.json", "path": null, "commit": "270c2458cf7f34fc252afe7c9d697f2cd6c93a59", "at": "2026-10-12T14:41:59Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": "Own explicitly selected finite source core, exact RAW and complete program commitments, full own PLAN/OWNERS and fresh complete physical invoice; newly counted direct Gaussian realization with retained operator, phase, owned, all-size and analytic contracts. No earlier invoice or cutoff transfer.", "own_source_record_tail_quantified": true, "own_source_certificate": "pr584-early-frame-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 4, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/584/priority-manifest.json", "sha256": "ef79a7432246b37ec0383c057bd37ef757aa28ed20ea8c52ed0dccca5131e259" } ], "source_head": "e580557d85eb8b8a100361926252d120eb447a44" } }, { "pr": 586, "title": "Verify conditional \u03ba = 0.001602080856660739 with bundled macOS/Linux cold replay", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/586", "author": "chafreaky", "created_at": "2026-10-12T12:22:03Z", "accepted_at": "2026-10-12T15:45:40Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001602080856660739", "kappa_fraction": "1602080856660739/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr586-cold14-typed-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr586-cold14-typed-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/586/priority-manifest.json", "sha256": "fb6c8da32589a3b0fdb810c1533b2578e2438bbe3d6fac5b2ad2562796275a83" } ], "source_head": "4846fee5b06af770e9b3a10c36200f673d656725" } }, { "pr": 587, "title": "Witness spec tools: declarative WITNESS.json inputs, EXPECTED.json comparisons and a generic verifier (no \u03ba claim)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/587", "author": "jeremykothe2", "created_at": "2026-10-12T12:35:49Z", "accepted_at": "2026-10-12T15:45:40Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001601486955392486", "kappa_fraction": "800743477696243/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/587-manifest.json", "sha256": "0ef7d5bf7e449524be07eeb82fd97af7d36d6ed86876962fe10a3bfc6563542e" }, { "file": "remaining-record-audit/artifacts/587/priority-manifest.json", "sha256": "f7dae0176abc30e29b7a61258018a3d1b3157ab17630ad8bcc502de41718fea6" } ], "source_head": "9bf577d56312f7491e4bb39b5fa7d844f318cde9" } }, { "pr": 588, "title": "Conditional \u03ba = 0.001602278921983212: two gate-move frame coalescences on PR584", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/588", "author": "jeremykothe2", "created_at": "2026-10-12T12:37:12Z", "accepted_at": "2026-10-12T15:45:40Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001602278921983212", "kappa_fraction": "400569730495803/250000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr588-mixed-finite-controller-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own arbitrary-input operator-valued native phase, normalized-wrapper, ascending typed-helper and whole Gaussian endpoint contracts remain explicit; scalar specialization is not their proof.", "Exact own selected canonical/program/orientation hashes, actual scalar/frame incidence and dyadic Horner/prefix counts are checked independently. Derived objects are rebuilt from earlier hash-pinned recipes, sometimes using exact matching later archive bytes; no later supplier is imported.", "Each own PLAN/order/dispatch/OWNERS/window, complete role namespace, residual/spectator chart, primitive/wrapper invoice and no-prior-invoice finite stock is freshly checked.", "The counted parent is a primary-fixture source-equivalent numeric realization matching own physical windows; historical parent provenance metadata byte identity is not claimed.", "Common-label, mutable-source, arbitrary-input owned restore and all-size unequal-child occupied-row batching remain fixed-protocol hypotheses; completed Gaussian children have norm one under the endpoint contract.", "Own C0=2^210000 and actual512-bit payload fund the semantic precision reserve. Same direct analytic fine-prime/boundary/recovery, candidate-only Fermat helper and repaired unlimited GMP correctness/halting interfaces." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "historical_selected_or_reviewed_conditional_checkpoint_source", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 80, "source_index": 122, "at": "2026-10-12T12:37:12Z", "until": "2026-10-12T14:10:49Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001602278921983212", "dashboard_float_text": "0.001602278921983212", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/588", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 97, "source_index": null, "at": "2026-10-12T12:37:12Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001602278921983212", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/588", "evidence_excerpt": "Conditional \u03ba = 0.001602278921983212: two gate-move frame coalescences on PR584", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 366, "source_index": null, "at": "2026-10-12T12:37:12Z", "until": null, "date_basis": "body-version", "fraction": "400569730495803/250000000000000000", "value_decimal": "0.001602278921983212", "dashboard_float_text": null, "expression": "0.001602278921983212", "historical_title": "Conditional \u03ba = 0.001602278921983212: two gate-move frame coalescences on PR584", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/588", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001602278921983212. This is +1.98e-7 over our PR584 and PR586 (0.001602080856660739) and +6.17e-7 over PR583. The conservative model gives 0.001602278919174953.\n\nThis PR is PR584 plus two new frame ", "automated_comparable": true, "body_sha256": "43d687e8bd30aea06b03a788f7a81c50175ea63b1c8f715ce7e0da6a19f48c95" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/cold617.json", "path": "certificates/checkpoints/cold617.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "400569730495803/250000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "first_listed_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/family588.json", "path": "certificates/checkpoints/family588.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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Integration Linux CI status is separate." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier890.json", "path": "certificates/checkpoints/frontier890.json", "commit": null, "at": null, "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier942.json", "path": "certificates/checkpoints/frontier942.json", "commit": null, "at": null, "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "16127213726553/10000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/hyperplane596.json", "path": "certificates/checkpoints/hyperplane596.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "51110230636731/31250000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/k492626.json", "path": "certificates/checkpoints/k492626.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/87db776d70ad1d28a27e9f7906237e5a279414f3/certificates/selected-result.json", "path": null, "commit": "87db776d70ad1d28a27e9f7906237e5a279414f3", "at": "2026-10-13T18:05:11Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3825dc0ea1317629864ebeb6929719cc4bbf525f/certificates/selected-result.json", "path": null, "commit": "3825dc0ea1317629864ebeb6929719cc4bbf525f", "at": "2026-10-13T15:06:01Z", "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3b83e4f14825ce1ae038a8c8159f130646991086/certificates/selected-result.json", "path": null, "commit": "3b83e4f14825ce1ae038a8c8159f130646991086", "at": "2026-10-13T13:30:30Z", "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d6dfd8f21b1e0b7e3f93b7e30e64639390e48504/certificates/selected-result.json", "path": null, "commit": "d6dfd8f21b1e0b7e3f93b7e30e64639390e48504", "at": "2026-10-13T06:44:14Z", "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. Not a full Lean multiplication theorem. Integration Linux CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/c290b7b919790300e14004a75d8d24b55ca3c5b5/certificates/selected-result.json", "path": null, "commit": "c290b7b919790300e14004a75d8d24b55ca3c5b5", "at": "2026-10-13T06:10:31Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/2cdd93d0250554e5160edbb8535c4500c4227349/certificates/selected-result.json", "path": null, "commit": "2cdd93d0250554e5160edbb8535c4500c4227349", "at": "2026-10-13T05:57:09Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "51110230636731/31250000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/5c5567d15bd019186519a4db267914257b5f1ac0/certificates/selected-result.json", "path": null, "commit": "5c5567d15bd019186519a4db267914257b5f1ac0", "at": "2026-10-12T22:36:34Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/2e9ed969d09570fbe949324b80da27a7f31d9399/certificates/selected-result.json", "path": null, "commit": "2e9ed969d09570fbe949324b80da27a7f31d9399", "at": "2026-10-12T21:01:12Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "16127213726553/10000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/1db1fbe68cb5186899cf1fd691bc92056a845e49/certificates/selected-result.json", "path": null, "commit": "1db1fbe68cb5186899cf1fd691bc92056a845e49", "at": "2026-10-12T16:59:30Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "400569730495803/250000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "first_listed_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7f6ccd7ed1e5ee7fba9599f44f9a6fe08f582d62/certificates/selected-result.json", "path": null, "commit": "7f6ccd7ed1e5ee7fba9599f44f9a6fe08f582d62", "at": "2026-10-12T15:44:15Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "400569730495803/250000000000000000", "status": "Prepared locally for publication: maintainer-reviewed conditional finite construction; frozen-family integration still in progress", "role": "first_listed_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/270c2458cf7f34fc252afe7c9d697f2cd6c93a59/certificates/selected-result.json", "path": null, "commit": "270c2458cf7f34fc252afe7c9d697f2cd6c93a59", "at": "2026-10-12T14:41:59Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own arbitrary-input operator-valued native phase, normalized-wrapper, ascending typed-helper and whole Gaussian endpoint contracts remain explicit; scalar specialization is not their proof.", "Exact own selected canonical/program/orientation hashes, actual scalar/frame incidence and dyadic Horner/prefix counts are checked independently. Derived objects are rebuilt from earlier hash-pinned recipes, sometimes using exact matching later archive bytes; no later supplier is imported.", "Each own PLAN/order/dispatch/OWNERS/window, complete role namespace, residual/spectator chart, primitive/wrapper invoice and no-prior-invoice finite stock is freshly checked.", "The counted parent is a primary-fixture source-equivalent numeric realization matching own physical windows; historical parent provenance metadata byte identity is not claimed.", "Common-label, mutable-source, arbitrary-input owned restore and all-size unequal-child occupied-row batching remain fixed-protocol hypotheses; completed Gaussian children have norm one under the endpoint contract.", "Own C0=2^210000 and actual512-bit payload fund the semantic precision reserve. Same direct analytic fine-prime/boundary/recovery, candidate-only Fermat helper and repaired unlimited GMP correctness/halting interfaces." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr588-mixed-finite-controller-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 4, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/588/priority-manifest.json", "sha256": "820cecb878614e109fa50b2799f104fdeb6b9a59fd6c76796c2f95ad206b1b22" } ], "source_head": "6d0e53b66c29abd17981881a09eaff41ac862d85" } }, { "pr": 538, "title": "Conditional \u03ba = 0.001530327580902932: kernel92 with native-body frame lifts", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/538", "author": "chafreaky", "created_at": "2026-10-12T02:31:24Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001530327580902932", "kappa_fraction": "382581895225733/250000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public switching policies for this own source-selected literal complete O(73,2) cover enhancement: keep one actual selected public real ADD at every cover vertex with guarded width>=2 and the stipulated ADD lowering; no pruning, CSE, compression, aggregation or native bypass. A branch without such a native invocation is the identical fixed GMP reference. This added inactive rule is a comparison-family definition, not an original source fact. No other implementation or original BIT composition is covered.", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source": "data/operation-audit/pr538-open-legacy-literal-cover-lower.json" }, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr538-legacy-kernel92-literal-cover-range.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "Own selected native all-input Gaussian/helper endpoints, exact physical entry/output frames and absolute phases, normalized residual wrappers and identity spectators remain substantive universal interfaces. Actual finite local phase/source checks strengthen the evidence but do not prove arbitrary all-size operator identities.", "Own common-label/mutable-basis owned restore, normalized completed-child semantic height, all-size compiler/occupied-row/stock/tape and analytic recovery remain conditional. The bounded73-axis binary-affine/even-quadratic-Z4 finite-phase grammar is required for the charged universal compiler tariff.", "Actual own constructor/kernel controls, native scalar/frame/wrapper and every finite local phase edge/endpoint, complete owner emitter plus seven mutations and fresh invoice with no retained prior allowance were executed. Original full global CLI, unchanged global data-phase replay and original BIT runtime are not claimed.", "This newly counted direct Gaussian/Fermat circuit uses the exact own selected source body and literal complete finite cover. No source equivalence, previous upper threshold, prior invoice or fabricated BIT saving is consumed. The fixed fallback density tax, per-coefficient40e fallback and full u^(1000000Q) stopped reserve remain paid in all seven operation rows.", "All valid public switching policies for this own source-selected literal complete O(73,2) cover enhancement: keep one actual selected public real ADD at every cover vertex with guarded width>=2 and the stipulated ADD lowering; no pruning, CSE, compression, aggregation or native bypass. A branch without such a native invocation is the identical fixed GMP reference. This added inactive rule is a comparison-family definition, not an original source fact. No other implementation or original BIT composition is covered.", "All valid public switching policies for this own source-selected literal complete O(73,2) cover enhancement: keep one actual selected public real ADD at every cover vertex with guarded width>=2 and the stipulated ADD lowering; no pruning, CSE, compression, aggregation or native bypass. A branch without such a native invocation is the identical fixed GMP reference. This added inactive rule is a comparison-family definition, not an original source fact. No other implementation or original BIT composition is covered.", "Exact same own literal selected programme and full-cover body; complete new group invoice pays it. Both early and record domains separately imply a nonempty native H row above the full1e6Q stopped base. Lower forall policies and constructive upper exists schedule remain distinct." ] }, "cost_status": "conditional_own_source_range", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "Own selected native all-input Gaussian/helper endpoints, exact physical entry/output frames and absolute phases, normalized residual wrappers and identity spectators remain substantive universal interfaces. Actual finite local phase/source checks strengthen the evidence but do not prove arbitrary all-size operator identities.", "Own common-label/mutable-basis owned restore, normalized completed-child semantic height, all-size compiler/occupied-row/stock/tape and analytic recovery remain conditional. The bounded73-axis binary-affine/even-quadratic-Z4 finite-phase grammar is required for the charged universal compiler tariff.", "Actual own constructor/kernel controls, native scalar/frame/wrapper and every finite local phase edge/endpoint, complete owner emitter plus seven mutations and fresh invoice with no retained prior allowance were executed. Original full global CLI, unchanged global data-phase replay and original BIT runtime are not claimed.", "This newly counted direct Gaussian/Fermat circuit uses the exact own selected source body and literal complete finite cover. No source equivalence, previous upper threshold, prior invoice or fabricated BIT saving is consumed. The fixed fallback density tax, per-coefficient40e fallback and full u^(1000000Q) stopped reserve remain paid in all seven operation rows.", "All valid public switching policies for this own source-selected literal complete O(73,2) cover enhancement: keep one actual selected public real ADD at every cover vertex with guarded width>=2 and the stipulated ADD lowering; no pruning, CSE, compression, aggregation or native bypass. A branch without such a native invocation is the identical fixed GMP reference. This added inactive rule is a comparison-family definition, not an original source fact. No other implementation or original BIT composition is covered.", "All valid public switching policies for this own source-selected literal complete O(73,2) cover enhancement: keep one actual selected public real ADD at every cover vertex with guarded width>=2 and the stipulated ADD lowering; no pruning, CSE, compression, aggregation or native bypass. A branch without such a native invocation is the identical fixed GMP reference. This added inactive rule is a comparison-family definition, not an original source fact. No other implementation or original BIT composition is covered.", "Exact same own literal selected programme and full-cover body; complete new group invoice pays it. Both early and record domains separately imply a nonempty native H row above the full1e6Q stopped base. Lower forall policies and constructive upper exists schedule remain distinct." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr538-legacy-kernel92-literal-cover-range.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 11, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/538-manifest.json", "sha256": "4faa8db16ac1758519a5a08bd9469eda37aaf376c971de85c328018525ed8ac1" }, { "file": "remaining-record-audit/artifacts/538/priority-manifest.json", "sha256": "e957635b7886bf44bd9cae2c04129f2ba4e471884b20f997ce9c6d4fd406195d" } ], "source_head": "a1460516226555dd375d9adb82a8e1dcbfe1ca79" } }, { "pr": 541, "title": "Conditional kappa 0.001587212454640692: trace refinement with a curvature-cone certificate", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/541", "author": "Dugongue", "created_at": "2026-10-12T03:00:27Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001587212454640692", "kappa_fraction": "396803113660173/250000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 55, "source_index": 89, "at": "2026-10-12T03:00:27Z", "until": "2026-10-12T03:24:58Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001587212454640692", "dashboard_float_text": "0.001587212454640692", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/541", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 72, "source_index": null, "at": "2026-10-12T03:00:27Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001587212454640692", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/541", "evidence_excerpt": "Conditional **kappa = 0.001587212454640692**, exactly `396803113660173/250000000000000000`: **+0.143940% over #535** at its pinned head `0d343e2f813f962405481f83d8935299812a7a1c`.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 341, "source_index": null, "at": "2026-10-12T03:00:27Z", "until": null, "date_basis": "body-version", "fraction": "396803113660173/250000000000000000", "value_decimal": "0.001587212454640692", "dashboard_float_text": null, "expression": "0.001587212454640692", "historical_title": "Conditional kappa 0.001587212454640692: trace refinement with a curvature-cone certificate", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/541", "evidence_excerpt": "## Result\n\nConditional kappa = 0.001587212454640692, exactly 396803113660173/250000000000000000: +0.143940% over #535 at its pinned head 0d343e2f813f962405481f83d8935299812a7a1c.\n\nThis combines a new bit word with #535's unchanged ", "automated_comparable": true, "body_sha256": "cf53cf7e0bdff772b9e092de5b45ae91252f48ebfde88ab323d3cfa9a9e667da" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/cold617.json", "path": "certificates/checkpoints/cold617.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "400569730495803/250000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/family588.json", "path": "certificates/checkpoints/family588.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier741.json", "path": "certificates/checkpoints/frontier741.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier799.json", "path": "certificates/checkpoints/frontier799.json", "commit": null, "at": null, "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. Not a full Lean multiplication theorem. Integration Linux CI status is separate." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier890.json", "path": "certificates/checkpoints/frontier890.json", "commit": null, "at": null, "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier942.json", "path": "certificates/checkpoints/frontier942.json", "commit": null, "at": null, "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "16127213726553/10000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/hyperplane596.json", "path": "certificates/checkpoints/hyperplane596.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "51110230636731/31250000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/k492626.json", "path": "certificates/checkpoints/k492626.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/87db776d70ad1d28a27e9f7906237e5a279414f3/certificates/selected-result.json", "path": null, "commit": "87db776d70ad1d28a27e9f7906237e5a279414f3", "at": "2026-10-13T18:05:11Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3825dc0ea1317629864ebeb6929719cc4bbf525f/certificates/selected-result.json", "path": null, "commit": "3825dc0ea1317629864ebeb6929719cc4bbf525f", "at": "2026-10-13T15:06:01Z", "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3b83e4f14825ce1ae038a8c8159f130646991086/certificates/selected-result.json", "path": null, "commit": "3b83e4f14825ce1ae038a8c8159f130646991086", "at": "2026-10-13T13:30:30Z", "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d6dfd8f21b1e0b7e3f93b7e30e64639390e48504/certificates/selected-result.json", "path": null, "commit": "d6dfd8f21b1e0b7e3f93b7e30e64639390e48504", "at": "2026-10-13T06:44:14Z", "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. Not a full Lean multiplication theorem. Integration Linux CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/c290b7b919790300e14004a75d8d24b55ca3c5b5/certificates/selected-result.json", "path": null, "commit": "c290b7b919790300e14004a75d8d24b55ca3c5b5", "at": "2026-10-13T06:10:31Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/2cdd93d0250554e5160edbb8535c4500c4227349/certificates/selected-result.json", "path": null, "commit": "2cdd93d0250554e5160edbb8535c4500c4227349", "at": "2026-10-13T05:57:09Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "51110230636731/31250000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/5c5567d15bd019186519a4db267914257b5f1ac0/certificates/selected-result.json", "path": null, "commit": "5c5567d15bd019186519a4db267914257b5f1ac0", "at": "2026-10-12T22:36:34Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/2e9ed969d09570fbe949324b80da27a7f31d9399/certificates/selected-result.json", "path": null, "commit": "2e9ed969d09570fbe949324b80da27a7f31d9399", "at": "2026-10-12T21:01:12Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "16127213726553/10000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/1db1fbe68cb5186899cf1fd691bc92056a845e49/certificates/selected-result.json", "path": null, "commit": "1db1fbe68cb5186899cf1fd691bc92056a845e49", "at": "2026-10-12T16:59:30Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "400569730495803/250000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7f6ccd7ed1e5ee7fba9599f44f9a6fe08f582d62/certificates/selected-result.json", "path": null, "commit": "7f6ccd7ed1e5ee7fba9599f44f9a6fe08f582d62", "at": "2026-10-12T15:44:15Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "400569730495803/250000000000000000", "status": "Prepared locally for publication: maintainer-reviewed conditional finite construction; frozen-family integration still in progress", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/270c2458cf7f34fc252afe7c9d697f2cd6c93a59/certificates/selected-result.json", "path": null, "commit": "270c2458cf7f34fc252afe7c9d697f2cd6c93a59", "at": "2026-10-12T14:41:59Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 12, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/trace-curvature-preload/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/trace-curvature-preload/EXPECTED.json, research/trace-curvature-preload/README.md, research/trace-curvature-preload/evidence/REPLAY.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/trace-curvature-preload/EXPECTED.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/541-manifest.json", "sha256": "3a42f16d3ef72fa7a9bb05caea84303a86df93daf3258ac2e08d0c593f91a74b" }, { "file": "remaining-record-audit/artifacts/541/priority-manifest.json", "sha256": "1799dbeeaabc8fe308649c41c8674a75907c56a47d1febdf87c8f96926a0cb80" } ], "source_head": "8725c162e4ffdbada8847e235ccdbcaedef87af9" } }, { "pr": 542, "title": "Conditional kappa 0.001587467473762886: PR541 trace plus sliced R480 frames", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/542", "author": "rohanarun", "created_at": "2026-10-12T03:03:18Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001587467473762886", "kappa_fraction": "793733736881443/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 56, "source_index": 90, "at": "2026-10-12T03:24:58Z", "until": "2026-10-12T03:28:05Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001587467473762886", "dashboard_float_text": "0.001587467473762886", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/542", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 73, "source_index": null, "at": "2026-10-12T03:24:58Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001587467473762886", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/542", "evidence_excerpt": "**Conditional kappa =0.001587467473762886**, exactly `793733736881443/500000000000000000`: **+0.0160671% over #541**. Fresh local finite physical verification passes; the unchanged cited complex supplier now binds.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 342, "source_index": null, "at": "2026-10-12T03:13:45Z", "until": null, "date_basis": "body-version", "fraction": "793733736881443/500000000000000000", "value_decimal": "0.001587467473762886", "dashboard_float_text": null, "expression": "0.001587467473762886", "historical_title": "Conditional candidate kappa 0.001587467473762886: PR541 trace plus sliced R480 frames", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/542", "evidence_excerpt": "Draft combined conditional kappa =0.001587467473762886, above #541's0.001587212454640692. Combined physical verification is pending; this update is published before that replay completes.\n\nThis integrates Dugongue #541's60 commuting p", "automated_comparable": true, "body_sha256": "0268fcb26ba16b5deac58d85beea4c2c5379cfae77c345fc61282d871121d8b8" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/r480-sliced-minimal-frames/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Recompute the complete own productive/paid histogram from research/r480-sliced-minimal-frames/evidence/NATIVE-LEGALITY314.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/r480-sliced-minimal-frames/EXPECTED.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/542-manifest.json", "sha256": "21eb54a97c82a2ffea39d2c049248dd1b028c55e5273ff56c41bbfb95ce4258f" }, { "file": "remaining-record-audit/artifacts/542/priority-manifest.json", "sha256": "bb9b5f3f258ece30299ceb63b155954f4da48377420625c6da04c4fccf78fe70" } ], "source_head": "fceff375b8308e793afbc684690341fab5affc39" } }, { "pr": 543, "title": "Conditional \u03ba = 0.001587467473762886: an E8 bit word with 420 helpers, c = 0.001653826988 (+4.18% over #510)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/543", "author": "eumemic", "created_at": "2026-10-12T03:28:05Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001587467473762886", "kappa_fraction": "793733736881443/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr543-paired-selected-complex-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own arbitrary-column local/frame/phase identities, absolute phases, all distinct live owners, full spectator/dirty-helper restoration.", "Own all-size unequal-child normalized Lemma A, common-label/mutable-basis compiler, once-only padding, and restored-row stock interfaces.", "Own precision/tape semantic completed-child guard C0=2^210000; completed exact Gaussian children have semantic norm one under their endpoint contract.", "Parameterized direct Gaussian/fine-prime/finite-section/boundary/recovery analytic interfaces; no finite-field BIT-routing wrapper.", "Same fixed XAG lowering and repaired unlimited optimized-GMP correctness/halting contracts as the prior source-specific certificates.", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "This NEW direct Gaussian/Fermat XAG realization executes the complete complex supplier explicitly named primary by the own paired construction. The changed own BIT circuit is wholly UNUSED: no claim is made to price it or to attribute the resulting runtime to its optimization.", "Both actually cited535 source heads have the exact complete52item MANIFEST of the separately closed535 native/physical/invoice component. Every actual selected source payload is rechecked; this is full serialized source identity, not equality of kappa, a histogram or an old upper.", "Required normalized Gaussian/native absolute-phase, entry/output frames, arbitrary-input helper/spectator restore, common-label/owned all-size compiler/row/tape and analytic contracts remain substantive explicit premises. No fresh original BIT/native-phase/global verifier run is claimed.", "All inherited fallback density tax, per-coefficient40e direct fallback, full u^(1000000Q) stopped reserve, concrete-scale Schur and all actual seven operation rows are retained. The optional BIT argument/saving is absent from this reduced branch." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own arbitrary-column local/frame/phase identities, absolute phases, all distinct live owners, full spectator/dirty-helper restoration.", "Own all-size unequal-child normalized Lemma A, common-label/mutable-basis compiler, once-only padding, and restored-row stock interfaces.", "Own precision/tape semantic completed-child guard C0=2^210000; completed exact Gaussian children have semantic norm one under their endpoint contract.", "Parameterized direct Gaussian/fine-prime/finite-section/boundary/recovery analytic interfaces; no finite-field BIT-routing wrapper.", "Same fixed XAG lowering and repaired unlimited optimized-GMP correctness/halting contracts as the prior source-specific certificates.", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "This NEW direct Gaussian/Fermat XAG realization executes the complete complex supplier explicitly named primary by the own paired construction. The changed own BIT circuit is wholly UNUSED: no claim is made to price it or to attribute the resulting runtime to its optimization.", "Both actually cited535 source heads have the exact complete52item MANIFEST of the separately closed535 native/physical/invoice component. Every actual selected source payload is rechecked; this is full serialized source identity, not equality of kappa, a histogram or an old upper.", "Required normalized Gaussian/native absolute-phase, entry/output frames, arbitrary-input helper/spectator restore, common-label/owned all-size compiler/row/tape and analytic contracts remain substantive explicit premises. No fresh original BIT/native-phase/global verifier run is claimed.", "All inherited fallback density tax, per-coefficient40e direct fallback, full u^(1000000Q) stopped reserve, concrete-scale Schur and all actual seven operation rows are retained. The optional BIT argument/saving is absent from this reduced branch." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr543-paired-selected-complex-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 6, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/543-manifest.json", "sha256": "31da007b9b95480fc7a031c92eb4abb0cc2cb88e2aee86415ecc8d27f69f71e8" }, { "file": "remaining-record-audit/artifacts/543/priority-manifest.json", "sha256": "dac34d7de554329b14658e45435c0126adf11eabee40447a2d46f25a1c0fc5f8" } ], "source_head": "2065fe4f72a914d907f1046603f5a36f17018535" } }, { "pr": 544, "title": "Conditional \u03ba = 0.001588602246663212: static44 with selective bit frames", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/544", "author": "chafreaky", "created_at": "2026-10-12T03:29:42Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001588602246663212", "kappa_fraction": "397150561665803/250000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 57, "source_index": 92, "at": "2026-10-12T03:29:42Z", "until": "2026-10-12T03:32:16Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001588602246663212", "dashboard_float_text": "0.001588602246663212", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/544", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 74, "source_index": null, "at": "2026-10-12T03:29:42Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001588602246663212", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/544", "evidence_excerpt": "Conditional \u03ba = 0.001588602246663212: static44 with selective bit frames", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 343, "source_index": null, "at": "2026-10-12T03:29:42Z", "until": null, "date_basis": "body-version", "fraction": "397150561665803/250000000000000000", "value_decimal": "0.001588602246663212", "dashboard_float_text": null, "expression": "0.001588602246663212", "historical_title": "Conditional \u03ba = 0.001588602246663212: static44 with selective bit frames", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/544", "evidence_excerpt": "This conditional finite witness reaches \u03ba = 0.001588602246663212: +0.08756181% over #541 and +0.07148322% over #542 at the reviewed heads. Newly opened #543 reports the same combined \u03ba as #542, with a stronger bit supplier that is not adopted i", "automated_comparable": true, "body_sha256": "72849274841f37605a83641b57693f9583942e50bd0a4d8987c6bf637b53ad3d" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 12, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/static44-selective/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Recompute the complete own productive/paid histogram from research/static44-selective/data/PLAN.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/static44-selective-validation/linux-python312/RESULT.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/544-manifest.json", "sha256": "dc13919672d16ded23ccff871a47fd5d767bd5295ecab3bb349ba93947724dac" }, { "file": "remaining-record-audit/artifacts/544/priority-manifest.json", "sha256": "da92b1401d644ec719870c431aefd9aecf9774f81bc093468d4af9e2078e3d49" } ], "source_head": "4858bb38da10cd8a1cd25ef85e7c14f4e2b529dd" } }, { "pr": 545, "title": "Punctured star bit unit: bit c = 0.00165947204563779652541 (+4.54% over #510)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/545", "author": "DreamingOfClouds", "created_at": "2026-10-12T03:32:14Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001587467473762886", "kappa_fraction": "793733736881443/500000000000000000", "kappa_status": "authenticated_actual_merged_source_selection", "kappa_scope": "The costed \u03ba comes from the explicitly selected source included at this merge. The original parser quote is retained and visibly distinguished. Own EXPECTED.kappa.pr535 and literal verifier select the complete primary composition. The frozen parser instead quoted own EXPECTED.pr535, explicitly the cited535 baseline. Both values are preserved; actual ownhead is eighth of43 merge parents.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr545-paired-selected-complex-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own arbitrary-column local/frame/phase identities, absolute phases, all distinct live owners, full spectator/dirty-helper restoration.", "Own all-size unequal-child normalized Lemma A, common-label/mutable-basis compiler, once-only padding, and restored-row stock interfaces.", "Own precision/tape semantic completed-child guard C0=2^210000; completed exact Gaussian children have semantic norm one under their endpoint contract.", "Parameterized direct Gaussian/fine-prime/finite-section/boundary/recovery analytic interfaces; no finite-field BIT-routing wrapper.", "Same fixed XAG lowering and repaired unlimited optimized-GMP correctness/halting contracts as the prior source-specific certificates.", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "This NEW direct Gaussian/Fermat XAG realization executes the complete complex supplier explicitly named primary by the own paired construction. The changed own BIT circuit is wholly UNUSED: no claim is made to price it or to attribute the resulting runtime to its optimization.", "Both actually cited535 source heads have the exact complete52item MANIFEST of the separately closed535 native/physical/invoice component. Every actual selected source payload is rechecked; this is full serialized source identity, not equality of kappa, a histogram or an old upper.", "Required normalized Gaussian/native absolute-phase, entry/output frames, arbitrary-input helper/spectator restore, common-label/owned all-size compiler/row/tape and analytic contracts remain substantive explicit premises. No fresh original BIT/native-phase/global verifier run is claimed.", "All inherited fallback density tax, per-coefficient40e direct fallback, full u^(1000000Q) stopped reserve, concrete-scale Schur and all actual seven operation rows are retained. The optional BIT argument/saving is absent from this reduced branch." ] }, "cost_status": "conditional_own_source_upper_only", "frozen_kappa_metadata": { "kappa_fraction": "1584931111785787/1000000000000000000", "kappa_decimal": "0.001584931111785787", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews." }, "source_selected_kappa_correction": true, "source_selected_kappa_correction_basis": "Own EXPECTED.kappa.pr535 and literal verifier select the complete primary composition. The frozen parser instead quoted own EXPECTED.pr535, explicitly the cited535 baseline. Both values are preserved; actual ownhead is eighth of43 merge parents.", "source_kappa_correction_primary_receipt": "data/operation-audit/paired-complex-selection-source/545/chronology.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own arbitrary-column local/frame/phase identities, absolute phases, all distinct live owners, full spectator/dirty-helper restoration.", "Own all-size unequal-child normalized Lemma A, common-label/mutable-basis compiler, once-only padding, and restored-row stock interfaces.", "Own precision/tape semantic completed-child guard C0=2^210000; completed exact Gaussian children have semantic norm one under their endpoint contract.", "Parameterized direct Gaussian/fine-prime/finite-section/boundary/recovery analytic interfaces; no finite-field BIT-routing wrapper.", "Same fixed XAG lowering and repaired unlimited optimized-GMP correctness/halting contracts as the prior source-specific certificates.", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "This NEW direct Gaussian/Fermat XAG realization executes the complete complex supplier explicitly named primary by the own paired construction. The changed own BIT circuit is wholly UNUSED: no claim is made to price it or to attribute the resulting runtime to its optimization.", "Both actually cited535 source heads have the exact complete52item MANIFEST of the separately closed535 native/physical/invoice component. Every actual selected source payload is rechecked; this is full serialized source identity, not equality of kappa, a histogram or an old upper.", "Required normalized Gaussian/native absolute-phase, entry/output frames, arbitrary-input helper/spectator restore, common-label/owned all-size compiler/row/tape and analytic contracts remain substantive explicit premises. No fresh original BIT/native-phase/global verifier run is claimed.", "All inherited fallback density tax, per-coefficient40e direct fallback, full u^(1000000Q) stopped reserve, concrete-scale Schur and all actual seven operation rows are retained. The optional BIT argument/saving is absent from this reduced branch." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr545-paired-selected-complex-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 6, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/545-manifest.json", "sha256": "633dfd53b4d7d85a6f4b421d3e7561318af71cee42bdf0e7fb4004b4bfb872b9" }, { "file": "remaining-record-audit/artifacts/545/priority-manifest.json", "sha256": "75425c80f16f5ac8182eff1d66d283179b66c4d280b958f517f6e6dd4edf82b3" } ], "source_head": "376426f3b2b26ab430d10baf16bbd9ff42990a7c" } }, { "pr": 547, "title": "Conditional kappa 0.001590984155135328: R420 bit plus PR548 complex", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/547", "author": "rohanarun", "created_at": "2026-10-12T03:38:02Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001590984155135328", "kappa_fraction": "49718254847979/31250000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 59, "source_index": 95, "at": "2026-10-12T03:51:03Z", "until": "2026-10-12T04:23:01Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001590984155135328", "dashboard_float_text": "0.001590984155135328", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/547", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 76, "source_index": null, "at": "2026-10-12T03:51:03Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001590984155135328", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/547", "evidence_excerpt": "Conditional kappa 0.001590984155135328: R420 bit plus PR548 complex", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 344, "source_index": null, "at": "2026-10-12T03:38:02Z", "until": null, "date_basis": "body-version", "fraction": "397677800014309/250000000000000000", "value_decimal": "0.001590984155135328", "dashboard_float_text": null, "expression": "0.001590711200057236", "historical_title": "Conditional kappa 0.001590711200057236: R420 bit plus static44 complex", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/547", "evidence_excerpt": "Conditional kappa = 0.001590711200057236, +0.1327553% over #544. Compose #543's R420 bit supplier with #544's globally admitted static44 complex supplier and owner allocation. The complex supplier now binds.\n\nPinned bit ", "automated_comparable": true, "body_sha256": "bf1309ec2a613cac682d25fbae0d9a4cdce29086ad6f4e872249fb97db16ff91" }, { "stream": "recovered_literal_highwater", "stream_row": 345, "source_index": null, "at": "2026-10-12T03:51:03Z", "until": null, "date_basis": "body-version", "fraction": "49718254847979/31250000000000000", "value_decimal": "0.001590984155135328", "dashboard_float_text": null, "expression": "0.001590984155135328", "historical_title": "Conditional kappa 0.001590984155135328: R420 bit plus PR548 complex", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/547", "evidence_excerpt": "Conditional kappa = 0.001590984155135328, +0.0171593% over this PR's earlier 0.001590711200057236. Compose #543's verified R420 bit supplier with #548's stronger complex component. The complex supplier binds.\n\nBit c =0.0", "automated_comparable": true, "body_sha256": "8a6285e2b7d75193070da08bb0a8f667aec07bc5bb52b4b2a20ec1140a310dd7" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/r420-static44-composition/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/r420-static44-composition/EXPECTED.json, research/r420-static44-composition/MANIFEST.json, research/r420-static44-composition/README.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/r420-static44-composition/EXPECTED.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/547-manifest.json", "sha256": "942aaf5b7493c965939098c2b906fbeae210199804d60247ae67da7c4451679e" }, { "file": "remaining-record-audit/artifacts/547/priority-manifest.json", "sha256": "e0f5fc63fe34601c3936c7310683101e6d2e554d0df05e3429f09fea8bfc580f" } ], "source_head": "eecca20a24258cb6d9f698b1984a95029bac0a1c" } }, { "pr": 548, "title": "Conditional kappa 0.001590591090759927: observable pruning, Steinberg cancellation and response-owner composition", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/548", "author": "Dugongue", "created_at": "2026-10-12T03:45:17Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001590591090759927", "kappa_fraction": "1590591090759927/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 58, "source_index": 94, "at": "2026-10-12T03:45:17Z", "until": "2026-10-12T03:51:03Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001590591090759927", "dashboard_float_text": "0.001590591090759927", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/548", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 75, "source_index": null, "at": "2026-10-12T03:45:17Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001590591090759927", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/548", "evidence_excerpt": "Conditional kappa 0.001590591090759927: observable pruning, Steinberg cancellation and response-owner composition", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/cold617.json", "path": "certificates/checkpoints/cold617.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "400569730495803/250000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/family588.json", "path": "certificates/checkpoints/family588.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. 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See review for replay reuse and Linux CI status." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/pruned-trace-response/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/pruned-trace-response/EXPECTED.json, research/pruned-trace-response/verify.py, research/pruned-trace-response/README.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/pruned-trace-response/EXPECTED.json#/ after native/invoice selection. 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No pruning/CSE/aggregation/cover quotient/compression/native bypass. Any branch without such a body returns identical fixed GMP; this inactive rule is an explicit additional comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source": "data/operation-audit/pr550-trace-rank5-v4-literal-cover-lower.json" }, "conditional_upper": null, "cost_status": "conditional_own_source_lower_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 60, "source_index": 96, "at": "2026-10-12T04:23:01Z", "until": "2026-10-12T04:33:32Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001591045666134196", "dashboard_float_text": "0.001591045666134196", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/550", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 77, "source_index": null, "at": "2026-10-12T04:23:01Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001591045666134196", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/550", "evidence_excerpt": "Conditional \u03ba = 0.001591045666134196: rank-five complex trace expansion", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 346, "source_index": null, "at": "2026-10-12T04:23:01Z", "until": null, "date_basis": "body-version", "fraction": "397761416533549/250000000000000000", "value_decimal": "0.001591045666134196", "dashboard_float_text": null, "expression": "0.001591045666134196", "historical_title": "Conditional \u03ba = 0.001591045666134196: rank-five complex trace expansion", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/550", "evidence_excerpt": "\u03ba = 0.001591045666134196 (conditional).\n\nThis new finite witness is 0.0038662232% above #547 at eecca20a24258cb6d9f698b1984a95029bac0a1c (0.001590984155135328). 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Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d6dfd8f21b1e0b7e3f93b7e30e64639390e48504/certificates/selected-result.json", "path": null, "commit": "d6dfd8f21b1e0b7e3f93b7e30e64639390e48504", "at": "2026-10-13T06:44:14Z", "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. Not a full Lean multiplication theorem. Integration Linux CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/c290b7b919790300e14004a75d8d24b55ca3c5b5/certificates/selected-result.json", "path": null, "commit": "c290b7b919790300e14004a75d8d24b55ca3c5b5", "at": "2026-10-13T06:10:31Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/2cdd93d0250554e5160edbb8535c4500c4227349/certificates/selected-result.json", "path": null, "commit": "2cdd93d0250554e5160edbb8535c4500c4227349", "at": "2026-10-13T05:57:09Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "51110230636731/31250000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/5c5567d15bd019186519a4db267914257b5f1ac0/certificates/selected-result.json", "path": null, "commit": "5c5567d15bd019186519a4db267914257b5f1ac0", "at": "2026-10-12T22:36:34Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/2e9ed969d09570fbe949324b80da27a7f31d9399/certificates/selected-result.json", "path": null, "commit": "2e9ed969d09570fbe949324b80da27a7f31d9399", "at": "2026-10-12T21:01:12Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "16127213726553/10000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/1db1fbe68cb5186899cf1fd691bc92056a845e49/certificates/selected-result.json", "path": null, "commit": "1db1fbe68cb5186899cf1fd691bc92056a845e49", "at": "2026-10-12T16:59:30Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "400569730495803/250000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7f6ccd7ed1e5ee7fba9599f44f9a6fe08f582d62/certificates/selected-result.json", "path": null, "commit": "7f6ccd7ed1e5ee7fba9599f44f9a6fe08f582d62", "at": "2026-10-12T15:44:15Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "400569730495803/250000000000000000", "status": "Prepared locally for publication: maintainer-reviewed conditional finite construction; frozen-family integration still in progress", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/270c2458cf7f34fc252afe7c9d697f2cd6c93a59/certificates/selected-result.json", "path": null, "commit": "270c2458cf7f34fc252afe7c9d697f2cd6c93a59", "at": "2026-10-12T14:41:59Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "397761416533549/250000000000000000", "own_source_scope": [ "Universal Gaussian/helper entry/output/required phase/identity-spectator, owned/all-size and fixed-reference correctness remain substantive hypotheses. Bounded actual source/native scalar-frame jobs do not prove universal phase/operator or original record correctness.", "All valid public policies of this own source-selected literal complete O(73,2) native body, with a surviving actual distinct public-main unit ADD at each vertex at guarded width>=2. No pruning/CSE/aggregation/cover quotient/compression/native bypass. Any branch without such a body returns identical fixed GMP; this inactive rule is an explicit additional comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "Lower only, V-only. No upper, actual crossing, original full phase/owner/invoice/CLI pass, human/formal proof or hardware claim.", "All valid public policies of this own source-selected literal complete O(73,2) native body, with a surviving actual distinct public-main unit ADD at each vertex at guarded width>=2. No pruning/CSE/aggregation/cover quotient/compression/native bypass. Any branch without such a body returns identical fixed GMP; this inactive rule is an explicit additional comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "Lower only. No upper, record saving, exact crossing, original full phase/owner/invoice/CLI pass or universal implementation bound is inferred." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr550-trace-rank5-v4-literal-cover-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 12, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/550-manifest.json", "sha256": "eaf9573ac64602c79c7305a9013e47c6319befd6f942e8eee764f9fe18ee05a1" }, { "file": "remaining-record-audit/artifacts/550/priority-manifest.json", "sha256": "78cf48a1ce236f2a60bb2543860b67edccb2c6167458d717357466d92ae10bea" } ], "source_head": "c7337040822978f1611ce9d9d44e7bb96d887e23" } }, { "pr": 551, "title": "Conditional \u03ba = 0.001591968902833346: subspace16 complex with full R420 replay", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/551", "author": "chafreaky", "created_at": "2026-10-12T04:33:32Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001591968902833346", "kappa_fraction": "795984451416673/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 61, "source_index": 97, "at": "2026-10-12T04:33:32Z", "until": "2026-10-12T04:35:15Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001591968902833346", "dashboard_float_text": "0.001591968902833346", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/551", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 78, "source_index": null, "at": "2026-10-12T04:33:32Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001591968902833346", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/551", "evidence_excerpt": "Conditional \u03ba = 0.001591968902833346: subspace16 complex with full R420 replay", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 347, "source_index": null, "at": "2026-10-12T04:33:32Z", "until": null, "date_basis": "body-version", "fraction": "795984451416673/500000000000000000", "value_decimal": "0.001591968902833346", "dashboard_float_text": null, "expression": "0.001591968902833346", "historical_title": "Conditional \u03ba = 0.001591968902833346: subspace16 complex with full R420 replay", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/551", "evidence_excerpt": "Conditional \u03ba = 0.001591968902833346, +0.06189551% over PR547 at eecca20a24258cb6d9f698b1984a95029bac0a1c (\u03ba = 0.001590984155135328). Complex b = 0.001594507308884431019637 binds; unchanged PR543 R420 bit c = 0.00165", "automated_comparable": true, "body_sha256": "b610c1fd99b8e6a8e9569a6baf02a52fbf7a87c48eea7ceb4d76506b27f02926" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/subspace16-r420/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Recompute the complete own productive/paid histogram from research/subspace16-r420/data/PLAN.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/subspace16-r420/EXPECTED.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/551-manifest.json", "sha256": "5b96eb85a663623344dfbdd79cae533fef9bd56fb32aebd17f8c0108d51c593f" }, { "file": "remaining-record-audit/artifacts/551/priority-manifest.json", "sha256": "01bc474cfd91d866a67e932875ced68a3a37600284e3198a887d66579dc29e18" } ], "source_head": "e7faafc4fec401d24080e5b2df12f964f1cfe123" } }, { "pr": 552, "title": "Conditional kappa 0.001591968902833346: collective hyperplane waves and weighted response decoding", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/552", "author": "Dugongue", "created_at": "2026-10-12T04:35:15Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001591968902833346", "kappa_fraction": "795984451416673/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/filtration-wavefront/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/filtration-wavefront/EXPECTED.json, research/filtration-wavefront/MANIFEST.json, research/filtration-wavefront/complex-global/SOURCES.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/filtration-wavefront/EXPECTED.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/552-manifest.json", "sha256": "ca208db3b1e76f86a020cd8cbd5ed1b06f68cd07b263bdab64a6989d4d09fb8f" }, { "file": "remaining-record-audit/artifacts/552/priority-manifest.json", "sha256": "2e59a877b9621558d2f61c2d9a8eea2518fa93d01e7803af7c07b40d9567706b" } ], "source_head": "33c33af0b7697155be1ea708e08cbd3f0707d94c" } }, { "pr": 554, "title": "Conditional kappa 0.001591209947088545: jointly retimed complex trace", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/554", "author": "rohanarun", "created_at": "2026-10-12T04:39:48Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001591209947088545", "kappa_fraction": "318241989417709/200000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public policies of this own source-selected literal complete O(73,2) native body, with a surviving actual distinct public-main unit ADD at each vertex at guarded width>=2. No pruning/CSE/aggregation/cover quotient/compression/native bypass. Any branch without such a body returns identical fixed GMP; this inactive rule is an explicit additional comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source": "data/operation-audit/pr554-trace-rank5-v4-literal-cover-lower.json" }, "conditional_upper": null, "cost_status": "conditional_own_source_lower_only", "own_source_cost_extension": true, "early_effective_kappa": "318241989417709/200000000000000000", "own_source_scope": [ "Universal Gaussian/helper entry/output/required phase/identity-spectator, owned/all-size and fixed-reference correctness remain substantive hypotheses. Bounded actual source/native scalar-frame jobs do not prove universal phase/operator or original record correctness.", "All valid public policies of this own source-selected literal complete O(73,2) native body, with a surviving actual distinct public-main unit ADD at each vertex at guarded width>=2. No pruning/CSE/aggregation/cover quotient/compression/native bypass. Any branch without such a body returns identical fixed GMP; this inactive rule is an explicit additional comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "Lower only, V-only. No upper, actual crossing, original full phase/owner/invoice/CLI pass, human/formal proof or hardware claim.", "All valid public policies of this own source-selected literal complete O(73,2) native body, with a surviving actual distinct public-main unit ADD at each vertex at guarded width>=2. No pruning/CSE/aggregation/cover quotient/compression/native bypass. Any branch without such a body returns identical fixed GMP; this inactive rule is an explicit additional comparison-family definition, not an original source fact. Other implementations and original BIT compositions are excluded.", "Lower only. No upper, record saving, exact crossing, original full phase/owner/invoice/CLI pass or universal implementation bound is inferred." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr554-trace-rank5-v4-literal-cover-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 12, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/554-manifest.json", "sha256": "24af5a4a2d900c5acb6e6fac2498175ed54515ad40a588ca9d2ab59fd4aed398" }, { "file": "remaining-record-audit/artifacts/554/priority-manifest.json", "sha256": "d02084049b632c186ec8e3220545913d58561dafb9e40155302a18fe670ce3f8" } ], "source_head": "c1c252e2838918f3de866b228f5a3f21cb9f4b2d" } }, { "pr": 555, "title": "Bit c = 0.001733052823: #545's punctured unit on the R420 skeleton (111 live ports, +4.79% over #543)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/555", "author": "eumemic", "created_at": "2026-10-12T04:54:34Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001590984155135328", "kappa_fraction": "49718254847979/31250000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/e8-bit-p111/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Recompute the complete own productive/paid histogram from research/e8-bit-p111/data/complex/pr535/EXPECTED.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/e8-bit-p111/EXPECTED.json#/eleven after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/555-manifest.json", "sha256": "62c0f9a10b442ef3804fbbccb8da41223b167230c53a18db3a2c0db4b575f89d" }, { "file": "remaining-record-audit/artifacts/555/priority-manifest.json", "sha256": "0ed3f82a618b5da4a2cd193c94604da0f2c5cfbbdd615eb475cc8509044e19f8" } ], "source_head": "65a6bc19f820c8b1873f65a517bcf70cd6887223" } }, { "pr": 558, "title": "Conditional \u03ba = 0.001592517889315014: eight rank-five kernel pivots", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/558", "author": "eumemic", "created_at": "2026-10-12T05:09:48Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001592517889315014", "kappa_fraction": "796258944657507/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 62, "source_index": 100, "at": "2026-10-12T05:09:48Z", "until": "2026-10-12T05:24:31.602043Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001592517889315014", "dashboard_float_text": "0.001592517889315014", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/558", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 79, "source_index": null, "at": "2026-10-12T05:09:48Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001592517889315014", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/558", "evidence_excerpt": "\u03ba = 0.001592517889315014 (conditional).", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 348, "source_index": null, "at": "2026-10-12T05:09:48Z", "until": null, "date_basis": "body-version", "fraction": "796258944657507/500000000000000000", "value_decimal": "0.001592517889315014", "dashboard_float_text": null, "expression": "0.001592517889315014", "historical_title": "Conditional \u03ba = 0.001592517889315014: eight rank-five kernel pivots", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/558", "evidence_excerpt": "\u03ba = 0.001592517889315014 (conditional).\n\nThis new finite witness is 0.034484749% above the tied #551/#552 value 0.001591968902833346. 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See review for replay reuse and Linux CI status." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/complex-rank5-pivots8-validation/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Recompute the complete own productive/paid histogram from research/complex-rank5-pivots8/data/PLAN.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/complex-rank5-pivots8-validation/python312-clean-archive/RESULT.json#/ after native/invoice selection. 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See review for replay reuse and Linux CI status." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "supporting_contract_audit_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "If a cutoff for a referenced earlier construction is sought, separately bind its complete selected program, physical invoice and parameters; no numerical cutoff transfers from this scope audit." ], "source_manifest": [ { "file": "individual-primary-interface-source/559-manifest.json", "sha256": "ee636658daa7220a01acab18fa6cd3f3f1b3de623d006fad6f26b5c286c64051" }, { "file": "remaining-record-audit/artifacts/559/priority-manifest.json", "sha256": "c542b8f3b8279983ec955c2a98127e7b4d7cc0c6fd4f8fc493926c1e30bab2c0" } ], "source_head": "d858c0b2edcc704ef370b3c96dc51a75439b77b0" } }, { "pr": 560, "title": "Conditional kappa = 0.001591975256487475: five-copy remainder pooling and exact carrier epochs", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/560", "author": "Dugongue", "created_at": "2026-10-12T05:38:10Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001591975256487475", "kappa_fraction": "63679010259499/40000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/pooled-clone-epochs/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/pooled-clone-epochs/EXPECTED.json, research/pooled-clone-epochs/MANIFEST.json, research/pooled-clone-epochs/complex-global/vendor531/evidence/audit/PREFIX-AND-INVOICE.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/pooled-clone-epochs/EXPECTED.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/560-manifest.json", "sha256": "23cd81feb61f104085ef6d0e6291a8abf92690ba03cefc3282bd0035f9b96ace" }, { "file": "remaining-record-audit/artifacts/560/priority-manifest.json", "sha256": "e8ccf35eda90844fae9e830e6272595b6251799c025a0336df9d8b87fefda9e8" } ], "source_head": "15246a063cac02653d702a80f79b36081e7f596a" } }, { "pr": 561, "title": "Conditional \u03ba = 0.001592518729588709: one call-specific cold-kernel provider", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/561", "author": "eumemic", "created_at": "2026-10-12T05:39:25Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001592518729588709", "kappa_fraction": "1592518729588709/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source": "data/operation-audit/pr561-open-multicold-v3-literal-cover-lower.json" }, "conditional_upper": null, "cost_status": "conditional_own_source_lower_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 64, "source_index": 103, "at": "2026-10-12T05:39:25Z", "until": "2026-10-12T05:56:47Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001592518729588709", "dashboard_float_text": "0.001592518729588709", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/561", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 81, "source_index": null, "at": "2026-10-12T05:39:25Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001592518729588709", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/561", "evidence_excerpt": "\u03ba = 0.001592518729588709 (conditional).", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 350, "source_index": null, "at": "2026-10-12T05:39:25Z", "until": null, "date_basis": "body-version", "fraction": "1592518729588709/1000000000000000000", "value_decimal": "0.001592518729588709", "dashboard_float_text": null, "expression": "0.001592518729588709", "historical_title": "Conditional \u03ba = 0.001592518729588709: one call-specific cold-kernel provider", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/561", "evidence_excerpt": "\u03ba = 0.001592518729588709 (conditional).\n\nThis new finite mixed-provider witness exceeds frozen #558 at 060b137c8a6f9d73fd7864c7f8cf2736d6441774 (0.001592517889315014) and the latest #559 at d858c0b2edcc70", "automated_comparable": true, "body_sha256": "ea21271d4e49b5a680f614abeb64cf56ac1aa32aca2986f45a746ade6187a8f3" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/cold617.json", "path": "certificates/checkpoints/cold617.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. 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See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "400569730495803/250000000000000000", "status": "Prepared locally for publication: maintainer-reviewed conditional finite construction; frozen-family integration still in progress", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/270c2458cf7f34fc252afe7c9d697f2cd6c93a59/certificates/selected-result.json", "path": null, "commit": "270c2458cf7f34fc252afe7c9d697f2cd6c93a59", "at": "2026-10-12T14:41:59Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1592518729588709/1000000000000000000", "own_source_scope": [ "Own universal Gaussian/helper required entry/output/absolute-phase/identity-spectator and owned/all-size correctness remain substantive hypotheses. This lower proves compulsory cost of the prescribed literal body, not correctness or original record validity of unexecuted providers.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Only V is used; no coordinate-volume factor, stock upper used as lower, selected activation threshold, sufficient upper, exact crossing, human/formal proof or hardware claim.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Lower only; one positively used exact own-source provider suffices for compulsory work in the complete prescribed kernel. Other changed providers are not substituted or claimed validated. No upper or actual crossing." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr561-open-multicold-v3-literal-cover-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 12, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/561-manifest.json", "sha256": "d3cc53b6d194e155fa9e2219eb386c55110e343bb409669fb177f36c837c1a88" }, { "file": "remaining-record-audit/artifacts/561/priority-manifest.json", "sha256": "413745a3039be68ceeb0235e305bb17919d098f199e041a06b11450320a74930" } ], "source_head": "210dfa4896e77a8fb5e22ca5a970b0fb0ac984a6" } }, { "pr": 562, "title": "Conditional \u03ba = 0.001592584727281865: three complete complex providers and reassigned owners", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/562", "author": "eumemic", "created_at": "2026-10-12T05:56:47Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001592584727281865", "kappa_fraction": "318516945456373/200000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. 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Eighteen literal whole-owner reassi", "automated_comparable": true, "body_sha256": "ea0da0208fe4a0a87a8d15021ad6ac2d39aa2754595408de2e605b6f3d79b57c" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/cold617.json", "path": "certificates/checkpoints/cold617.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. 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See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "400569730495803/250000000000000000", "status": "Prepared locally for publication: maintainer-reviewed conditional finite construction; frozen-family integration still in progress", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/270c2458cf7f34fc252afe7c9d697f2cd6c93a59/certificates/selected-result.json", "path": null, "commit": "270c2458cf7f34fc252afe7c9d697f2cd6c93a59", "at": "2026-10-12T14:41:59Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "318516945456373/200000000000000000", "own_source_scope": [ "Own universal Gaussian/helper required entry/output/absolute-phase/identity-spectator and owned/all-size correctness remain substantive hypotheses. This lower proves compulsory cost of the prescribed literal body, not correctness or original record validity of unexecuted providers.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Only V is used; no coordinate-volume factor, stock upper used as lower, selected activation threshold, sufficient upper, exact crossing, human/formal proof or hardware claim.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Lower only; one positively used exact own-source provider suffices for compulsory work in the complete prescribed kernel. Other changed providers are not substituted or claimed validated. No upper or actual crossing." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr562-open-multicold-v3-literal-cover-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 10, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/562-manifest.json", "sha256": "2571669bddc7d1d6a415a49a6125f24dd69fa52c7de65c6c5ec86b87a26db927" }, { "file": "remaining-record-audit/artifacts/562/priority-manifest.json", "sha256": "125ca1a8951d2de5aeb3f2f2d8d5d77f3e0263c90db353ced780cf324cdea7ac" } ], "source_head": "27070553cfbf094148a74170481738f8b747d82e" } }, { "pr": 563, "title": "Contextual rank-5 provider selection and finite pooling: conditional kappa 0.001592576636390595", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/563", "author": "Dugongue", "created_at": "2026-10-12T06:07:55Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001592576636390595", "kappa_fraction": "318515327278119/200000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/contextual-provider-pooling/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Recompute the complete own productive/paid histogram from research/contextual-provider-pooling/complex-global/inputs558/PLAN.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/contextual-provider-pooling/EXPECTED.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/563-manifest.json", "sha256": "00f827fcabe579744df79825b2b3fa3df0fc4265b5577055fd4bd61d958986f8" }, { "file": "remaining-record-audit/artifacts/563/priority-manifest.json", "sha256": "1d65d6f75fa3023ed06f4f5cbc99705d6a45b7b799dd485f168a562c18da1071" } ], "source_head": "35925c7f36d06676c7e9d2a052826b0864a2dd9b" } }, { "pr": 564, "title": "Conditional \u03ba = 0.001593134158181640: cold kernels in all 72 complex calls", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/564", "author": "eumemic", "created_at": "2026-10-12T06:16:22Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00159313415818164", "kappa_fraction": "39828353954541/25000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 66, "source_index": 106, "at": "2026-10-12T06:16:22Z", "until": "2026-10-12T07:56:38Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001593134158181640", "dashboard_float_text": "0.00159313415818164", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/564", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 83, "source_index": null, "at": "2026-10-12T06:16:22Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001593134158181640", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/564", "evidence_excerpt": "Conditional \u03ba = 0.001593134158181640: cold kernels in all 72 complex calls", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 352, "source_index": null, "at": "2026-10-12T06:16:22Z", "until": null, "date_basis": "body-version", "fraction": "39828353954541/25000000000000000", "value_decimal": "0.001593134158181640", "dashboard_float_text": null, "expression": "0.001593134158181640", "historical_title": "Conditional \u03ba = 0.001593134158181640: cold kernels in all 72 complex calls", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/564", "evidence_excerpt": "\u03ba = 0.001593134158181640 (conditional).\n\nEvery one of the 72 complex calls now uses an actual cold-kernel provider: 15 zero-pivot, two four-pivot and 55 eight-pivot words. Each checks the five-donor suffi", "automated_comparable": true, "body_sha256": "08057fecb1026f9b1a15cf1a4d126851bdb7866f324f807c49024c88b083dabe" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/cold617.json", "path": "certificates/checkpoints/cold617.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. 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Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier942.json", "path": "certificates/checkpoints/frontier942.json", "commit": null, "at": null, "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. 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Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3b83e4f14825ce1ae038a8c8159f130646991086/certificates/selected-result.json", "path": null, "commit": "3b83e4f14825ce1ae038a8c8159f130646991086", "at": "2026-10-13T13:30:30Z", "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d6dfd8f21b1e0b7e3f93b7e30e64639390e48504/certificates/selected-result.json", "path": null, "commit": "d6dfd8f21b1e0b7e3f93b7e30e64639390e48504", "at": "2026-10-13T06:44:14Z", "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. Not a full Lean multiplication theorem. Integration Linux CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/c290b7b919790300e14004a75d8d24b55ca3c5b5/certificates/selected-result.json", "path": null, "commit": "c290b7b919790300e14004a75d8d24b55ca3c5b5", "at": "2026-10-13T06:10:31Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/2cdd93d0250554e5160edbb8535c4500c4227349/certificates/selected-result.json", "path": null, "commit": "2cdd93d0250554e5160edbb8535c4500c4227349", "at": "2026-10-13T05:57:09Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "51110230636731/31250000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/5c5567d15bd019186519a4db267914257b5f1ac0/certificates/selected-result.json", "path": null, "commit": "5c5567d15bd019186519a4db267914257b5f1ac0", "at": "2026-10-12T22:36:34Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/2e9ed969d09570fbe949324b80da27a7f31d9399/certificates/selected-result.json", "path": null, "commit": "2e9ed969d09570fbe949324b80da27a7f31d9399", "at": "2026-10-12T21:01:12Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "16127213726553/10000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/1db1fbe68cb5186899cf1fd691bc92056a845e49/certificates/selected-result.json", "path": null, "commit": "1db1fbe68cb5186899cf1fd691bc92056a845e49", "at": "2026-10-12T16:59:30Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "400569730495803/250000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7f6ccd7ed1e5ee7fba9599f44f9a6fe08f582d62/certificates/selected-result.json", "path": null, "commit": "7f6ccd7ed1e5ee7fba9599f44f9a6fe08f582d62", "at": "2026-10-12T15:44:15Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "400569730495803/250000000000000000", "status": "Prepared locally for publication: maintainer-reviewed conditional finite construction; frozen-family integration still in progress", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/270c2458cf7f34fc252afe7c9d697f2cd6c93a59/certificates/selected-result.json", "path": null, "commit": "270c2458cf7f34fc252afe7c9d697f2cd6c93a59", "at": "2026-10-12T14:41:59Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1596133352130093/1000000000000000000", "own_source_scope": [ "Own universal Gaussian/helper required entry/output/absolute-phase/identity-spectator and owned/all-size correctness remain substantive hypotheses. This lower proves compulsory cost of the prescribed literal body, not correctness or original record validity of unexecuted providers.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Only V is used; no coordinate-volume factor, stock upper used as lower, selected activation threshold, sufficient upper, exact crossing, human/formal proof or hardware claim.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Lower only; one positively used exact own-source provider suffices for compulsory work in the complete prescribed kernel. Other changed providers are not substituted or claimed validated. No upper or actual crossing." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr568-open-multicold-v3-literal-cover-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 12, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/568-manifest.json", "sha256": "0950b369d50bc5685827c05c925f68259434043157ef996d846d88f36f31f288" }, { "file": "remaining-record-audit/artifacts/568/priority-manifest.json", "sha256": "fff0bf4b73a17877647b920fa35b5b98f387520d8b04c76082f9e027866c2557" } ], "source_head": "71c99ac935a33bb7b59a1b4a7af8725a939b0b90" } }, { "pr": 569, "title": "Conditional \u03ba = 0.001600067494703216: width-seven providers and whole-owner packing", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/569", "author": "DominikScholz", "created_at": "2026-10-12T08:22:59Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001600067494703216", "kappa_fraction": "100004218418951/62500000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public switching policies for this own source-selected literal complete O(73,2) cover enhancement: keep one actual selected public real ADD at every cover vertex with guarded width>=2 and the stipulated ADD lowering; no pruning, CSE, compression, aggregation or native bypass. A branch without such a native invocation is the identical fixed GMP reference. This added inactive rule is a comparison-family definition, not an original source fact. No other implementation or original BIT composition is covered.", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source": "data/operation-audit/pr569-open-legacy-literal-cover-lower.json" }, "conditional_upper": null, "cost_status": "conditional_own_source_lower_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 69, "source_index": 109, "at": "2026-10-12T08:22:59Z", "until": "2026-10-12T09:18:53Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001600067494703216", "dashboard_float_text": "0.001600067494703216", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/569", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 86, "source_index": null, "at": "2026-10-12T08:22:59Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001600067494703216", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/569", "evidence_excerpt": "Conditional \u03ba = 0.001600067494703216: width-seven providers and whole-owner packing", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 355, "source_index": null, "at": "2026-10-12T08:22:59Z", "until": null, "date_basis": "body-version", "fraction": "100004218418951/62500000000000000", "value_decimal": "0.001600067494703216", "dashboard_float_text": null, "expression": "0.001600067494703216", "historical_title": "Conditional \u03ba = 0.001600067494703216: width-seven providers and whole-owner packing", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/569", "evidence_excerpt": "## Change and mathematical scope\n\nThis adds a conditional finite construction at \u03ba = 0.001600067494703216, improving PR564's 0.001593134158181640 by 0.435201%.\n\nThree extra exact cold relations and 32 entrance-frame promotions create width-seven residual helpers. Whole-owner repacking", "automated_comparable": true, "body_sha256": "11295a7c56cfdfe099666dc99935a7a31773208e4c708147ae45da10a809576e" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/cold617.json", "path": "certificates/checkpoints/cold617.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "400569730495803/250000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/family588.json", "path": "certificates/checkpoints/family588.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier741.json", "path": "certificates/checkpoints/frontier741.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier799.json", "path": "certificates/checkpoints/frontier799.json", "commit": null, "at": null, "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. Not a full Lean multiplication theorem. Integration Linux CI status is separate." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier890.json", "path": "certificates/checkpoints/frontier890.json", "commit": null, "at": null, "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier942.json", "path": "certificates/checkpoints/frontier942.json", "commit": null, "at": null, "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "16127213726553/10000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/hyperplane596.json", "path": "certificates/checkpoints/hyperplane596.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. 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This added inactive rule is a comparison-family definition, not an original source fact. No other implementation or original BIT composition is covered.", "Lower only. No upper, record saving, exact crossing, original full phase/owner replay or universal implementation bound is inferred." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr569-open-legacy-literal-cover-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 11, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/569-manifest.json", "sha256": "06ca86d494976d27fa9057703f2a1f2a62361a7e49e4232dd6e5be6568dbaae9" }, { "file": "remaining-record-audit/artifacts/569/priority-manifest.json", "sha256": "f103bb6d527a7dcf228e44ba88ff4109bc239815a986e1afa66f6e7a066bd6da" } ], "source_head": "1424da81263a5305b35e4cf74ef686c275f03f3f" } }, { "pr": 571, "title": "Conditional \u03ba = 0.001600682403612293: joint-prefix kernels and structural bounds", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/571", "author": "DominikScholz", "created_at": "2026-10-12T09:18:53Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001600682403612293", "kappa_fraction": "1600682403612293/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public switching policies for this own source-selected literal complete O(73,2) cover enhancement: keep one actual selected public real ADD at every cover vertex with guarded width>=2 and the stipulated ADD lowering; no pruning, CSE, compression, aggregation or native bypass. A branch without such a native invocation is the identical fixed GMP reference. This added inactive rule is a comparison-family definition, not an original source fact. 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Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "16127213726553/10000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/hyperplane596.json", "path": "certificates/checkpoints/hyperplane596.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. 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See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/87db776d70ad1d28a27e9f7906237e5a279414f3/certificates/selected-result.json", "path": null, "commit": "87db776d70ad1d28a27e9f7906237e5a279414f3", "at": "2026-10-13T18:05:11Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3825dc0ea1317629864ebeb6929719cc4bbf525f/certificates/selected-result.json", "path": null, "commit": "3825dc0ea1317629864ebeb6929719cc4bbf525f", "at": "2026-10-13T15:06:01Z", "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3b83e4f14825ce1ae038a8c8159f130646991086/certificates/selected-result.json", "path": null, "commit": "3b83e4f14825ce1ae038a8c8159f130646991086", "at": "2026-10-13T13:30:30Z", "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d6dfd8f21b1e0b7e3f93b7e30e64639390e48504/certificates/selected-result.json", "path": null, "commit": "d6dfd8f21b1e0b7e3f93b7e30e64639390e48504", "at": "2026-10-13T06:44:14Z", "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. Not a full Lean multiplication theorem. Integration Linux CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/c290b7b919790300e14004a75d8d24b55ca3c5b5/certificates/selected-result.json", "path": null, "commit": "c290b7b919790300e14004a75d8d24b55ca3c5b5", "at": "2026-10-13T06:10:31Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/2cdd93d0250554e5160edbb8535c4500c4227349/certificates/selected-result.json", "path": null, "commit": "2cdd93d0250554e5160edbb8535c4500c4227349", "at": "2026-10-13T05:57:09Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "51110230636731/31250000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/5c5567d15bd019186519a4db267914257b5f1ac0/certificates/selected-result.json", "path": null, "commit": "5c5567d15bd019186519a4db267914257b5f1ac0", "at": "2026-10-12T22:36:34Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/2e9ed969d09570fbe949324b80da27a7f31d9399/certificates/selected-result.json", "path": null, "commit": "2e9ed969d09570fbe949324b80da27a7f31d9399", "at": "2026-10-12T21:01:12Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "16127213726553/10000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/1db1fbe68cb5186899cf1fd691bc92056a845e49/certificates/selected-result.json", "path": null, "commit": "1db1fbe68cb5186899cf1fd691bc92056a845e49", "at": "2026-10-12T16:59:30Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "400569730495803/250000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7f6ccd7ed1e5ee7fba9599f44f9a6fe08f582d62/certificates/selected-result.json", "path": null, "commit": "7f6ccd7ed1e5ee7fba9599f44f9a6fe08f582d62", "at": "2026-10-12T15:44:15Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "400569730495803/250000000000000000", "status": "Prepared locally for publication: maintainer-reviewed conditional finite construction; frozen-family integration still in progress", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/270c2458cf7f34fc252afe7c9d697f2cd6c93a59/certificates/selected-result.json", "path": null, "commit": "270c2458cf7f34fc252afe7c9d697f2cd6c93a59", "at": "2026-10-12T14:41:59Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1600682403612293/1000000000000000000", "own_source_scope": [ "Own selected native/operator absolute-phase and full-column/spectator identities, dirty helpers and owned restoration, and compiler/all-size correctness remain conditional.", "Actual paid literal complete-cover family only; alternate compressed, simplified, bypassed or unrelated BIT implementations are excluded.", "All valid public switching policies for this own source-selected literal complete O(73,2) cover enhancement: keep one actual selected public real ADD at every cover vertex with guarded width>=2 and the stipulated ADD lowering; no pruning, CSE, compression, aggregation or native bypass. A branch without such a native invocation is the identical fixed GMP reference. This added inactive rule is a comparison-family definition, not an original source fact. No other implementation or original BIT composition is covered.", "Lower only. No upper, record saving, exact crossing, original full phase/owner replay or universal implementation bound is inferred." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr571-open-legacy-literal-cover-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 12, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/571-manifest.json", "sha256": "96bda00df2819eec68c9aa45ec404d6863133ebc3984cd707d0e1d51f82c2e6d" }, { "file": "remaining-record-audit/artifacts/571/priority-manifest.json", "sha256": "4ae42c16420dc3637c0ee5197491414732e54820e36b35e24ca769497f6b5eb3" } ], "source_head": "b7bdc5a8de18fcf418cfb9c7d83a2b1097a5e4a3" } }, { "pr": 572, "title": "Eight-cold / width-seven composition and cold replay: conditional \u03ba = 0.001600535778621932", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/572", "author": "chafreaky", "created_at": "2026-10-12T09:33:54Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001600535778621932", "kappa_fraction": "400133944655483/250000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source": "data/operation-audit/pr572-open-multicold-v3-literal-cover-lower.json" }, "conditional_upper": null, "cost_status": "conditional_own_source_lower_only", "own_source_cost_extension": true, "early_effective_kappa": "400133944655483/250000000000000000", "own_source_scope": [ "Own universal Gaussian/helper required entry/output/absolute-phase/identity-spectator and owned/all-size correctness remain substantive hypotheses. This lower proves compulsory cost of the prescribed literal body, not correctness or original record validity of unexecuted providers.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Only V is used; no coordinate-volume factor, stock upper used as lower, selected activation threshold, sufficient upper, exact crossing, human/formal proof or hardware claim.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Lower only; one positively used exact own-source provider suffices for compulsory work in the complete prescribed kernel. Other changed providers are not substituted or claimed validated. No upper or actual crossing." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr572-open-multicold-v3-literal-cover-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 11, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/572-manifest.json", "sha256": "411343caf64a66d8c351b0ca2caa8e9700a3c113d4886981c78e4ddde827f906" }, { "file": "remaining-record-audit/artifacts/572/priority-manifest.json", "sha256": "763b9781e94cb0e51191f459dee4b68941374866fdbc5319532cefdea59c7c1d" } ], "source_head": "0c3a7d1b0d99dbc6a1cc5ec1675ddd74aa959586" } }, { "pr": 574, "title": "Conditional \u03ba = 0.00160073442456167: PR568 eight-cold provider at PR571's nine plain calls", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/574", "author": "jeremykothe2", "created_at": "2026-10-12T09:52:31Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00160073442456167", "kappa_fraction": "160073442456167/100000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source": "data/operation-audit/pr574-open-multicold-v3-literal-cover-lower.json" }, "conditional_upper": null, "cost_status": "conditional_own_source_lower_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 71, "source_index": 112, "at": "2026-10-12T09:52:31Z", "until": "2026-10-12T10:08:24Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.00160073442456167", "dashboard_float_text": "0.00160073442456167", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/574", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 88, "source_index": null, "at": "2026-10-12T09:52:31Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00160073442456167", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/574", "evidence_excerpt": "Conditional \u03ba = 0.00160073442456167: PR568 eight-cold provider at PR571's nine plain calls", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 357, "source_index": null, "at": "2026-10-12T09:52:31Z", "until": null, "date_basis": "body-version", "fraction": "160073442456167/100000000000000000", "value_decimal": "0.00160073442456167", "dashboard_float_text": null, "expression": "0.00160073442456167", "historical_title": "Conditional \u03ba = 0.00160073442456167: PR568 eight-cold provider at PR571's nine plain calls", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/574", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.00160073442456167, against PR571's 0.001600682403612293 (+5.2e-8). The conservative model gives 0.001600734421779035.\n\nThis is a small change to DominikScholz's PR571. Its 63 width-seven prefix-wor", "automated_comparable": true, "body_sha256": "330293f8a928e8b5b431748925eaf363942cb26eaf5c61a689675cfdf9cb7afa" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/cold617.json", "path": "certificates/checkpoints/cold617.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "400569730495803/250000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/family588.json", "path": "certificates/checkpoints/family588.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "400569730495803/250000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/family588.json", "path": "certificates/checkpoints/family588.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier942.json", "path": "certificates/checkpoints/frontier942.json", "commit": null, "at": null, "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "16127213726553/10000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/hyperplane596.json", "path": "certificates/checkpoints/hyperplane596.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "51110230636731/31250000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/k492626.json", "path": "certificates/checkpoints/k492626.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/87db776d70ad1d28a27e9f7906237e5a279414f3/certificates/selected-result.json", "path": null, "commit": "87db776d70ad1d28a27e9f7906237e5a279414f3", "at": "2026-10-13T18:05:11Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3825dc0ea1317629864ebeb6929719cc4bbf525f/certificates/selected-result.json", "path": null, "commit": "3825dc0ea1317629864ebeb6929719cc4bbf525f", "at": "2026-10-13T15:06:01Z", "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3b83e4f14825ce1ae038a8c8159f130646991086/certificates/selected-result.json", "path": null, "commit": "3b83e4f14825ce1ae038a8c8159f130646991086", "at": "2026-10-13T13:30:30Z", "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d6dfd8f21b1e0b7e3f93b7e30e64639390e48504/certificates/selected-result.json", "path": null, "commit": "d6dfd8f21b1e0b7e3f93b7e30e64639390e48504", "at": "2026-10-13T06:44:14Z", "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. Not a full Lean multiplication theorem. Integration Linux CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/c290b7b919790300e14004a75d8d24b55ca3c5b5/certificates/selected-result.json", "path": null, "commit": "c290b7b919790300e14004a75d8d24b55ca3c5b5", "at": "2026-10-13T06:10:31Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. 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Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "51110230636731/31250000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/5c5567d15bd019186519a4db267914257b5f1ac0/certificates/selected-result.json", "path": null, "commit": "5c5567d15bd019186519a4db267914257b5f1ac0", "at": "2026-10-12T22:36:34Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. 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See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "16127213726553/10000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/1db1fbe68cb5186899cf1fd691bc92056a845e49/certificates/selected-result.json", "path": null, "commit": "1db1fbe68cb5186899cf1fd691bc92056a845e49", "at": "2026-10-12T16:59:30Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "400569730495803/250000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7f6ccd7ed1e5ee7fba9599f44f9a6fe08f582d62/certificates/selected-result.json", "path": null, "commit": "7f6ccd7ed1e5ee7fba9599f44f9a6fe08f582d62", "at": "2026-10-12T15:44:15Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "400569730495803/250000000000000000", "status": "Prepared locally for publication: maintainer-reviewed conditional finite construction; frozen-family integration still in progress", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/270c2458cf7f34fc252afe7c9d697f2cd6c93a59/certificates/selected-result.json", "path": null, "commit": "270c2458cf7f34fc252afe7c9d697f2cd6c93a59", "at": "2026-10-12T14:41:59Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1600770286423653/1000000000000000000", "own_source_scope": [ "Own universal Gaussian/helper required entry/output/absolute-phase/identity-spectator and owned/all-size correctness remain substantive hypotheses. This lower proves compulsory cost of the prescribed literal body, not correctness or original record validity of unexecuted providers.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Only V is used; no coordinate-volume factor, stock upper used as lower, selected activation threshold, sufficient upper, exact crossing, human/formal proof or hardware claim.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Lower only; one positively used exact own-source provider suffices for compulsory work in the complete prescribed kernel. Other changed providers are not substituted or claimed validated. No upper or actual crossing." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr575-open-multicold-v3-literal-cover-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 10, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/575-manifest.json", "sha256": "e2fb8d7acc0f12b31275ba1e410b73240b8bb8b8255cb1dbbcffad94f5c1d0ea" }, { "file": "remaining-record-audit/artifacts/575/priority-manifest.json", "sha256": "3f80d30b063161f0b40b79523fb090e844da893d7e6ec831155293cf39528e70" } ], "source_head": "eac6f7e378ab622dac50a2fd4b7ef6eab014de44" } }, { "pr": 576, "title": "Conditional \u03ba = 0.00160109005167629: PR568 kernels and eight-cold provider on PR571's prefix word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/576", "author": "jeremykothe2", "created_at": "2026-10-12T10:16:01Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00160109005167629", "kappa_fraction": "160109005167629/100000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr576-exact-mixed-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 74, "source_index": 115, "at": "2026-10-12T10:22:48.371993Z", "until": "2026-10-12T10:36:32Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.00160109005167629", "dashboard_float_text": "0.00160109005167629", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/576", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 91, "source_index": null, "at": "2026-10-12T10:22:48.371993+00:00", "until": null, "date_basis": "observed_revision", "fraction": null, "value_decimal": "0.00160109005167629", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/576", "evidence_excerpt": "Conditional \u03ba = **0.00160109005167629**. This is +4.08e-7 over PR571 (0.001600682403612293), +3.20e-7 over PR575 (0.001600770286423653) and +2.42e-7 over PR577 (0.001600848528154892). The conservative model gives 0.001601090048890878.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 359, "source_index": null, "at": "2026-10-12T10:16:01Z", "until": null, "date_basis": "body-version", "fraction": "800475700384307/500000000000000000", "value_decimal": "0.00160109005167629", "dashboard_float_text": null, "expression": "0.001600951400768614", "historical_title": "Conditional \u03ba = 0.001600951400768614: PR568 kernels and eight-cold provider on PR571's prefix word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/576", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001600951400768614. This is +2.69e-7 over PR571 (0.001600682403612293) and +1.81e-7 over PR575 (0.001600770286423653). The conservative model gives 0.001600951397983358.\n\nThe construction keeps Domi", "automated_comparable": true, "body_sha256": "9c392cf5833a7c31d46ef371d9daeb9875835b54ac8e64f2358932f2a15339c4" }, { "stream": "recovered_literal_highwater", "stream_row": 360, "source_index": null, "at": "2026-10-12T10:22:20Z", "until": null, "date_basis": "body-version", "fraction": "160109005167629/100000000000000000", "value_decimal": "0.00160109005167629", "dashboard_float_text": null, "expression": "0.00160109005167629", "historical_title": "Conditional \u03ba = 0.00160109005167629: PR568 kernels and eight-cold provider on PR571's prefix word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/576", "evidence_excerpt": "## Summary\r\n\r\nConditional \u03ba = 0.00160109005167629. This is +4.08e-7 over PR571 (0.001600682403612293), +3.20e-7 over PR575 (0.001600770286423653) and +2.42e-7 over PR577 (0.001600848528154892). The conservative model gives 0.0016", "automated_comparable": true, "body_sha256": "b1e958ae57791f2aa44447b63dbe9362d9aefc54b949c7ee4c06a0233482dfd5" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/cold617.json", "path": "certificates/checkpoints/cold617.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. 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See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "400569730495803/250000000000000000", "status": "Prepared locally for publication: maintainer-reviewed conditional finite construction; frozen-family integration still in progress", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/270c2458cf7f34fc252afe7c9d697f2cd6c93a59/certificates/selected-result.json", "path": null, "commit": "270c2458cf7f34fc252afe7c9d697f2cd6c93a59", "at": "2026-10-12T14:41:59Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr576-exact-mixed-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 7, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/576-manifest.json", "sha256": "974faf113c84e7895ff1f0accd4e5db7e1599ed72eb11ad3303eb46160dc41c2" }, { "file": "remaining-record-audit/artifacts/576/priority-manifest.json", "sha256": "cb16b3ef8d6f171d9f8cb4b0e2af70838bacc51bd42fec82dd35f4f58324863b" } ], "source_head": "f4e9f7e85e9211cf6ba6c5789da2aa0902d9121e" } }, { "pr": 577, "title": "Conditional \u03ba = 0.001600848528154892: four-provider joint-prefix packing", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/577", "author": "chafreaky", "created_at": "2026-10-12T10:16:50Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001600848528154892", "kappa_fraction": "400212132038723/250000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source": "data/operation-audit/pr577-open-multicold-v3-literal-cover-lower.json" }, "conditional_upper": null, "cost_status": "conditional_own_source_lower_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 73, "source_index": 114, "at": "2026-10-12T10:16:50Z", "until": "2026-10-12T10:22:48.371993Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001600848528154892", "dashboard_float_text": "0.001600848528154892", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/577", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 90, "source_index": null, "at": "2026-10-12T10:16:50Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001600848528154892", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/577", "evidence_excerpt": "Conditional **\u03ba = 0.001600848528154892**, **0.01037836% above #571**. The complex supplier binds at **b = 0.001603415353263184744465**. The conservative complex model separately admits \u03ba = **0.001600848525369710**; the unchanged cited #543 bit supplier remains nonbinding with its surcharge retained.", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "400212132038723/250000000000000000", "own_source_scope": [ "Own universal Gaussian/helper required entry/output/absolute-phase/identity-spectator and owned/all-size correctness remain substantive hypotheses. This lower proves compulsory cost of the prescribed literal body, not correctness or original record validity of unexecuted providers.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Only V is used; no coordinate-volume factor, stock upper used as lower, selected activation threshold, sufficient upper, exact crossing, human/formal proof or hardware claim.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Lower only; one positively used exact own-source provider suffices for compulsory work in the complete prescribed kernel. Other changed providers are not substituted or claimed validated. No upper or actual crossing." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr577-open-multicold-v3-literal-cover-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 11, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/577-manifest.json", "sha256": "359b1deccf34ef8e5d409293bc5d6deaa13e376a241603cd332a6718bb987ac7" }, { "file": "remaining-record-audit/artifacts/577/priority-manifest.json", "sha256": "4eb3de4baa4db2b6f60d8b1f1ea89781e98e72c7e6d61c15bfff1062d3913921" } ], "source_head": "086bd33ff5c1ce46f3ff23298b8dc756a54414db" } }, { "pr": 578, "title": "Conditional \u03ba = 0.001601159251759369: improved literal owner map for the three-provider PR571 prefix witness", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/578", "author": "jeremykothe2", "created_at": "2026-10-12T10:36:32Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001601159251759369", "kappa_fraction": "1601159251759369/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr578-exact-mixed-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 75, "source_index": 116, "at": "2026-10-12T10:36:32Z", "until": "2026-10-12T10:53:57Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001601159251759369", "dashboard_float_text": "0.001601159251759369", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/578", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 92, "source_index": null, "at": "2026-10-12T10:36:32Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001601159251759369", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/578", "evidence_excerpt": "Conditional \u03ba = **0.001601159251759369**. This is +6.92e-8 over our PR576 (0.00160109005167629), +4.77e-7 over PR571 and +3.89e-7 over PR575. The conservative model gives 0.001601159248973933.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 361, "source_index": null, "at": "2026-10-12T10:36:32Z", "until": null, "date_basis": "body-version", "fraction": "1601159251759369/1000000000000000000", "value_decimal": "0.001601159251759369", "dashboard_float_text": null, "expression": "0.001601159251759369", "historical_title": "Conditional \u03ba = 0.001601159251759369: improved literal owner map for the three-provider PR571 prefix witness", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/578", "evidence_excerpt": "## Summary\r\n\r\nConditional \u03ba = 0.001601159251759369. This is +6.92e-8 over our PR576 (0.00160109005167629), +4.77e-7 over PR571 and +3.89e-7 over PR575. The conservative model gives 0.001601159248973933.\r\n\r\nThis is the same three-p", "automated_comparable": true, "body_sha256": "68b81f83922544eb0f7d1996622fe69698e0866dc131447d3f402b6aed2eec7d" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr578-exact-mixed-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 7, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/578-manifest.json", "sha256": "6e2a7a3af4f8306828c3e2f36d9cc6b9c0e27273b0b8639cb06074422e9bda90" }, { "file": "remaining-record-audit/artifacts/578/priority-manifest.json", "sha256": "36c731a36a08b309c5c2ef908c2b47b5cf4e134a6bcd8191a027821349d4b7ae" } ], "source_head": "2aacc1f2edae76fc963699be5cfaf31bcf3ef56b" } }, { "pr": 579, "title": "Conditional \u03ba = 0.001601260169988325: 48 added-kernel and 24 plain joint-prefix calls", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/579", "author": "chafreaky", "created_at": "2026-10-12T10:53:57Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001601260169988325", "kappa_fraction": "64050406799533/40000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source": "data/operation-audit/pr579-open-multicold-v3-literal-cover-lower.json" }, "conditional_upper": null, "cost_status": "conditional_own_source_lower_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 76, "source_index": 117, "at": "2026-10-12T10:53:57Z", "until": "2026-10-12T11:35:56Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001601260169988325", "dashboard_float_text": "0.001601260169988325", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/579", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 93, "source_index": null, "at": "2026-10-12T10:53:57Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001601260169988325", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/579", "evidence_excerpt": "Conditional **\u03ba = 0.001601260169988325**, with conservative \u03ba = **0.001601260167198213**. The complex supplier binds at **b = 400957079097715286561 / 250000000000000000000000**; the unchanged cited PR543 bit supplier remains nonbinding with its surcharge retained.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 362, "source_index": null, "at": "2026-10-12T10:53:57Z", "until": null, "date_basis": "body-version", "fraction": "64050406799533/40000000000000000", "value_decimal": "0.001601260169988325", "dashboard_float_text": null, "expression": "0.001601260169988325", "historical_title": "Conditional \u03ba = 0.001601260169988325: 48 added-kernel and 24 plain joint-prefix calls", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/579", "evidence_excerpt": "Conditional \u03ba = 0.001601260169988325, with conservative \u03ba = 0.001601260167198213. The complex supplier binds at b = 400957079097715286561 / 250000000000000000000000; the unchanged cited PR543 bit supplier remains non", "automated_comparable": true, "body_sha256": "851be6ff26c197976df3e280b381fecfd92ec9ef02f3e3ab8cead55d396e929a" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/cold617.json", "path": "certificates/checkpoints/cold617.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "400569730495803/250000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/family588.json", "path": "certificates/checkpoints/family588.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier741.json", "path": "certificates/checkpoints/frontier741.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier799.json", "path": "certificates/checkpoints/frontier799.json", "commit": null, "at": null, "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. Not a full Lean multiplication theorem. Integration Linux CI status is separate." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier890.json", "path": "certificates/checkpoints/frontier890.json", "commit": null, "at": null, "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. 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Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3b83e4f14825ce1ae038a8c8159f130646991086/certificates/selected-result.json", "path": null, "commit": "3b83e4f14825ce1ae038a8c8159f130646991086", "at": "2026-10-13T13:30:30Z", "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d6dfd8f21b1e0b7e3f93b7e30e64639390e48504/certificates/selected-result.json", "path": null, "commit": "d6dfd8f21b1e0b7e3f93b7e30e64639390e48504", "at": "2026-10-13T06:44:14Z", "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. 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See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "400569730495803/250000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7f6ccd7ed1e5ee7fba9599f44f9a6fe08f582d62/certificates/selected-result.json", "path": null, "commit": "7f6ccd7ed1e5ee7fba9599f44f9a6fe08f582d62", "at": "2026-10-12T15:44:15Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "400569730495803/250000000000000000", "status": "Prepared locally for publication: maintainer-reviewed conditional finite construction; frozen-family integration still in progress", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/270c2458cf7f34fc252afe7c9d697f2cd6c93a59/certificates/selected-result.json", "path": null, "commit": "270c2458cf7f34fc252afe7c9d697f2cd6c93a59", "at": "2026-10-12T14:41:59Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "64050406799533/40000000000000000", "own_source_scope": [ "Own universal Gaussian/helper required entry/output/absolute-phase/identity-spectator and owned/all-size correctness remain substantive hypotheses. This lower proves compulsory cost of the prescribed literal body, not correctness or original record validity of unexecuted providers.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Only V is used; no coordinate-volume factor, stock upper used as lower, selected activation threshold, sufficient upper, exact crossing, human/formal proof or hardware claim.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Lower only; one positively used exact own-source provider suffices for compulsory work in the complete prescribed kernel. Other changed providers are not substituted or claimed validated. No upper or actual crossing." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr579-open-multicold-v3-literal-cover-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 11, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/579-manifest.json", "sha256": "6eb01ea811071029b45699978af3d2dbdbe79b5424007b77c861b6493b506828" }, { "file": "remaining-record-audit/artifacts/579/priority-manifest.json", "sha256": "6234ffbe6d887b18342a7739392ef800e1377436c0f95b910b807da0ff49cb8e" } ], "source_head": "970d38a3862ee35064a827b671d196744ee2a928" } }, { "pr": 582, "title": "Conditional \u03ba = 0.001601486955392486: PR576 kernels with A-entrance 5-to-4 promotions and PR575 plain joint prefix", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/582", "author": "jeremykothe2", "created_at": "2026-10-12T11:35:56Z", "accepted_at": "2026-10-12T15:45:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001601486955392486", "kappa_fraction": "800743477696243/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr582-early-frame-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": "Own explicitly selected finite source core, exact RAW and complete program commitments, full own PLAN/OWNERS and fresh complete physical invoice; newly counted direct Gaussian realization with retained operator, phase, owned, all-size and analytic contracts. No earlier invoice or cutoff transfer." }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 77, "source_index": 118, "at": "2026-10-12T11:35:56Z", "until": "2026-10-12T11:49:10Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001601486955392486", "dashboard_float_text": "0.001601486955392486", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/582", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 94, "source_index": null, "at": "2026-10-12T11:35:56Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001601486955392486", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/582", "evidence_excerpt": "Conditional \u03ba = 0.001601486955392486: PR576 kernels with A-entrance 5-to-4 promotions and PR575 plain joint prefix", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 363, "source_index": null, "at": "2026-10-12T11:35:56Z", "until": null, "date_basis": "body-version", "fraction": "800743477696243/500000000000000000", "value_decimal": "0.001601486955392486", "dashboard_float_text": null, "expression": "0.001601486955392486", "historical_title": "Conditional \u03ba = 0.001601486955392486: PR576 kernels with A-entrance 5-to-4 promotions and PR575 plain joint prefix", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/582", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001601486955392486. This is +2.27e-7 over PR579 (0.001601260169988325) and +3.28e-7 over our PR578. The conservative model gives 0.001601486952579549.\n\nThis PR combines three existing providers with", "automated_comparable": true, "body_sha256": "ae47e41362e8bab906b87d2d2e162ee77f72f8b204f45a44f7461794c2a1ef40" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/cold617.json", "path": "certificates/checkpoints/cold617.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "400569730495803/250000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/family588.json", "path": "certificates/checkpoints/family588.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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Integration Linux CI status is separate." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier890.json", "path": "certificates/checkpoints/frontier890.json", "commit": null, "at": null, "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier942.json", "path": "certificates/checkpoints/frontier942.json", "commit": null, "at": null, "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "16127213726553/10000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/hyperplane596.json", "path": "certificates/checkpoints/hyperplane596.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "51110230636731/31250000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/k492626.json", "path": "certificates/checkpoints/k492626.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/87db776d70ad1d28a27e9f7906237e5a279414f3/certificates/selected-result.json", "path": null, "commit": "87db776d70ad1d28a27e9f7906237e5a279414f3", "at": "2026-10-13T18:05:11Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3825dc0ea1317629864ebeb6929719cc4bbf525f/certificates/selected-result.json", "path": null, "commit": "3825dc0ea1317629864ebeb6929719cc4bbf525f", "at": "2026-10-13T15:06:01Z", "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3b83e4f14825ce1ae038a8c8159f130646991086/certificates/selected-result.json", "path": null, "commit": "3b83e4f14825ce1ae038a8c8159f130646991086", "at": "2026-10-13T13:30:30Z", "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d6dfd8f21b1e0b7e3f93b7e30e64639390e48504/certificates/selected-result.json", "path": null, "commit": "d6dfd8f21b1e0b7e3f93b7e30e64639390e48504", "at": "2026-10-13T06:44:14Z", "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. Not a full Lean multiplication theorem. Integration Linux CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/c290b7b919790300e14004a75d8d24b55ca3c5b5/certificates/selected-result.json", "path": null, "commit": "c290b7b919790300e14004a75d8d24b55ca3c5b5", "at": "2026-10-13T06:10:31Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/2cdd93d0250554e5160edbb8535c4500c4227349/certificates/selected-result.json", "path": null, "commit": "2cdd93d0250554e5160edbb8535c4500c4227349", "at": "2026-10-13T05:57:09Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "51110230636731/31250000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/5c5567d15bd019186519a4db267914257b5f1ac0/certificates/selected-result.json", "path": null, "commit": "5c5567d15bd019186519a4db267914257b5f1ac0", "at": "2026-10-12T22:36:34Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/2e9ed969d09570fbe949324b80da27a7f31d9399/certificates/selected-result.json", "path": null, "commit": "2e9ed969d09570fbe949324b80da27a7f31d9399", "at": "2026-10-12T21:01:12Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "16127213726553/10000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/1db1fbe68cb5186899cf1fd691bc92056a845e49/certificates/selected-result.json", "path": null, "commit": "1db1fbe68cb5186899cf1fd691bc92056a845e49", "at": "2026-10-12T16:59:30Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "400569730495803/250000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7f6ccd7ed1e5ee7fba9599f44f9a6fe08f582d62/certificates/selected-result.json", "path": null, "commit": "7f6ccd7ed1e5ee7fba9599f44f9a6fe08f582d62", "at": "2026-10-12T15:44:15Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "400569730495803/250000000000000000", "status": "Prepared locally for publication: maintainer-reviewed conditional finite construction; frozen-family integration still in progress", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/270c2458cf7f34fc252afe7c9d697f2cd6c93a59/certificates/selected-result.json", "path": null, "commit": "270c2458cf7f34fc252afe7c9d697f2cd6c93a59", "at": "2026-10-12T14:41:59Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "800830761063899/500000000000000000", "own_source_scope": [ "Own universal Gaussian/helper required entry/output/absolute-phase/identity-spectator and owned/all-size correctness remain substantive hypotheses. This lower proves compulsory cost of the prescribed literal body, not correctness or original record validity of unexecuted providers.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Only V is used; no coordinate-volume factor, stock upper used as lower, selected activation threshold, sufficient upper, exact crossing, human/formal proof or hardware claim.", "All valid public policies of this own selected literal complete O(73,2) source body. A positive actual own PLAN call executes the pinned programme with its surviving public-main unit ADD at every cover vertex, guarded width>=2, without pruning/CSE/aggregation/cover quotienting/compression/native bypass. Any branch without such a body returns identical fixed GMP; that inactive rule is an explicit added comparison-family definition, not a historical fact. Other implementations and original BIT compositions are excluded.", "Lower only; one positively used exact own-source provider suffices for compulsory work in the complete prescribed kernel. Other changed providers are not substituted or claimed validated. No upper or actual crossing." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr583-open-multicold-v3-literal-cover-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 11, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/583-manifest.json", "sha256": "637aa68161c4917d0b135ceb0ed6f601fe59b83406de7d7c79f5d29f850943f2" }, { "file": "remaining-record-audit/artifacts/583/priority-manifest.json", "sha256": "983890f985d7314580c33533939c0b6184419d3d5cea143100bca366468ad076" } ], "source_head": "89be768f0157f5a3d8e4db69cf1748768605eac9" } }, { "pr": 539, "title": "Conditional kappa 0.001584931113695072: literal bit bad-class charge on PR535", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/539", "author": "rohanarun", "created_at": "2026-10-12T02:38:50Z", "accepted_at": "2026-10-12T15:45:42Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001584931113695072", "kappa_fraction": "49529097302971/31250000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 54, "source_index": 88, "at": "2026-10-12T02:38:50Z", "until": "2026-10-12T03:00:27Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001584931113695072", "dashboard_float_text": "0.001584931113695072", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/539", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 71, "source_index": null, "at": "2026-10-12T02:38:50Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001584931113695072", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/539", "evidence_excerpt": "**Conditional \u03ba = 0.001584931113695072**, versus #535's `0.001584931111785787`.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 340, "source_index": null, "at": "2026-10-12T02:38:50Z", "until": null, "date_basis": "body-version", "fraction": "49529097302971/31250000000000000", "value_decimal": "0.001584931113695072", "dashboard_float_text": null, "expression": "0.001584931113695072", "historical_title": "Conditional kappa 0.001584931113695072: literal bit bad-class charge on PR535", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/539", "evidence_excerpt": "Conditional \u03ba = 0.001584931113695072, versus #535's 0.001584931111785787.\n\nThis is a tiny arithmetic refinement: absolute gain 1.909285e-12, approximately 0.0000001205%. It leaves #510's R480 bit word, #535's complex", "automated_comparable": true, "body_sha256": "326eb97e7f1800120e00e2f5a1fcbed4de8a7262ec114b9bed5910468b922bc3" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/r480-sharp-charge535/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/r480-sharp-charge535/EXPECTED.json, research/r480-sharp-charge535/MANIFEST.json, research/r480-sharp-charge535/README.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/r480-sharp-charge535/EXPECTED.json, research/r480-sharp-charge535/MANIFEST.json, research/r480-sharp-charge535/README.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/r480-sharp-charge535/EXPECTED.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/539-manifest.json", "sha256": "2496e3c8b3e941b5db7cdb7fde398deb218c23b178b58ab8ea75d75cf1425b97" }, { "file": "remaining-record-audit/artifacts/539/priority-manifest.json", "sha256": "f9f2bf26af48e89bcf30ae8cc74186f3470f18bb1df06168fdef251ef3a335bf" } ], "source_head": "915ca69db7f98c70b97ce96e1fcc96818517584c" } }, { "pr": 546, "title": "Conditional kappa 0.001587480974500277: static44 global admission plus PR542 bit", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/546", "author": "rohanarun", "created_at": "2026-10-12T03:32:16Z", "accepted_at": "2026-10-12T15:45:42Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001587480974500277", "kappa_fraction": "1587480974500277/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/static44-r480-composition/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/static44-r480-composition/EXPECTED.json, research/static44-r480-composition/MANIFEST.json, research/static44-r480-composition/README.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/static44-r480-composition/EXPECTED.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/546-manifest.json", "sha256": "505f4043e0428cf7333d781615cff41c843a4f63fec6ae5228e53232bf6627e1" }, { "file": "remaining-record-audit/artifacts/546/priority-manifest.json", "sha256": "4ce22cea6b754f98148dc57266ea9c9c0e6c361234348fdf32277c58696fa1e7" } ], "source_head": "77833ffa1110c6645f5d0866ebf41510ee3d27a3" } }, { "pr": 591, "title": "Conditional \u03ba = 0.001609915765452068: hyperplane-ended helpers on the PR588 witness", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/591", "author": "jeremykothe2", "created_at": "2026-10-12T14:10:49Z", "accepted_at": "2026-10-12T17:00:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001609915765452068", "kappa_fraction": "402478941363017/250000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr591-hyperplane-cold-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": "New direct Gaussian realization of the exact own-selected native words and complete owner map, with a fresh physical invoice. The prior successful 1645-check native reconstruction is authenticated; the final source reviewer freshly checked uncached scalar/frame data and complete physical costs, and does not claim a new full native/operator/phase pipeline pass. Partial operator/absolute-phase, normalized-child, owned/common-label/all-size and analytic contracts remain explicit. No prior invoice or cutoff is transferred; no actual first crossing is known." }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 81, "source_index": 123, "at": "2026-10-12T14:10:49Z", "until": "2026-10-12T14:30:59Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001609915765452068", "dashboard_float_text": "0.001609915765452068", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/591", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 98, "source_index": null, "at": "2026-10-12T14:10:49Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001609915765452068", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/591", "evidence_excerpt": "Conditional \u03ba = 0.001609915765452068: hyperplane-ended helpers on the PR588 witness", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 367, "source_index": null, "at": "2026-10-12T14:10:49Z", "until": null, "date_basis": "body-version", "fraction": "402478941363017/250000000000000000", "value_decimal": "0.001609915765452068", "dashboard_float_text": null, "expression": "0.001609915765452068", "historical_title": "Conditional \u03ba = 0.001609915765452068: hyperplane-ended helpers on the PR588 witness", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/591", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001609915765452068. This is +7.64e-6 over our PR588 (0.001602278921983212). The conservative model gives 0.001609915762605935.\n\nThis PR keeps PR588's construction (PR582's three providers with all e", "automated_comparable": true, "body_sha256": "09fe0eb929e6795e727d9d7104acc54237aadfafd2f1331a52da65e0e07cb812" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/cold617.json", "path": "certificates/checkpoints/cold617.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 82, "source_index": 124, "at": "2026-10-12T14:30:59Z", "until": "2026-10-12T15:23:43Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001612719427075359", "dashboard_float_text": "0.001612719427075359", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/592", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 99, "source_index": null, "at": "2026-10-12T14:30:59Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001612719427075359", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/592", "evidence_excerpt": "Conditional \u03ba = 0.001612719427075359: hyperplane-ended helpers with ck/atm3 dispatch", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 368, "source_index": null, "at": "2026-10-12T14:30:59Z", "until": null, "date_basis": "body-version", "fraction": "1612719427075359/1000000000000000000", "value_decimal": "0.001612719427075359", "dashboard_float_text": null, "expression": "0.001612719427075359", "historical_title": "Conditional \u03ba = 0.001612719427075359: hyperplane-ended helpers with ck/atm3 dispatch", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/592", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001612719427075359. This is +2.80e-6 over our PR591 (0.001609915765452068) and +1.04e-5 over PR588. The conservative model gives 0.001612719424224312.\n\nThis PR has the same construction, providers, ", "automated_comparable": true, "body_sha256": "687f0481525d1de6f0fa4d7bd222421f60b1d8b4946e61a3186342508ce4dcc0" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/cold617.json", "path": "certificates/checkpoints/cold617.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. 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Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr592-dispatched-finite-controller-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 6, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/592/priority-manifest.json", "sha256": "80a4fc4c9c5e582b3d2c4be30bbeb511e566cd1218bbcfd92bf45e0c23a124ac" } ], "source_head": "1f471c445c06a45a32e2c47e8d74c8264b68356b" } }, { "pr": 596, "title": "Conditional \u03ba = 0.0016127213726553: improved owner map for the PR592 hyperplane-ended witness", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/596", "author": "jeremykothe2", "created_at": "2026-10-12T15:23:43Z", "accepted_at": "2026-10-12T17:00:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0016127213726553", "kappa_fraction": "16127213726553/10000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr596-mixed-finite-controller-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own arbitrary-input operator-valued native phase, normalized-wrapper, ascending typed-helper and whole Gaussian endpoint contracts remain explicit; scalar specialization is not their proof.", "Exact own selected canonical/program/orientation hashes, actual scalar/frame incidence and dyadic Horner/prefix counts are checked independently. Derived objects are rebuilt from earlier hash-pinned recipes, sometimes using exact matching later archive bytes; no later supplier is imported.", "Each own PLAN/order/dispatch/OWNERS/window, complete role namespace, residual/spectator chart, primitive/wrapper invoice and no-prior-invoice finite stock is freshly checked.", "The counted parent is a primary-fixture source-equivalent numeric realization matching own physical windows; historical parent provenance metadata byte identity is not claimed.", "Common-label, mutable-source, arbitrary-input owned restore and all-size unequal-child occupied-row batching remain fixed-protocol hypotheses; completed Gaussian children have norm one under the endpoint contract.", "Own C0=2^210000 and actual512-bit payload fund the semantic precision reserve. Same direct analytic fine-prime/boundary/recovery, candidate-only Fermat helper and repaired unlimited GMP correctness/halting interfaces." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "historical_selected_or_reviewed_conditional_checkpoint_source", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 83, "source_index": 125, "at": "2026-10-12T15:23:43Z", "until": "2026-10-12T16:43:16Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.0016127213726553", "dashboard_float_text": "0.0016127213726553", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/596", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 100, "source_index": null, "at": "2026-10-12T15:23:43Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.0016127213726553", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/596", "evidence_excerpt": "Conditional \u03ba = 0.0016127213726553: improved owner map for the PR592 hyperplane-ended witness", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 369, "source_index": null, "at": "2026-10-12T15:23:43Z", "until": null, "date_basis": "body-version", "fraction": "16127213726553/10000000000000000", "value_decimal": "0.0016127213726553", "dashboard_float_text": null, "expression": "0.0016127213726553", "historical_title": "Conditional \u03ba = 0.0016127213726553: improved owner map for the PR592 hyperplane-ended witness", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/596", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.0016127213726553. This is +1.95e-9 over our PR592 (0.001612719427075359). The conservative model gives 0.001612721369804261.\n\nThis PR has the same construction, providers, dispatch (ck *53, atm3 *", "automated_comparable": true, "body_sha256": "9ddd2c190f9519effc28ba0b503ac1b0c36d2eba28f4c86f7d52f4c102480ed9" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/cold617.json", "path": "certificates/checkpoints/cold617.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. 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See review for replay reuse and Linux CI status." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own arbitrary-input operator-valued native phase, normalized-wrapper, ascending typed-helper and whole Gaussian endpoint contracts remain explicit; scalar specialization is not their proof.", "Exact own selected canonical/program/orientation hashes, actual scalar/frame incidence and dyadic Horner/prefix counts are checked independently. Derived objects are rebuilt from earlier hash-pinned recipes, sometimes using exact matching later archive bytes; no later supplier is imported.", "Each own PLAN/order/dispatch/OWNERS/window, complete role namespace, residual/spectator chart, primitive/wrapper invoice and no-prior-invoice finite stock is freshly checked.", "The counted parent is a primary-fixture source-equivalent numeric realization matching own physical windows; historical parent provenance metadata byte identity is not claimed.", "Common-label, mutable-source, arbitrary-input owned restore and all-size unequal-child occupied-row batching remain fixed-protocol hypotheses; completed Gaussian children have norm one under the endpoint contract.", "Own C0=2^210000 and actual512-bit payload fund the semantic precision reserve. Same direct analytic fine-prime/boundary/recovery, candidate-only Fermat helper and repaired unlimited GMP correctness/halting interfaces." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr596-mixed-finite-controller-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 6, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/596/priority-manifest.json", "sha256": "b87ea08ba8c3eaab22328217aaed3abf5b18b274c8cbaf5d9681b80c7999b5cb" } ], "source_head": "7732dd5e46863ff294b5e443661cb9d99abf4e01" } }, { "pr": 598, "title": "Leech/Turyn research (no \u03ba claim): scoped fitting bounds and cost screens", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/598", "author": "DominikScholz", "created_at": "2026-10-12T15:56:10Z", "accepted_at": "2026-10-12T17:00:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0014261182", "kappa_fraction": "7130591/5000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 12, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "A numerical whole-multiplier comparison must separately identify an actual complete selected native/caller/owner/recursive work-height-stock interface and precision/analytic/outer realization. This source-scope disposition neither supplies nor transfers that bound, and does not extend a restricted negative result beyond its stated family." ], "source_manifest": [ { "file": "individual-primary-interface-source/598-manifest.json", "sha256": "982687ee5f489fa30a02b7aecf9368d188f6f982b558a1221c5c1358e612e1c7" }, { "file": "remaining-record-audit/artifacts/598/priority-manifest.json", "sha256": "59fc8a4ca46195c29d09a17612dfef13af6170a3ea9c1672583af89fe9726abe" } ], "source_head": "615ca6f06fdea0c50dbef733370c47349e25c555" } }, { "pr": 600, "title": "Conditional \u03ba = 0.001612722852614221: improved owner map for the PR596 hyperplane-ended witness", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/600", "author": "jeremykothe2", "created_at": "2026-10-12T16:43:16Z", "accepted_at": "2026-10-12T21:01:43Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001612722852614221", "kappa_fraction": "1612722852614221/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr600-dispatched-finite-controller-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 84, "source_index": 126, "at": "2026-10-12T16:43:16Z", "until": "2026-10-12T17:11:01Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001612722852614221", "dashboard_float_text": "0.001612722852614221", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/600", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 101, "source_index": null, "at": "2026-10-12T16:43:16Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001612722852614221", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/600", "evidence_excerpt": "Conditional \u03ba = 0.001612722852614221: improved owner map for the PR596 hyperplane-ended witness", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 370, "source_index": null, "at": "2026-10-12T16:43:16Z", "until": null, "date_basis": "body-version", "fraction": "1612722852614221/1000000000000000000", "value_decimal": "0.001612722852614221", "dashboard_float_text": null, "expression": "0.001612722852614221", "historical_title": "Conditional \u03ba = 0.001612722852614221: improved owner map for the PR596 hyperplane-ended witness", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/600", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001612722852614221. This is +1.48e-9 over our PR596 (0.0016127213726553). The conservative model gives 0.001612722849763179.\n\nThis PR has the same construction, providers, dispatch (ck *53, atm3 *19", "automated_comparable": true, "body_sha256": "fae0a920b0f5897d5d9c82ccaa3540259c17d0803b24f501b9f38c7772f55f02" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr600-dispatched-finite-controller-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 6, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/600/priority-manifest.json", "sha256": "be51397e85ef237e27cbbad89cba24a61231d7c68d5bd4d8ea95b55655f7e476" } ], "source_head": "dfb7b827990d7b586b3cd778e3d750c050dd4778" } }, { "pr": 603, "title": "Conditional \u03ba = 0.001614217970939911: improved owner map for the PR601 46-helper witness", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/603", "author": "jeremykothe2", "created_at": "2026-10-12T17:26:10Z", "accepted_at": "2026-10-12T21:01:43Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001614217970939911", "kappa_fraction": "1614217970939911/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr603-cold14-typed-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 86, "source_index": 128, "at": "2026-10-12T17:26:10Z", "until": "2026-10-12T17:47:07.995285Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001614217970939911", "dashboard_float_text": "0.001614217970939911", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/603", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 103, "source_index": null, "at": "2026-10-12T17:26:10Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001614217970939911", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/603", "evidence_excerpt": "Conditional \u03ba = **0.001614217970939911**. This is +1.563e-8 over our PR601 (0.001614202339036103). The conservative model gives 0.001614217968086404.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 372, "source_index": null, "at": "2026-10-12T17:26:10Z", "until": null, "date_basis": "body-version", "fraction": "1614217970939911/1000000000000000000", "value_decimal": "0.001614217970939911", "dashboard_float_text": null, "expression": "0.001614217970939911", "historical_title": "Conditional \u03ba = 0.001614217970939911: improved owner map for the PR601 46-helper witness", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/603", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001614217970939911. This is +1.563e-8 over our PR601 (0.001614202339036103). The conservative model gives 0.001614217968086404.\n\nThis PR has the same construction, providers, dispatch (ck *45, atm3 ", "automated_comparable": true, "body_sha256": "11c94be9a0280948cc715b2dde8649b17c8d5ea08ec5fa482a8d0402cc7c3f87" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr603-cold14-typed-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 6, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/603/priority-manifest.json", "sha256": "b0199a2be32826ddfb742483d0e180e96b31f8a8c498a27fd592a2d39a1009e2" } ], "source_head": "c64200242bedc5256dee992de0a0c500be0567d3" } }, { "pr": 604, "title": "Conditional \u03ba = 0.00162128508944984: cold factory-scratch helpers end at 4-dimensional frames on the PR601 witness (+0.439%)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/604", "author": "DreamingOfClouds", "created_at": "2026-10-12T17:31:39Z", "accepted_at": "2026-10-12T21:01:43Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00162128508944984", "kappa_fraction": "20266063618123/12500000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr604-cold14-typed-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 87, "source_index": 129, "at": "2026-10-12T17:47:07.995285Z", "until": "2026-10-12T18:03:47Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.00162128508944984", "dashboard_float_text": "0.00162128508944984", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/604", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 104, "source_index": null, "at": "2026-10-12T17:47:07.995285+00:00", "until": null, "date_basis": "observed_revision", "fraction": null, "value_decimal": "0.00162128508944984", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/604", "evidence_excerpt": "**Conditional \u03ba = 0.00162128508944984, +0.439% over #601** (0.001614202339036103). The conservative model gives 0.001621285086572193. The dispatch is ck \u00d744, atm3 \u00d722, jp8 \u00d76. The value comes from `ASSEMBLY.json` of the strict `verify.py` run on this package's literal owner map. **Stacked on #601** (open); the diff includes #601's package until it merges.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 373, "source_index": null, "at": "2026-10-12T17:31:39Z", "until": null, "date_basis": "body-version", "fraction": "1620147045734211/1000000000000000000", "value_decimal": "0.00162128508944984", "dashboard_float_text": null, "expression": "0.001620147045734211", "historical_title": "Conditional \u03ba = 0.001620147045734211: cold factory-scratch helpers end at 4-dimensional frames on the PR601 witness (+0.368%)", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/604", "evidence_excerpt": "cation (full fresh-copy replays, CI) is still running. Build on this at your own risk.\n\nConditional \u03ba = 0.001620147045734211, +0.368% over #601 (0.001614202339036103). The conservative model gives 0.001620147042858282. The dispatch is ck *44, atm3 *22, jp8 *6. The value comes from ASSEMBLY.json of the s", "automated_comparable": true, "body_sha256": "55ae27fda8d0f4292efa0eab2d3a32fdbed0a0f13b2b782e7606cd3889caa365" }, { "stream": "recovered_literal_highwater", "stream_row": 374, "source_index": null, "at": "2026-10-12T17:45:18Z", "until": null, "date_basis": "body-version", "fraction": "20266063618123/12500000000000000", "value_decimal": "0.00162128508944984", "dashboard_float_text": null, "expression": "0.00162128508944984", "historical_title": "Conditional \u03ba = 0.00162128508944984: cold factory-scratch helpers end at 4-dimensional frames on the PR601 witness (+0.439%)", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/604", "evidence_excerpt": "cation (full fresh-copy replays, CI) is still running. Build on this at your own risk.\n\nConditional \u03ba = 0.00162128508944984, +0.439% over #601 (0.001614202339036103). The conservative model gives 0.001621285086572193. The dispatch is ck *44, atm3 *22, jp8 *6. The value comes from ASSEMBLY.json of the s", "automated_comparable": true, "body_sha256": "55c161a35a592365c3ec95bae187c367c27de063a9aec9d2ac411d5496e5e06f" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/cold617.json", "path": "certificates/checkpoints/cold617.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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No prior invoice or cutoff is transferred; no actual first crossing is known." }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": "A new direct Gaussian realization uses the exact own608 selected native words and physical schedule. Its original PLAN contains four redundant registry fields with stale programme/profile values; a separate numeric descriptor updates only those four fields. Actual full artefact semantics and every call-programme digest were already current and are mandatory. Every other PLAN field, all36288 roles, six negative controls and the complete fresh invoice agree exactly. The original source PLAN and its V23 rejection are preserved; no original CLI or universal native/operator/phase PASS is claimed. A subsequent cached-replay defect was repaired by moving the existing integer profile-key restoration before the exact equality guard; two cached passes agree and only provenance hashes changed. Partial operator/absolute-phase, normalized-child, owned/common-label/all-size and analytic contracts remain explicit. No prior invoice or cutoff is transferred; no actual first crossing is known.", "own_source_record_tail_quantified": true, "own_source_certificate": "pr608-registry-reconciled-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 6, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/608/priority-manifest.json", "sha256": "79b3797f304c8c057476c44e543475ad71e764ff1d0e9637f5a3bdfc83516242" } ], "source_head": "702e397432df9233cdd02e43f1f6f32e195eba84" } }, { "pr": 609, "title": "Conditional \u03ba = 0.001622285497914735: exact per-time-Hall owner map for the PR604 cold-ended witness", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/609", "author": "jeremykothe2", "created_at": "2026-10-12T18:13:39Z", "accepted_at": "2026-10-12T21:01:43Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001622285497914735", "kappa_fraction": "324457099582947/200000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr609-cold14-typed-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 88, "source_index": 132, "at": "2026-10-12T18:13:39Z", "until": "2026-10-12T18:15:34Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001622285497914735", "dashboard_float_text": "0.001622285497914735", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/609", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 105, "source_index": null, "at": "2026-10-12T18:13:39Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001622285497914735", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/609", "evidence_excerpt": "Conditional \u03ba = **0.001622285497914735**. This is +1.0004e-6 (+0.062%) over PR604's current head (0.00162128508944984, `1b795c5`, which re-solved its owner map) and +0.132% over PR604's original commit `af8c23b` (0.001620147045734211), on which this package is built. The conservative model gives 0.001622285495037214.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 375, "source_index": null, "at": "2026-10-12T18:13:39Z", "until": null, "date_basis": "body-version", "fraction": "324457099582947/200000000000000000", "value_decimal": "0.001622285497914735", "dashboard_float_text": null, "expression": "0.001622285497914735", "historical_title": "Conditional \u03ba = 0.001622285497914735: exact per-time-Hall owner map for the PR604 cold-ended witness", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/609", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001622285497914735. This is +1.0004e-6 (+0.062%) over PR604's current head (0.00162128508944984, 1b795c5, which re-solved its owner map) and +0.132% over PR604's original commit af8c23b (0.001620147", "automated_comparable": true, "body_sha256": "b126e3e0a20a780c27fcf3a5fe763068cfaaa4cf9640f84131337faae7a9029e" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr609-cold14-typed-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 5, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/609/priority-manifest.json", "sha256": "0a5f31001e91977ca3eb35e473a7dac98f987bdb22e1d552ba8c99a4423a2fbb" } ], "source_head": "10255d48152ed9f159f7c51028b1fc34a4ccc982" } }, { "pr": 610, "title": "Conditional \u03ba = 0.00162536523418317: jp8-heavy dispatch with an exact integer owner map on the PR604 cold witness (+0.692% over PR601)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/610", "author": "DreamingOfClouds", "created_at": "2026-10-12T18:15:34Z", "accepted_at": "2026-10-12T21:01:43Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00162536523418317", "kappa_fraction": "162536523418317/100000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr610-cold14-typed-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts.", "Own source descriptive entering counter 16344 differs from actual nonzero initial-frame roles 15564; width-below9 roles are 16572. The new complete invoice/stock/precision bound is independently verified not to read that counter. Historical metadata is preserved; original global verifier full PASS is not claimed." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 89, "source_index": 133, "at": "2026-10-12T18:15:34Z", "until": "2026-10-12T18:58:15Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.00162536523418317", "dashboard_float_text": "0.00162536523418317", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/610", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 106, "source_index": null, "at": "2026-10-12T18:15:34Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00162536523418317", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/610", "evidence_excerpt": "**Conditional \u03ba = 0.00162536523418317, +0.252% over #604 and +0.692% over #601.** The conservative model gives 0.001625365231365566. The value comes from `ASSEMBLY.json` of the strict `verify.py` run on this package's literal owner map. The complex side binds; the bit value (#543, 0.0016538) does not, so \u03ba is the same capped and uncapped.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 376, "source_index": null, "at": "2026-10-12T18:15:34Z", "until": null, "date_basis": "body-version", "fraction": "162536523418317/100000000000000000", "value_decimal": "0.00162536523418317", "dashboard_float_text": null, "expression": "0.00162536523418317", "historical_title": "Conditional \u03ba = 0.00162536523418317: jp8-heavy dispatch with an exact integer owner map on the PR604 cold witness (+0.692% over PR601)", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/610", "evidence_excerpt": "cation (full fresh-copy replays, CI) is still running. Build on this at your own risk.\n\nConditional \u03ba = 0.00162536523418317, +0.252% over #604 and +0.692% over #601. The conservative model gives 0.001625365231365566. The value comes from ASSEMBLY.json of the strict verify.py run on this package's liter", "automated_comparable": true, "body_sha256": "54fee0b832496edd31fea19e379f84ca83a5e3eb11caea7d36ccef5c324b6df7" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts.", "Own source descriptive entering counter 16344 differs from actual nonzero initial-frame roles 15564; width-below9 roles are 16572. The new complete invoice/stock/precision bound is independently verified not to read that counter. Historical metadata is preserved; original global verifier full PASS is not claimed." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr610-cold14-typed-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 7, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/610/priority-manifest.json", "sha256": "e0a9deaa7daca5b221a0bc7299aaf0a7649d14d890fe982749e08c14aecda25f" } ], "source_head": "b7c680ea38b9a25a89fce189bb927b45842362d0" } }, { "pr": 613, "title": "\u03ba = 0.00162536523418317: independent exact-head replay of PR610", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/613", "author": "eumemic", "created_at": "2026-10-12T18:43:13Z", "accepted_at": "2026-10-12T21:01:43Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00162536523418317", "kappa_fraction": "162536523418317/100000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No independent whole-multiplier cutoff is defined by this supplied contribution. Price the explicitly referenced complete algorithm only after binding its actual native/operator, ownership, recursive invoice, precision and outer parameters. Relevant local constants, guards and negative hypotheses remain attached to that target; they are not discarded." ], "source_manifest": [ { "file": "individual-primary-interface-source/613-manifest.json", "sha256": "cd80b3b76354dd482e3c4e3c4ebc2a237dd3de90e5843c83910caf2cdd28aef0" }, { "file": "remaining-record-audit/artifacts/613/priority-manifest.json", "sha256": "f74081473cbdc7bec63feae43837481c41b31fe568758b8ab84d3963b1f5c587" } ], "source_head": "be939d7014b6244ada9cf6a9697db31e3886b1d9" } }, { "pr": 614, "title": "Conditional \u03ba = 0.001625715867072461: jp8-heavy exact owner map on the PR604 cold-ended witness", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/614", "author": "jeremykothe2", "created_at": "2026-10-12T18:58:15Z", "accepted_at": "2026-10-12T21:01:43Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001625715867072461", "kappa_fraction": "1625715867072461/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr614-cold14-typed-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts.", "Own source descriptive entering counter 16584 differs from actual nonzero initial-frame roles 15576; width-below9 roles are 16584. The new complete invoice/stock/precision bound is independently verified not to read that counter. Historical metadata is preserved; original global verifier full PASS is not claimed." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 90, "source_index": 134, "at": "2026-10-12T18:58:15Z", "until": "2026-10-12T19:11:09Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001625715867072461", "dashboard_float_text": "0.001625715867072461", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/614", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 107, "source_index": null, "at": "2026-10-12T18:58:15Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001625715867072461", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/614", "evidence_excerpt": "Conditional \u03ba = **0.001625715867072461**. This is +3.51e-7 over PR610 (0.00162536523418317) and +3.43e-6 over our PR609. The conservative model gives 0.001625715864253489.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 377, "source_index": null, "at": "2026-10-12T18:58:15Z", "until": null, "date_basis": "body-version", "fraction": "1625715867072461/1000000000000000000", "value_decimal": "0.001625715867072461", "dashboard_float_text": null, "expression": "0.001625715867072461", "historical_title": "Conditional \u03ba = 0.001625715867072461: jp8-heavy exact owner map on the PR604 cold-ended witness", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/614", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001625715867072461. This is +3.51e-7 over PR610 (0.00162536523418317) and +3.43e-6 over our PR609. The conservative model gives 0.001625715864253489.\n\nThis PR uses DreamingOfClouds' PR604 cold-ended", "automated_comparable": true, "body_sha256": "b5804979e6f75b3c00bc22751b1192ffe80ae0611ecd0306aab34e21eb5e0349" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts.", "Own source descriptive entering counter 16584 differs from actual nonzero initial-frame roles 15576; width-below9 roles are 16584. The new complete invoice/stock/precision bound is independently verified not to read that counter. Historical metadata is preserved; original global verifier full PASS is not claimed." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr614-cold14-typed-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 6, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/614/priority-manifest.json", "sha256": "b8b39f58203056ea17dcd259cf7f3f8ca3de0fe198eaa647655d00108b1928bb" } ], "source_head": "6cfd7e2039078f80a8a39dec5e958d8df304cb90" } }, { "pr": 615, "title": "Conditional \u03ba = 0.001626010676080313: E1 entering-pair hyperplane ends on the PR604 cold-ended witness", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/615", "author": "jeremykothe2", "created_at": "2026-10-12T19:11:09Z", "accepted_at": "2026-10-12T21:01:43Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001626010676080313", "kappa_fraction": "1626010676080313/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr615-hyperplane-cold-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": "New direct Gaussian realization of the exact own-selected native words and complete owner map, with a fresh physical invoice. The prior successful 1645-check native reconstruction is authenticated; the final source reviewer freshly checked uncached scalar/frame data and complete physical costs, and does not claim a new full native/operator/phase pipeline pass. Partial operator/absolute-phase, normalized-child, owned/common-label/all-size and analytic contracts remain explicit. No prior invoice or cutoff is transferred; no actual first crossing is known. The source descriptive entering count16608 differs from actual initial-frame roles15600; the source value is preserved and independently proved unused by work, stock or precision. No original global-verifier PASS is claimed." }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 91, "source_index": 135, "at": "2026-10-12T19:11:09Z", "until": "2026-10-12T19:27:00Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001626010676080313", "dashboard_float_text": "0.001626010676080313", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/615", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 108, "source_index": null, "at": "2026-10-12T19:11:09Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001626010676080313", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/615", "evidence_excerpt": "Conditional \u03ba = **0.001626010676080313**. This is +2.95e-7 over our PR614 (0.001625715867072461) and +6.45e-7 over PR610 (0.00162536523418317). The conservative model gives 0.001626010673257238.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 378, "source_index": null, "at": "2026-10-12T19:11:09Z", "until": null, "date_basis": "body-version", "fraction": "1626010676080313/1000000000000000000", "value_decimal": "0.001626010676080313", "dashboard_float_text": null, "expression": "0.001626010676080313", "historical_title": "Conditional \u03ba = 0.001626010676080313: E1 entering-pair hyperplane ends on the PR604 cold-ended witness", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/615", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001626010676080313. This is +2.95e-7 over our PR614 (0.001625715867072461) and +6.45e-7 over PR610 (0.00162536523418317). The conservative model gives 0.001626010673257238.\n\nThis PR builds on Dreami", "automated_comparable": true, "body_sha256": "19fe8a67a7465186dc63a03a7628683265c760e95285a269ba656c21c3b8324e" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/cold617.json", "path": "certificates/checkpoints/cold617.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier741.json", "path": "certificates/checkpoints/frontier741.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier799.json", "path": "certificates/checkpoints/frontier799.json", "commit": null, "at": null, "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. Not a full Lean multiplication theorem. Integration Linux CI status is separate." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier890.json", "path": "certificates/checkpoints/frontier890.json", "commit": null, "at": null, "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier942.json", "path": "certificates/checkpoints/frontier942.json", "commit": null, "at": null, "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "51110230636731/31250000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/k492626.json", "path": "certificates/checkpoints/k492626.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/87db776d70ad1d28a27e9f7906237e5a279414f3/certificates/selected-result.json", "path": null, "commit": "87db776d70ad1d28a27e9f7906237e5a279414f3", "at": "2026-10-13T18:05:11Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3b83e4f14825ce1ae038a8c8159f130646991086/certificates/selected-result.json", "path": null, "commit": "3b83e4f14825ce1ae038a8c8159f130646991086", "at": "2026-10-13T13:30:30Z", "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d6dfd8f21b1e0b7e3f93b7e30e64639390e48504/certificates/selected-result.json", "path": null, "commit": "d6dfd8f21b1e0b7e3f93b7e30e64639390e48504", "at": "2026-10-13T06:44:14Z", "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. Not a full Lean multiplication theorem. Integration Linux CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/c290b7b919790300e14004a75d8d24b55ca3c5b5/certificates/selected-result.json", "path": null, "commit": "c290b7b919790300e14004a75d8d24b55ca3c5b5", "at": "2026-10-13T06:10:31Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/2cdd93d0250554e5160edbb8535c4500c4227349/certificates/selected-result.json", "path": null, "commit": "2cdd93d0250554e5160edbb8535c4500c4227349", "at": "2026-10-13T05:57:09Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "51110230636731/31250000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/5c5567d15bd019186519a4db267914257b5f1ac0/certificates/selected-result.json", "path": null, "commit": "5c5567d15bd019186519a4db267914257b5f1ac0", "at": "2026-10-12T22:36:34Z", "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. 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See review for replay reuse and Linux CI status." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": "New direct Gaussian realization of the exact own-selected native words and complete owner map, with a fresh physical invoice. The prior successful 1645-check native reconstruction is authenticated; the final source reviewer freshly checked uncached scalar/frame data and complete physical costs, and does not claim a new full native/operator/phase pipeline pass. Partial operator/absolute-phase, normalized-child, owned/common-label/all-size and analytic contracts remain explicit. No prior invoice or cutoff is transferred; no actual first crossing is known. The source descriptive entering count16608 differs from actual initial-frame roles15600; the source value is preserved and independently proved unused by work, stock or precision. No original global-verifier PASS is claimed.", "own_source_record_tail_quantified": true, "own_source_certificate": "pr615-hyperplane-cold-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 6, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/615/priority-manifest.json", "sha256": "6add40b8917dcb72a2869033853d94380022d86a9f031c9a235c4003c5f93509" } ], "source_head": "bf8a49a34350599763cced8592db81dc62c2c1c0" } }, { "pr": 616, "title": "Conditional \u03ba = 0.001625744726006285: coordinated owner repair on PR614", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/616", "author": "chafreaky", "created_at": "2026-10-12T19:27:00Z", "accepted_at": "2026-10-12T21:01:43Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001625744726006285", "kappa_fraction": "325148945201257/200000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr616-cold14-typed-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts.", "Own source descriptive entering counter 16584 differs from actual nonzero initial-frame roles 15576; width-below9 roles are 16584. The new complete invoice/stock/precision bound is independently verified not to read that counter. Historical metadata is preserved; original global verifier full PASS is not claimed." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts.", "Own source descriptive entering counter 16584 differs from actual nonzero initial-frame roles 15576; width-below9 roles are 16584. The new complete invoice/stock/precision bound is independently verified not to read that counter. Historical metadata is preserved; original global verifier full PASS is not claimed." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr616-cold14-typed-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/616/priority-manifest.json", "sha256": "50dfd3811b175e2d01d8c025325af6e15552f0ec5f2624b99e49172968a69a00" } ], "source_head": "5611a9048e4388bb2f330520796379926084c69e" } }, { "pr": 617, "title": "Conditional \u03ba = 0.001635183729255778: second dim-4 cold end per factory block (28 per word) on the PR604 cold-ended witness", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/617", "author": "jeremykothe2", "created_at": "2026-10-12T20:02:05Z", "accepted_at": "2026-10-12T21:01:43Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001635183729255778", "kappa_fraction": "817591864627889/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr617-mixed-finite-controller-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own arbitrary-input operator-valued native phase, normalized-wrapper, ascending typed-helper and whole Gaussian endpoint contracts remain explicit; scalar specialization is not their proof.", "Exact own selected canonical/program/orientation hashes, actual scalar/frame incidence and dyadic Horner/prefix counts are checked independently. Derived objects are rebuilt from earlier hash-pinned recipes, sometimes using exact matching later archive bytes; no later supplier is imported.", "Each own PLAN/order/dispatch/OWNERS/window, complete role namespace, residual/spectator chart, primitive/wrapper invoice and no-prior-invoice finite stock is freshly checked.", "The counted parent is a primary-fixture source-equivalent numeric realization matching own physical windows; historical parent provenance metadata byte identity is not claimed.", "Common-label, mutable-source, arbitrary-input owned restore and all-size unequal-child occupied-row batching remain fixed-protocol hypotheses; completed Gaussian children have norm one under the endpoint contract.", "Own C0=2^210000 and actual512-bit payload fund the semantic precision reserve. Same direct analytic fine-prime/boundary/recovery, candidate-only Fermat helper and repaired unlimited GMP correctness/halting interfaces." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "historical_selected_or_reviewed_conditional_checkpoint_source", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 92, "source_index": 137, "at": "2026-10-12T20:02:05Z", "until": "2026-10-12T20:20:26Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001635183729255778", "dashboard_float_text": "0.001635183729255778", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/617", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 109, "source_index": null, "at": "2026-10-12T20:02:05Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001635183729255778", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/617", "evidence_excerpt": "Conditional \u03ba = 0.001635183729255778: second dim-4 cold end per factory block (28 per word) on the PR604 cold-ended witness", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 379, "source_index": null, "at": "2026-10-12T20:02:05Z", "until": null, "date_basis": "body-version", "fraction": "817591864627889/500000000000000000", "value_decimal": "0.001635183729255778", "dashboard_float_text": null, "expression": "0.001635183729255778", "historical_title": "Conditional \u03ba = 0.001635183729255778: second dim-4 cold end per factory block (28 per word) on the PR604 cold-ended witness", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/617", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001635183729255778. This is +0.564% over our PR615 (0.001626010676080313) and +0.604% over PR610. The conservative model gives 0.001635183726407116.\n\nThis PR doubles the cold low-frame ends of Dream", "automated_comparable": true, "body_sha256": "75fb124d9c17fdff477d3a29df523e8a6f67c9d9154f4f4b4ad0900f6a1ea7bc" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "first_listed_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/cold617.json", "path": "certificates/checkpoints/cold617.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. See review for replay reuse and Linux CI status." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "51110230636731/31250000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/k492626.json", "path": "certificates/checkpoints/k492626.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. All-size/compiler/common-label/mutable-basis/pooled-cell hosting/residual/precision/tape/analytic assumptions remain. This is not a full Lean multiplication theorem. 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Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3b83e4f14825ce1ae038a8c8159f130646991086/certificates/selected-result.json", "path": null, "commit": "3b83e4f14825ce1ae038a8c8159f130646991086", "at": "2026-10-13T13:30:30Z", "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d6dfd8f21b1e0b7e3f93b7e30e64639390e48504/certificates/selected-result.json", "path": null, "commit": "d6dfd8f21b1e0b7e3f93b7e30e64639390e48504", "at": "2026-10-13T06:44:14Z", "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. Not a full Lean multiplication theorem. Integration Linux CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/c290b7b919790300e14004a75d8d24b55ca3c5b5/certificates/selected-result.json", "path": null, "commit": "c290b7b919790300e14004a75d8d24b55ca3c5b5", "at": "2026-10-13T06:10:31Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. 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Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 85, "source_index": 127, "at": "2026-10-12T17:11:01Z", "until": "2026-10-12T17:26:10Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001614202339036103", "dashboard_float_text": "0.001614202339036103", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/601", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 102, "source_index": null, "at": "2026-10-12T17:11:01Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001614202339036103", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/601", "evidence_excerpt": "Conditional \u03ba = 0.001614202339036103: 46 hyperplane-ended helpers per call via commuting-prefix cleanup", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 371, "source_index": null, "at": "2026-10-12T17:11:01Z", "until": null, "date_basis": "body-version", "fraction": "1614202339036103/1000000000000000000", "value_decimal": "0.001614202339036103", "dashboard_float_text": null, "expression": "0.001614202339036103", "historical_title": "Conditional \u03ba = 0.001614202339036103: 46 hyperplane-ended helpers per call via commuting-prefix cleanup", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/601", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001614202339036103. This is +1.479e-6 over PR600 (0.001612722852614221) and +1.481e-6 over PR596. The conservative model gives 0.001614202336182603.\n\nThis PR extends the hyperplane-end construction ", "automated_comparable": true, "body_sha256": "9083b8a0c8128d5a76c6457fbf44c091fd956c745cd2a54ce9caafcd9fdc965b" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "817591864627889/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/cold617.json", "path": "certificates/checkpoints/cold617.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, invoice and exact assembly checks. 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Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr601-cold14-typed-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 4, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/601/priority-manifest.json", "sha256": "84cb3c6661c8660ba1f8bdc51e43d56a123a3caab1713ae0a04c264bf83756a6" } ], "source_head": "529ab7dcb59d5ea7a5798e9e06cf5b3aee8a1550" } }, { "pr": 618, "title": "Owner consolidation on PR610: conditional \u03ba = 0.001625434703655052", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/618", "author": "jeremydiviney", "created_at": "2026-10-12T20:20:26Z", "accepted_at": "2026-10-12T22:36:46Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001625434703655052", "kappa_fraction": "406358675913763/250000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr618-cold14-typed-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts.", "Own source descriptive entering counter 16344 differs from actual nonzero initial-frame roles 15564; width-below9 roles are 16572. The new complete invoice/stock/precision bound is independently verified not to read that counter. Historical metadata is preserved; original global verifier full PASS is not claimed." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts.", "Own source descriptive entering counter 16344 differs from actual nonzero initial-frame roles 15564; width-below9 roles are 16572. The new complete invoice/stock/precision bound is independently verified not to read that counter. Historical metadata is preserved; original global verifier full PASS is not claimed." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr618-cold14-typed-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/618/priority-manifest.json", "sha256": "70a362551a1dd2f3b5df4135f2cd9d0c1f4a2e5972c9cae643010bebde8ec732" } ], "source_head": "a0d472c7459952f5e55fd9d829adb0484cc0f648" } }, { "pr": 619, "title": "Exact packing ceiling for the PR615 supplier family", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/619", "author": "chafreaky", "created_at": "2026-10-12T20:23:43Z", "accepted_at": "2026-10-12T22:36:46Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001626010676080313339567", "kappa_fraction": "1626010676080313339567/1000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr619-ceiling-refined-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": "PR619 retains the PR615 native core and refines the output grid. Its own complete289-file manifest, literal selector and exact native/physical commitments are checked; a fresh direct Gaussian invoice and both runtime schedules are computed. The prior successful1645-check source615 byte recovery is used only where its actual RAW/canonical/programme/both-orientation objects match direct own619 commitments. No fresh619 native constructor, complete CLI or operator/phase pipeline pass is claimed. The final source reviewer independently checked own289API/blob bindings, the exact eight SPEC changes, uncached scalar/frame data and complete physical costs. Partial operator/absolute-phase, normalized-child, owned/common-label/all-size and analytic contracts remain explicit. No prior invoice or cutoff is transferred; no actual first crossing is known. The source descriptive entering count16608 differs from actual initial-frame roles15600; the source value is preserved and independently proved unused by work, stock or precision. No original global-verifier PASS is claimed." }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": "PR619 retains the PR615 native core and refines the output grid. Its own complete289-file manifest, literal selector and exact native/physical commitments are checked; a fresh direct Gaussian invoice and both runtime schedules are computed. The prior successful1645-check source615 byte recovery is used only where its actual RAW/canonical/programme/both-orientation objects match direct own619 commitments. No fresh619 native constructor, complete CLI or operator/phase pipeline pass is claimed. The final source reviewer independently checked own289API/blob bindings, the exact eight SPEC changes, uncached scalar/frame data and complete physical costs. Partial operator/absolute-phase, normalized-child, owned/common-label/all-size and analytic contracts remain explicit. No prior invoice or cutoff is transferred; no actual first crossing is known. The source descriptive entering count16608 differs from actual initial-frame roles15600; the source value is preserved and independently proved unused by work, stock or precision. No original global-verifier PASS is claimed.", "own_source_record_tail_quantified": true, "own_source_certificate": "pr619-ceiling-refined-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/619/priority-manifest.json", "sha256": "aaad5106ba8833fc119dfa692bde560bfe8c97f32fa1ab71d452b6cda8fd89dd" } ], "source_head": "9879380b4e9fd922842a35cb3edefd712debfdac" } }, { "pr": 622, "title": "Conditional \u03ba = 0.00163542231500688: K-triangle skeleton atom (492 helpers per call) on the PR617 cold-ended witness", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/622", "author": "jeremykothe2", "created_at": "2026-10-12T20:57:03Z", "accepted_at": "2026-10-12T22:36:46Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00163542231500688", "kappa_fraction": "10221389468793/6250000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr622-dispatched-finite-controller-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 93, "source_index": 140, "at": "2026-10-12T20:57:03Z", "until": "2026-10-12T21:27:40Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.00163542231500688", "dashboard_float_text": "0.00163542231500688", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/622", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 110, "source_index": null, "at": "2026-10-12T20:57:03Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00163542231500688", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/622", "evidence_excerpt": "Conditional \u03ba = 0.00163542231500688: K-triangle skeleton atom (492 helpers per call) on the PR617 cold-ended witness", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 380, "source_index": null, "at": "2026-10-12T20:57:03Z", "until": null, "date_basis": "body-version", "fraction": "10221389468793/6250000000000000", "value_decimal": "0.00163542231500688", "dashboard_float_text": null, "expression": "0.00163542231500688", "historical_title": "Conditional \u03ba = 0.00163542231500688: K-triangle skeleton atom (492 helpers per call) on the PR617 cold-ended witness", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/622", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.00163542231500688. This is +2.39e-7 (+0.0146%) over our PR617 (0.001635183729255778). The conservative model gives 0.001635422312138865.\n\nThis is the first change to the helper skeleton itself sinc", "automated_comparable": true, "body_sha256": "4b59f0d79ee58a08b14de18724aa0fa0a818a9323bfcff2ac73cd03102f74716" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr623-dispatched-finite-controller-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 6, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/623/priority-manifest.json", "sha256": "65623b72cf9242d2d809ebd54749bbe5a2f8fbed2ff6cb493a80c03b6b5bd96e" } ], "source_head": "e39a615ca601ce5d62abeb24f3fcdb8644ca1005" } }, { "pr": 624, "title": "Owner repacking on PR622: conditional \u03ba = 0.001635425470780892", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/624", "author": "jeremydiviney", "created_at": "2026-10-12T21:33:05Z", "accepted_at": "2026-10-12T22:36:46Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001635425470780892", "kappa_fraction": "408856367695223/250000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr624-dispatched-finite-controller-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr624-dispatched-finite-controller-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/624/priority-manifest.json", "sha256": "7ba45556725e497e0c78a36000d145b62c3311e68fe0c010b81732d17009a57d" } ], "source_head": "036753ed33d4e620932262646e3d02a1927256a6" } }, { "pr": 625, "title": "Conditional \u03ba = 0.001635502740907482: owner map with one LNS improvement for the PR622 K-triangle witness", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/625", "author": "jeremykothe2", "created_at": "2026-10-12T21:41:31Z", "accepted_at": "2026-10-12T22:36:46Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001635502740907482", "kappa_fraction": "817751370453741/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr625-dispatched-finite-controller-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 95, "source_index": 143, "at": "2026-10-12T21:41:31Z", "until": "2026-10-12T21:53:17Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001635502740907482", "dashboard_float_text": "0.001635502740907482", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/625", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 112, "source_index": null, "at": "2026-10-12T21:41:31Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001635502740907482", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/625", "evidence_excerpt": "Conditional \u03ba = 0.001635502740907482: owner map with one LNS improvement for the PR622 K-triangle witness", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 382, "source_index": null, "at": "2026-10-12T21:41:31Z", "until": null, "date_basis": "body-version", "fraction": "817751370453741/500000000000000000", "value_decimal": "0.001635502740907482", "dashboard_float_text": null, "expression": "0.001635502740907482", "historical_title": "Conditional \u03ba = 0.001635502740907482: owner map with one LNS improvement for the PR622 K-triangle witness", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/625", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001635502740907482. This is +1.21e-8 over our PR623 (0.001635490664920455), +8.04e-8 over PR622 and +3.19e-7 over main's selected PR617. The conservative model gives 0.001635502738038541.\n\nThis PR h", "automated_comparable": true, "body_sha256": "6940bf90dcac4efe5277e17fef0f6111d1b31a3f983e2895be745c9acaf1db67" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr625-dispatched-finite-controller-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 6, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/625/priority-manifest.json", "sha256": "36b4cec4535e82c8673774f87c13c6a9a1eef784bab788c5d64ff60a9e28c56c" } ], "source_head": "386712d06fe4b163596370af4646fec390bd7eb3" } }, { "pr": 626, "title": "Conditional \u03ba = 0.001635527380375392: coordinated owner repair on PR623", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/626", "author": "chafreaky", "created_at": "2026-10-12T21:53:17Z", "accepted_at": "2026-10-12T22:36:46Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001635527380375392", "kappa_fraction": "51110230636731/31250000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr626-mixed-finite-controller-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own arbitrary-input operator-valued native phase, normalized-wrapper, ascending typed-helper and whole Gaussian endpoint contracts remain explicit; scalar specialization is not their proof.", "Exact own selected canonical/program/orientation hashes, actual scalar/frame incidence and dyadic Horner/prefix counts are checked independently. Derived objects are rebuilt from earlier hash-pinned recipes, sometimes using exact matching later archive bytes; no later supplier is imported.", "Each own PLAN/order/dispatch/OWNERS/window, complete role namespace, residual/spectator chart, primitive/wrapper invoice and no-prior-invoice finite stock is freshly checked.", "The counted parent is a primary-fixture source-equivalent numeric realization matching own physical windows; historical parent provenance metadata byte identity is not claimed.", "Common-label, mutable-source, arbitrary-input owned restore and all-size unequal-child occupied-row batching remain fixed-protocol hypotheses; completed Gaussian children have norm one under the endpoint contract.", "Own C0=2^210000 and actual512-bit payload fund the semantic precision reserve. Same direct analytic fine-prime/boundary/recovery, candidate-only Fermat helper and repaired unlimited GMP correctness/halting interfaces." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "historical_selected_or_reviewed_conditional_checkpoint_source", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 96, "source_index": 144, "at": "2026-10-12T21:53:17Z", "until": "2026-10-12T23:51:39Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001635527380375392", "dashboard_float_text": "0.001635527380375392", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/626", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 113, "source_index": null, "at": "2026-10-12T21:53:17Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001635527380375392", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/626", "evidence_excerpt": "Conditional \u03ba = 0.001635527380375392: coordinated owner repair on PR623", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 383, "source_index": null, "at": "2026-10-12T21:53:17Z", "until": null, "date_basis": "opening-title", "fraction": "51110230636731/31250000000000000", "value_decimal": "0.001635527380375392", "dashboard_float_text": null, "expression": "0.001635527380375392", "historical_title": "Conditional \u03ba = 0.001635527380375392: coordinated owner repair on PR623", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/626", "evidence_excerpt": "Conditional \u03ba = 0.001635527380375392: coordinated owner repair on PR623", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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Source PR Linux CI passed; combined integration CI status is separate." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "upper_only_finite_source": true, "native_coordinate_rank": 73, "early_effective_kappa": "1/5000", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 0, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [], "source_head": "e516b1463606840a15f80aac1995d64ce0092e89" } }, { "pr": 799, "title": "Conditional \u03ba = 0.001661634653669567: four paired read exchanges on PR741's frame-coalesced word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/799", "author": "jeremykothe2", "created_at": "2026-10-13T05:49:47Z", "accepted_at": "2026-10-13T06:44:20Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661634653669567", "kappa_fraction": "1661634653669567/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews. The upper costs this own-source finite-controller branch. Its original record tail has also been counted independently.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr799-finite-gate-refined-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": "Own PR799 selected dyadic finite-controller branch, with separately quantified own original-record tail. Retained native/all-column, phase, all-size and analytic contracts apply. No meaningful numerical lower or exact first crossing is claimed. The current numerical upper additionally uses the independently checked integral gate refinement." }, "cost_status": "conditional_finite_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "historical_selected_or_reviewed_conditional_checkpoint_source", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 109, "source_index": 158, "at": "2026-10-13T05:49:47Z", "until": "2026-10-13T08:44:55Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001661634653669567", "dashboard_float_text": "0.001661634653669567", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/799", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 126, "source_index": null, "at": "2026-10-13T05:49:47Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001661634653669567", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/799", "evidence_excerpt": "Conditional \u03ba = 0.001661634653669567: four paired read exchanges on PR741's frame-coalesced word", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 410, "source_index": null, "at": "2026-10-13T05:49:47Z", "until": null, "date_basis": "body-version", "fraction": "1661634653669567/1000000000000000000", "value_decimal": "0.001661634653669567", "dashboard_float_text": null, "expression": "0.001661634653669567", "historical_title": "Conditional \u03ba = 0.001661634653669567: four paired read exchanges on PR741's frame-coalesced word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/799", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001661634653669567. This is +4.32*10^-7 over PR741 (0.001661202643272239). The complex side binds; PR589's bit supplier gives 0.0017334.\n\nConstruction, on PR699's word (sha d232183f):\n1. chafreaky's", "automated_comparable": true, "body_sha256": "3fa488048efffe92cd47cc2fdb2d0894f5990ac6efc8b4059b93b744799e4708" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "first_listed_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier799.json", "path": "certificates/checkpoints/frontier799.json", "commit": null, "at": null, "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. Not a full Lean multiplication theorem. Integration Linux CI status is separate." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier890.json", "path": "certificates/checkpoints/frontier890.json", "commit": null, "at": null, "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier942.json", "path": "certificates/checkpoints/frontier942.json", "commit": null, "at": null, "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/87db776d70ad1d28a27e9f7906237e5a279414f3/certificates/selected-result.json", "path": null, "commit": "87db776d70ad1d28a27e9f7906237e5a279414f3", "at": "2026-10-13T18:05:11Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3825dc0ea1317629864ebeb6929719cc4bbf525f/certificates/selected-result.json", "path": null, "commit": "3825dc0ea1317629864ebeb6929719cc4bbf525f", "at": "2026-10-13T15:06:01Z", "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3b83e4f14825ce1ae038a8c8159f130646991086/certificates/selected-result.json", "path": null, "commit": "3b83e4f14825ce1ae038a8c8159f130646991086", "at": "2026-10-13T13:30:30Z", "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "first_listed_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d6dfd8f21b1e0b7e3f93b7e30e64639390e48504/certificates/selected-result.json", "path": null, "commit": "d6dfd8f21b1e0b7e3f93b7e30e64639390e48504", "at": "2026-10-13T06:44:14Z", "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. Not a full Lean multiplication theorem. Integration Linux CI status is separate." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "upper_only_finite_source": true, "native_coordinate_rank": 73, "early_effective_kappa": "1/5000", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 0, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [], "source_head": "80e6463157cfc80b85af09e7e2f14748fe2dac60" } }, { "pr": 777, "title": "Independent verification: point-set replay of \u03ba = 0.001661202643272239", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/777", "author": "tekuuu", "created_at": "2026-10-13T05:27:40Z", "accepted_at": "2026-10-13T06:44:21Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661202643272239", "kappa_fraction": "1661202643272239/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr777-frame-retimed-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": "PR777 own complete26-file manifest, literal verifier and direct own native/physical commitments are checked. A fresh direct Gaussian invoice and both runtime schedules are computed. Actual earlier741 canonical and programme bytes are reused only where their full canonical, complete programme and both-orientation hashes match the direct own777 SPEC. No741 invoice, exponent or cutoff is transferred; no original777 native constructor, complete CLI or operator/phase pipeline pass is claimed. Actual canonical initial/final frames, all36288 roles and six owner controls are checked. The source does not declare an expected entering-role counter; actual15552 initial-frame roles and width-below-nine20736 are distinguished. Universal operator/absolute-phase, normalized-child, owned/common-label/all-size and analytic contracts remain explicit. No actual first crossing is known." }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": "PR777 own complete26-file manifest, literal verifier and direct own native/physical commitments are checked. A fresh direct Gaussian invoice and both runtime schedules are computed. Actual earlier741 canonical and programme bytes are reused only where their full canonical, complete programme and both-orientation hashes match the direct own777 SPEC. No741 invoice, exponent or cutoff is transferred; no original777 native constructor, complete CLI or operator/phase pipeline pass is claimed. Actual canonical initial/final frames, all36288 roles and six owner controls are checked. The source does not declare an expected entering-role counter; actual15552 initial-frame roles and width-below-nine20736 are distinguished. Universal operator/absolute-phase, normalized-child, owned/common-label/all-size and analytic contracts remain explicit. No actual first crossing is known.", "own_source_record_tail_quantified": true, "own_source_certificate": "pr777-frame-retimed-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/777/priority-manifest.json", "sha256": "704d06153f64ebfc15fc700ae75c18a43476ec399c5e1da6e8fde5a50b5fa923" } ], "source_head": "eca5c317d8176401a1f71a5ea1e81384c2eab1e0" } }, { "pr": 870, "title": "Conditional \u03ba = 0.001661956299899884: PR858's sixteen-replica owner controller on the U8 word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/870", "author": "jeremykothe2", "created_at": "2026-10-13T08:45:42Z", "accepted_at": "2026-10-13T13:30:39Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661956299899884", "kappa_fraction": "415489074974971/250000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr870-u8-selected-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 111, "source_index": 160, "at": "2026-10-13T08:45:42Z", "until": "2026-10-13T10:26:05Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001661956299899884", "dashboard_float_text": "0.001661956299899884", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/870", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 128, "source_index": null, "at": "2026-10-13T08:45:42Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001661956299899884", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/870", "evidence_excerpt": "Conditional \u03ba = **0.001661956299899884** (conservative 0.001661956297017522). This is +7.60\u00d710\u207b\u2079 over the U8 package (research/gauge44-barch, 0.001661948695165034).", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 413, "source_index": null, "at": "2026-10-13T08:45:42Z", "until": null, "date_basis": "body-version", "fraction": "415489074974971/250000000000000000", "value_decimal": "0.001661956299899884", "dashboard_float_text": null, "expression": "0.001661956299899884", "historical_title": "Conditional \u03ba = 0.001661956299899884: PR858's sixteen-replica owner controller on the U8 word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/870", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001661956299899884 (conservative 0.001661956297017522). This is +7.60*10^-9 over the U8 package (research/gauge44-barch, 0.001661948695165034).\n\nChange: FanPUYen's PR858 sixteen-replica owner contro", "automated_comparable": true, "body_sha256": "1d947002517cd9707c1cd975ea135dc7cf303f6dc484a966fcce26bd60bb606b" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier890.json", "path": "certificates/checkpoints/frontier890.json", "commit": null, "at": null, "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier942.json", "path": "certificates/checkpoints/frontier942.json", "commit": null, "at": null, "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. 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Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/881-manifest.json", "sha256": "447bd98dfc16c99437d7d8c212fdd9ac2a3c7178e77a5563f5cf0b6e3b764e37" }, { "file": "remaining-record-audit/artifacts/881/priority-manifest.json", "sha256": "5515d80fb34d5525c12f53cc5295df22ef2e574902d8e0e273f1af02262b15be" } ], "source_head": "2730da199c4dad53b52b32b6be8ed6328f014648" } }, { "pr": 890, "title": "Conditional \u03ba = 0.001661957774647029: T21 whole-owner packing and fixed-family bound", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/890", "author": "chafreaky", "created_at": "2026-10-13T10:26:05Z", "accepted_at": "2026-10-13T13:30:39Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661957774647029", "kappa_fraction": "1661957774647029/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "Declared own literal complete O(73,2) early/record Gaussian enhancement family. 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It does not claim historical parent-template or PLAN provenance-string byte identity.", "Completed exact Gaussian children have semantic norm one under the source endpoint interface; own finite literal inequalities fund C0=2^210000 and the full own 512/1024 payload charges.", "Same direct Gaussian/fine-prime/finite-section/boundary/recovery analytic conditions, exact candidate-only Fermat helper, fixed XAG tariff and repaired unlimited optimized-GMP correctness/halting assumptions.", "Declared own literal complete O(73,2) early/record Gaussian enhancement family. Every active counted source body retains all cover vertices and the actual selected public ADD with no pruning, aggregation, quotienting or bypass; any no-native synthesis returns the identical optimized GMP reference. This is an added comparison-family policy and excludes other historical BIT/original hybrid or compressed implementations.", "Declared own literal complete O(73,2) early/record Gaussian enhancement family. Every active counted source body retains all cover vertices and the actual selected public ADD with no pruning, aggregation, quotienting or bypass; any no-native synthesis returns the identical optimized GMP reference. This is an added comparison-family policy and excludes other historical BIT/original hybrid or compressed implementations.", "Full same own counted source body and complete group E; own early and record verified domains both contain a nonempty native H stage above the full stopped base. No optional unrelated original-record hybrid is included." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr890-finite73-literal-cover-range.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/890/priority-manifest.json", "sha256": "ab5ee000881e33fb262cae38cf00fa752f1c74d2bf54b9381c49b1117abf948b" } ], "source_head": "4b3bd8cbe8e3e81c44161017c9b72c905a8040a8" } }, { "pr": 841, "title": "Tooling: bind selected primary-proof pointers to verified digests (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/841", "author": "mihir-s-05", "created_at": "2026-10-13T07:09:58Z", "accepted_at": "2026-10-13T13:30:40Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661202643272239", "kappa_fraction": "1661202643272239/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "individual-primary-interface-source/841-manifest.json", "sha256": "c523bb6d1634046d59f0b34ed2d3e3762de9b37203e3882fbf7f1d7eec08e24c" }, { "file": "remaining-record-audit/artifacts/841/priority-manifest.json", "sha256": "7e5cb6ec4cd9ad84c738de259bfccaef810c495b757920666e69b14e455bc15e" } ], "source_head": "2fedd468c0bb69722fbc402be01daa7701f0c7d6" } }, { "pr": 853, "title": "Tooling: 1.54-1.71x faster #741 complex replay by running independent pinned stages concurrently", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/853", "author": "navinor", "created_at": "2026-10-13T07:39:52Z", "accepted_at": "2026-10-13T13:30:40Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661202643272239", "kappa_fraction": "1661202643272239/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/853-manifest.json", "sha256": "11f1b855369475b352125379b219a1f1c2f8c5cb191918d4d16eb5f5679ec96a" }, { "file": "remaining-record-audit/artifacts/853/priority-manifest.json", "sha256": "1d756e064805a98d58a7b91cb1630d1a1b2b1d5f357d452b3570a014301bd8ad" } ], "source_head": "9910c23b154e05cca2834f45797455200cadf6e4" } }, { "pr": 869, "title": "Conditional \u03ba = 0.001661948695165034: eight triangle-hybrid B deliveries in block 0 on PR799's word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/869", "author": "jeremykothe2", "created_at": "2026-10-13T08:44:55Z", "accepted_at": "2026-10-13T13:30:40Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661948695165034", "kappa_fraction": "830974347582517/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr869-u8-selected-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 110, "source_index": 159, "at": "2026-10-13T08:44:55Z", "until": "2026-10-13T08:45:42Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001661948695165034", "dashboard_float_text": "0.001661948695165034", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/869", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 127, "source_index": null, "at": "2026-10-13T08:44:55Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001661948695165034", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/869", "evidence_excerpt": "Conditional \u03ba = **0.001661948695165034** (conservative 0.00166194869228268). This is +3.14\u00d710\u207b\u2077 over PR799 (0.001661634653669567). The complex side binds; PR589's bit supplier gives 0.0017334.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 412, "source_index": null, "at": "2026-10-13T08:44:55Z", "until": null, "date_basis": "body-version", "fraction": "830974347582517/500000000000000000", "value_decimal": "0.001661948695165034", "dashboard_float_text": null, "expression": "0.001661948695165034", "historical_title": "Conditional \u03ba = 0.001661948695165034: eight triangle-hybrid B deliveries in block 0 on PR799's word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/869", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001661948695165034 (conservative 0.00166194869228268). This is +3.14*10^-7 over PR799 (0.001661634653669567). The complex side binds; PR589's bit supplier gives 0.0017334.\n\nChange: eight triangle-hy", "automated_comparable": true, "body_sha256": "9fea83867b4d2f9b9119753da23e943722ccd2a9293fc163dd09f29d43eada4f" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier890.json", "path": "certificates/checkpoints/frontier890.json", "commit": null, "at": null, "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier942.json", "path": "certificates/checkpoints/frontier942.json", "commit": null, "at": null, "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/87db776d70ad1d28a27e9f7906237e5a279414f3/certificates/selected-result.json", "path": null, "commit": "87db776d70ad1d28a27e9f7906237e5a279414f3", "at": "2026-10-13T18:05:11Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3825dc0ea1317629864ebeb6929719cc4bbf525f/certificates/selected-result.json", "path": null, "commit": "3825dc0ea1317629864ebeb6929719cc4bbf525f", "at": "2026-10-13T15:06:01Z", "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3b83e4f14825ce1ae038a8c8159f130646991086/certificates/selected-result.json", "path": null, "commit": "3b83e4f14825ce1ae038a8c8159f130646991086", "at": "2026-10-13T13:30:30Z", "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr869-u8-selected-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/869/priority-manifest.json", "sha256": "086cdda96ab0efc861497a6554747af0d4f008bfa05ef4e98380defce85d9a2f" } ], "source_head": "73e86f69bf9a391e3c334999f7bbe3825dc42759" } }, { "pr": 894, "title": "Research audit: exact endpoint-to-kappa reduction of the selected frontier799 assembly (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/894", "author": "navinor", "created_at": "2026-10-13T10:46:10Z", "accepted_at": "2026-10-13T13:30:40Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661634653669567", "kappa_fraction": "1661634653669567/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "supporting_endpoint_audit_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 3, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No distinct numerical point should be fabricated for this support artifact. Bind a referenced implementation separately if displaying its inherited cutoff." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/894/priority-manifest.json", "sha256": "fb7d01e2e3fd361ca56b0246edd1061f90592ee96ca543fa69dd9773b25e888d" } ], "source_head": "144e7e21c4f6ab4afda1338fe25eaab5a53b4431" } }, { "pr": 837, "title": "Research: bidirectional Horner saves 312 SW4 primitives per orientation (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/837", "author": "bitplane", "created_at": "2026-10-13T06:53:02Z", "accepted_at": "2026-10-13T14:10:25Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661634653669567", "kappa_fraction": "1661634653669567/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/dyadic-horner-direction/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/dyadic-horner-direction/CLAIM.json, research/dyadic-horner-direction/EXPECTED.json, research/dyadic-horner-direction/README.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/dyadic-horner-direction/CLAIM.json, research/dyadic-horner-direction/EXPECTED.json, research/dyadic-horner-direction/README.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/dyadic-horner-direction/CLAIM.json#/result after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/837-manifest.json", "sha256": "348b412364c8913a73e459467fc0b151e56a9f166b55cc399e20f2a73bbed9e9" }, { "file": "remaining-record-audit/artifacts/837/priority-manifest.json", "sha256": "7cb114839c003a62f282e8405f45224b39088d4d05e9e25e0a6754b2bcf87d9e" } ], "source_head": "0a2977195efc8fb2a918fbfb694ec8d294387f08" } }, { "pr": 891, "title": "Research construction: R439 phase-B blocks 506/523 to 24/39 ADDs + certified single-write class boundaries (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/891", "author": "navinor", "created_at": "2026-10-13T10:26:26Z", "accepted_at": "2026-10-13T14:10:25Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661634653669567", "kappa_fraction": "1661634653669567/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/r439-bsection-survey/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/r439-bsection-survey/CERTIFICATE.json, research/r439-bsection-survey/EXPECTED.json, research/r439-bsection-survey/README.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/r439-bsection-survey/CERTIFICATE.json, research/r439-bsection-survey/EXPECTED.json, research/r439-bsection-survey/README.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/891-manifest.json", "sha256": "a601cfff577e7c1cb3f653a143dc69cf1c97112c294ead73078993bfe887c6c8" }, { "file": "remaining-record-audit/artifacts/891/priority-manifest.json", "sha256": "e2ee5ae4f52ca1fa48fe21d8507398fb6d4f699675a6656f170956926acc6cf1" } ], "source_head": "645fb93fcd21b86aca7e2bf81582be5c62411b27" } }, { "pr": 916, "title": "Integration: admit PR883 X4 primitive lowering through selected invoice and assembly (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/916", "author": "nightangelflowerwin-ops", "created_at": "2026-10-13T12:22:59Z", "accepted_at": "2026-10-13T14:10:25Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661634653669567", "kappa_fraction": "1661634653669567/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/x4-primitive-admission/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/x4-primitive-admission/EXPECTED.json, research/x4-primitive-admission/PROOF.md, research/x4-primitive-admission/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/x4-primitive-admission/EXPECTED.json, research/x4-primitive-admission/PROOF.md, research/x4-primitive-admission/SOURCES.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/x4-primitive-admission/EXPECTED.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/916-manifest.json", "sha256": "85a35a5a0513bb57698e7c60b544603dd4fa19517c5b1621b22a7ae03d3801d1" }, { "file": "remaining-record-audit/artifacts/916/priority-manifest.json", "sha256": "13498efbcc2846694dd1849a8faf7a0d43d342f901275849088d2dd866a44401" } ], "source_head": "1f0cd934f83ddf2f14f20275ecca072c5b85a7b9" } }, { "pr": 816, "title": "Research: signed CK target forests save 66,520 primitives with an exact class floor (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/816", "author": "dd-hemant", "created_at": "2026-10-13T06:20:32Z", "accepted_at": "2026-10-13T14:10:26Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661202643272239", "kappa_fraction": "1661202643272239/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/complex-ck-target-forest/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/complex-ck-target-forest/EXPECTED.json, research/complex-ck-target-forest/PROOF.md, research/complex-ck-target-forest/README.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/complex-ck-target-forest/EXPECTED.json, research/complex-ck-target-forest/PROOF.md, research/complex-ck-target-forest/README.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/complex-ck-target-forest/EXPECTED.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/816-manifest.json", "sha256": "ad9978fcf61029185bd682d0a04f0aa385d51d026a4996aecd74e58ff445002e" }, { "file": "remaining-record-audit/artifacts/816/priority-manifest.json", "sha256": "1280a0b425c4099573b619dff14dd2563e7ae43ae09f92a8428e559d106569c0" } ], "source_head": "133735a2cc2319c12ba5d786214b2217e083e7da" } }, { "pr": 857, "title": "Research construction: R439 block 8 saves ten ADDs within the existing payload cap (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/857", "author": "zeusinsight", "created_at": "2026-10-13T07:57:38Z", "accepted_at": "2026-10-13T15:06:48Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661634653669567", "kappa_fraction": "1661634653669567/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 9, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/r439-block8-integer-factor/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/r439-block8-integer-factor/CERTIFICATE.json, research/r439-block8-integer-factor/NATIVE-CERTIFICATE.json, research/r439-block8-integer-factor/README.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/r439-block8-integer-factor/CERTIFICATE.json#/native_records/replacement and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/857-manifest.json", "sha256": "1c7ed8edeac81cc4e06cca111a5f6f5a540f26a8c38789120fc80b72e373f5de" }, { "file": "remaining-record-audit/artifacts/857/priority-manifest.json", "sha256": "af2c1e90cbe00bbef8a8a07696f8e1076df76ba9ac0f30a78cb107930393eb63" } ], "source_head": "530c72042438f723782c834101427591f465dd0d" } }, { "pr": 908, "title": "Finite construction: R439 frame 519 saves 20 complete local ADDs (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/908", "author": "RossRichardson", "created_at": "2026-10-13T11:52:48Z", "accepted_at": "2026-10-13T15:06:48Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661634653669567", "kappa_fraction": "1661634653669567/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 9, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/r439-frame519-seed02/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/r439-frame519-seed02/CERTIFICATE.json, research/r439-frame519-seed02/NATIVE-CERTIFICATE.json, research/r439-frame519-seed02/README.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/r439-frame519-seed02/CERTIFICATE.json#/before and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/r439-frame519-seed02/CERTIFICATE.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/908-manifest.json", "sha256": "280de89cc2f0717b77b2fd4fb6432987d3e57bd9a47c9408b261f8775649dce6" }, { "file": "remaining-record-audit/artifacts/908/priority-manifest.json", "sha256": "157aae336061491378667fcd4ce66324b95d4653118144118c49e9d5b54b40f6" } ], "source_head": "7deb3ca8ee112249b5eec22acd24e214383078bd" } }, { "pr": 914, "title": "Finite bit construction: R439 frame 524 saves 28 complete local ADDs (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/914", "author": "RossRichardson", "created_at": "2026-10-13T12:17:12Z", "accepted_at": "2026-10-13T15:06:48Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661634653669567", "kappa_fraction": "1661634653669567/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/r439-frame524-seed13/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/r439-frame524-seed13/CERTIFICATE.json, research/r439-frame524-seed13/CLAIM.json, research/r439-frame524-seed13/NATIVE-CERTIFICATE.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/r439-frame524-seed13/CERTIFICATE.json#/candidate/invoice and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/914-manifest.json", "sha256": "9639fe7a159f03820dbe8966be0852a51c4c68a894a037c60a1679175e3f323b" }, { "file": "remaining-record-audit/artifacts/914/priority-manifest.json", "sha256": "b809282bb63602ddafbee9b9baef521ece9e4bd8266b21b83f1c4c0eb02cb4fb" } ], "source_head": "dba9199e8cbb0136bcba6b769c36753a61092190" } }, { "pr": 941, "title": "Finite bit construction: certify R439 matching floor and save 31 further ADDs", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/941", "author": "bitplane", "created_at": "2026-10-13T13:49:11Z", "accepted_at": "2026-10-13T15:06:48Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661957774647029", "kappa_fraction": "1661957774647029/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/r439-helper-matching/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/r439-helper-matching/CERTIFICATE.json, research/r439-helper-matching/CLAIM.json, research/r439-helper-matching/EXPECTED.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/r439-helper-matching/EXPECTED.json#/native/parent and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/941-manifest.json", "sha256": "c887fce323cd96c93f6be232d7927a0a856508102efd62ad933781220c0caed7" }, { "file": "remaining-record-audit/artifacts/941/priority-manifest.json", "sha256": "0e94e5e491dbaa12aadd193f872489f25885343207da17cf2962a0d61a23ee3f" } ], "source_head": "8af78333709a2eafd84463a7dc91467be5618b49" } }, { "pr": 942, "title": "Conditional \u03ba = 0.001661960547713947: T37 whole-owner packing and all-T bound", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/942", "author": "jon314159", "created_at": "2026-10-13T13:51:13Z", "accepted_at": "2026-10-13T15:06:48Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661960547713947", "kappa_fraction": "1661960547713947/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "all_PR_implementations": false, "exact_individual_crossing": false, "exact_log2_integer": 94, "input_bits": "2^94", "plot_triple_log": { "exact_log2_integer": 94, "expression": "log2(log2(94))" }, "scope": "Declared own literal complete O(73,2) early/record Gaussian enhancement family. Every active counted source body retains all cover vertices and the actual selected public ADD with no pruning, aggregation, quotienting or bypass; any no-native synthesis returns the identical optimized GMP reference. This is an added comparison-family policy and excludes other historical BIT/original hybrid or compressed implementations.", "source": "data/operation-audit/pr942-finite73-literal-cover-lower.json", "statistic": "necessary_no_strict_win_below_endpoint_for_declared_literal_family", "source_explanation": "Own complete O(73,2) invocation prescription and surviving actual selected U8 ADD, with the independently closed same-reference1875 upper; no coefficient-coordinate multiplier." }, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr942-finite73-literal-cover-range.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "The source exact absolute-phase/normalized-wrapper and whole Gaussian endpoint contracts, together with common-label/mutable-source and all-size unequal-child realization interfaces, remain explicit hypotheses of the fixed comparison protocol.", "Actual selected native scalar/frame columns were replayed; own whole-owner physical windows/charts, padded parent banks and complete numeric invoices were checked afresh. Original full phase engines are not claimed rerun.", "The numeric PLAN is a newly checked source-equivalent realization with identical selected program/owner/order/window/profile semantics. It does not claim historical parent-template or PLAN provenance-string byte identity.", "Completed exact Gaussian children have semantic norm one under the source endpoint interface; own finite literal inequalities fund C0=2^210000 and the full own 512/1024 payload charges.", "Same direct Gaussian/fine-prime/finite-section/boundary/recovery analytic conditions, exact candidate-only Fermat helper, fixed XAG tariff and repaired unlimited optimized-GMP correctness/halting assumptions.", "Declared own literal complete O(73,2) early/record Gaussian enhancement family. Every active counted source body retains all cover vertices and the actual selected public ADD with no pruning, aggregation, quotienting or bypass; any no-native synthesis returns the identical optimized GMP reference. This is an added comparison-family policy and excludes other historical BIT/original hybrid or compressed implementations.", "Declared own literal complete O(73,2) early/record Gaussian enhancement family. Every active counted source body retains all cover vertices and the actual selected public ADD with no pruning, aggregation, quotienting or bypass; any no-native synthesis returns the identical optimized GMP reference. This is an added comparison-family policy and excludes other historical BIT/original hybrid or compressed implementations.", "Full same own counted source body and complete group E; own early and record verified domains both contain a nonempty native H stage above the full stopped base. No optional unrelated original-record hybrid is included." ] }, "cost_status": "conditional_own_source_range", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "historical_selected_or_reviewed_conditional_checkpoint_source", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 113, "source_index": 162, "at": "2026-10-13T13:51:13Z", "until": "2026-10-13T14:59:06Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001661960547713947", "dashboard_float_text": "0.001661960547713947", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/942", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 130, "source_index": null, "at": "2026-10-13T13:51:13Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001661960547713947", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/942", "evidence_excerpt": "This frozen T37 whole-owner construction raises the conditional bound from PR #890's **0.001661957774647029** to **0.001661960547713947**, an absolute gain of **0.000000002773066918**. The gain is tiny; the U8 local word and PR589 bit supplier are unchanged.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 415, "source_index": null, "at": "2026-10-13T13:51:13Z", "until": null, "date_basis": "opening-title", "fraction": "1661960547713947/1000000000000000000", "value_decimal": "0.001661960547713947", "dashboard_float_text": null, "expression": "0.001661960547713947", "historical_title": "Conditional \u03ba = 0.001661960547713947: T37 whole-owner packing and all-T bound", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/942", "evidence_excerpt": "Conditional \u03ba = 0.001661960547713947: T37 whole-owner packing and all-T bound", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "first_listed_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier942.json", "path": "certificates/checkpoints/frontier942.json", "commit": null, "at": null, "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/87db776d70ad1d28a27e9f7906237e5a279414f3/certificates/selected-result.json", "path": null, "commit": "87db776d70ad1d28a27e9f7906237e5a279414f3", "at": "2026-10-13T18:05:11Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "first_listed_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3825dc0ea1317629864ebeb6929719cc4bbf525f/certificates/selected-result.json", "path": null, "commit": "3825dc0ea1317629864ebeb6929719cc4bbf525f", "at": "2026-10-13T15:06:01Z", "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "The source exact absolute-phase/normalized-wrapper and whole Gaussian endpoint contracts, together with common-label/mutable-source and all-size unequal-child realization interfaces, remain explicit hypotheses of the fixed comparison protocol.", "Actual selected native scalar/frame columns were replayed; own whole-owner physical windows/charts, padded parent banks and complete numeric invoices were checked afresh. Original full phase engines are not claimed rerun.", "The numeric PLAN is a newly checked source-equivalent realization with identical selected program/owner/order/window/profile semantics. It does not claim historical parent-template or PLAN provenance-string byte identity.", "Completed exact Gaussian children have semantic norm one under the source endpoint interface; own finite literal inequalities fund C0=2^210000 and the full own 512/1024 payload charges.", "Same direct Gaussian/fine-prime/finite-section/boundary/recovery analytic conditions, exact candidate-only Fermat helper, fixed XAG tariff and repaired unlimited optimized-GMP correctness/halting assumptions.", "Declared own literal complete O(73,2) early/record Gaussian enhancement family. Every active counted source body retains all cover vertices and the actual selected public ADD with no pruning, aggregation, quotienting or bypass; any no-native synthesis returns the identical optimized GMP reference. This is an added comparison-family policy and excludes other historical BIT/original hybrid or compressed implementations.", "Declared own literal complete O(73,2) early/record Gaussian enhancement family. Every active counted source body retains all cover vertices and the actual selected public ADD with no pruning, aggregation, quotienting or bypass; any no-native synthesis returns the identical optimized GMP reference. This is an added comparison-family policy and excludes other historical BIT/original hybrid or compressed implementations.", "Full same own counted source body and complete group E; own early and record verified domains both contain a nonempty native H stage above the full stopped base. No optional unrelated original-record hybrid is included." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr942-finite73-literal-cover-range.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/942/priority-manifest.json", "sha256": "e7c2430a13ba00046052567c3317d63d61802b182f006a219de78aee2e8ebf36" } ], "source_head": "1960cfa919a0945d0ca4cb14ea96237000037903" } }, { "pr": 950, "title": "Tooling: 1.61x faster exact historical central-factor audit (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/950", "author": "RossRichardson", "created_at": "2026-10-13T14:24:06Z", "accepted_at": "2026-10-13T15:06:48Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661957774647029", "kappa_fraction": "1661957774647029/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "supporting_verification_tooling_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/950-manifest.json", "sha256": "4c6074ff7675fe24d8671ccd85e0177d0186f1b8455fe7919cbd3d8294174788" }, { "file": "remaining-record-audit/artifacts/950/priority-manifest.json", "sha256": "57418813b429e18c3f26b36cd1235abd1e2ec085f54eb27060ce4eab762a2008" } ], "source_head": "5bafe2c91e045d10de207b9e5b21630dfebb9cd2" } }, { "pr": 873, "title": "Research construction: shorten R439 phase-B block 508 from 37 to 30 ADDs (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/873", "author": "navinor", "created_at": "2026-10-13T08:48:08Z", "accepted_at": "2026-10-13T15:06:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661634653669567", "kappa_fraction": "1661634653669567/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/r439-block508-schedule/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/r439-block508-schedule/CERTIFICATE.json, research/r439-block508-schedule/EXPECTED.json, research/r439-block508-schedule/README.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/r439-block508-schedule/EXPECTED.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/873-manifest.json", "sha256": "ef58de537b02ff51f9c06f37e17592320879528820c9ac8e5042c7dcc075958c" }, { "file": "remaining-record-audit/artifacts/873/priority-manifest.json", "sha256": "8eccfe4dd8403a140008575f57468b5ede4f3435c509a986b10eab41a689f999" } ], "source_head": "117c48527dd4f066dad103121761154cf1bb39cd" } }, { "pr": 957, "title": "Adversarial audit: frontier890 endpoint certification, reduction and surcharge stakes (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/957", "author": "navinor", "created_at": "2026-10-13T14:38:02Z", "accepted_at": "2026-10-13T15:39:43Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661957774647029", "kappa_fraction": "1661957774647029/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "supporting_endpoint_audit_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 2, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No distinct numerical point should be fabricated for this support artifact. Bind a referenced implementation separately if displaying its inherited cutoff." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/957/priority-manifest.json", "sha256": "ef7b34b2c44a12affe3087a848589e8950662fb7837149bdc700ad8f54f016c3" } ], "source_head": "65c931415587c444a7a1f48939842c4cf0aa0411" } }, { "pr": 960, "title": "Independent verification: PR890 T21 moment brackets via binomial enclosures", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/960", "author": "davidNbreslauer", "created_at": "2026-10-13T14:42:48Z", "accepted_at": "2026-10-13T15:39:43Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661957774647029", "kappa_fraction": "1661957774647029/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "supporting_arithmetic_audit_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "If a cutoff for a referenced earlier construction is sought, separately bind its complete selected program, physical invoice and parameters; no numerical cutoff transfers from this scope audit." ], "source_manifest": [ { "file": "individual-primary-interface-source/960-manifest.json", "sha256": "d3aa27082603dba12c749ff541412b05754ef44dc68451bad3821fd61172152f" }, { "file": "remaining-record-audit/artifacts/960/priority-manifest.json", "sha256": "0e5e3daf119066f6a5b1ed2532de59b6ca57bd9374432baf5b413d198460ed7a" } ], "source_head": "bf87e110106c997392645f76b429ab3cc4410419" } }, { "pr": 917, "title": "Finite construction: two-sided CK compensation saves 8,798 beyond target forests (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/917", "author": "RossRichardson", "created_at": "2026-10-13T12:23:50Z", "accepted_at": "2026-10-13T15:57:09Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661634653669567", "kappa_fraction": "1661634653669567/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/complex-ck-two-sided/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 2 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/complex-ck-two-sided/EXPECTED.json, research/complex-ck-two-sided/PROOF.md, research/complex-ck-two-sided/README.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/917-manifest.json", "sha256": "fd4f754baa389b87ca4760b0ccb99dc053e7302a596ba85dbc552e99c7f87059" }, { "file": "remaining-record-audit/artifacts/917/priority-manifest.json", "sha256": "79497aaf63e7d81f5cb59f73896bd1f91ced445c013bfe2c9449e4f0ec33c09d" } ], "source_head": "085c32a25e2a09b029fa816195b97fa93d6f0788" } }, { "pr": 937, "title": "Finite complex construction: two center shears save 5,562 primitives per invocation (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/937", "author": "RossRichardson", "created_at": "2026-10-13T13:40:37Z", "accepted_at": "2026-10-13T15:57:09Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "4.656612873077392578125E-10", "kappa_fraction": "1/2147483648", "kappa_status": "authenticated_actual_merged_source_selection", "kappa_scope": "The costed \u03ba comes from the explicitly selected source included at this merge. The original parser quote is retained and visibly distinguished. Own actual historical h26 complex construction retains2^-31 in own scripts/audit_complex_centers.py and explicit own historical research note. The preserved contemporary BASE-SELECTED PR799 quote is unrelated context and is not implemented or improved by937.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^1717986918404294967288)", "log2log2_input_bits": "1717986918404294967288", "plot_triple_log": { "exact_log2log2_integer": "1717986918404294967288" }, "source": "data/operation-audit/pr937-historical-two-shear-gaussian-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own historical937 full all-role native circuit, required physical entry/output maps and absolute phases; arbitrary dirty auxiliaries are restored. Finite scalar/frame checks are not a universal operator theorem.", "Own common-label/all-column/whole-call/all-size phase-transfer and normalized Gaussian endpoint contracts, with source nonlinear stopped-depth recurrence at arbitrary fixedtheta.", "New fixed-wiring arbitrary-rank complete-row realization and once-only padding; no free data arithmetic or unbounded descriptors are assumed.", "Exact dyadic augmented-grid native arithmetic, completed Gaussian-integer H return and disjoint complete coefficient blocks with nonlinear convexity are those of the closed global proof, with ownC0/C1 paid in full.", "Concrete normalized accretivity/finite-LDU/FFT/narrow/cyclic convolution/boundary/recovery and repaired optimized-reference correctness/halting remain explicit; the false scale-free general theorem is not imported." ] }, "cost_status": "conditional_own_source_upper_only", "frozen_kappa_metadata": { "kappa_fraction": "1661957774647029/1000000000000000000", "kappa_decimal": "0.001661957774647029", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities." }, "source_selected_kappa_correction": true, "source_selected_kappa_correction_basis": "Own actual historical h26 complex construction retains2^-31 in own scripts/audit_complex_centers.py and explicit own historical research note. The preserved contemporary BASE-SELECTED PR799 quote is unrelated context and is not implemented or improved by937.", "source_kappa_correction_primary_receipt": "data/operation-audit/pr937-finite-source/chronology.json", "own_source_cost_extension": true, "early_effective_kappa": "1/1000000000", "own_source_scope": [ "Own historical937 full all-role native circuit, required physical entry/output maps and absolute phases; arbitrary dirty auxiliaries are restored. Finite scalar/frame checks are not a universal operator theorem.", "Own common-label/all-column/whole-call/all-size phase-transfer and normalized Gaussian endpoint contracts, with source nonlinear stopped-depth recurrence at arbitrary fixedtheta.", "New fixed-wiring arbitrary-rank complete-row realization and once-only padding; no free data arithmetic or unbounded descriptors are assumed.", "Exact dyadic augmented-grid native arithmetic, completed Gaussian-integer H return and disjoint complete coefficient blocks with nonlinear convexity are those of the closed global proof, with ownC0/C1 paid in full.", "Concrete normalized accretivity/finite-LDU/FFT/narrow/cyclic convolution/boundary/recovery and repaired optimized-reference correctness/halting remain explicit; the false scale-free general theorem is not imported." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr937-historical-two-shear-gaussian-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 6, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/937/priority-manifest.json", "sha256": "7cc462dd6bc1027eb3e1085def120c186032cd90556b9b2edc7e736bb2605a04" } ], "source_head": "b303fed6dfe2066dcd78c0d8ed74d2a3b153ba72" } }, { "pr": 945, "title": "Finite construction: joint Horner saves 13,072 PR799 backward primitives (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/945", "author": "RossRichardson", "created_at": "2026-10-13T13:53:44Z", "accepted_at": "2026-10-13T15:57:09Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661957774647029", "kappa_fraction": "1661957774647029/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/x4-joint-horner-seed29/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/x4-joint-horner-seed29/CLAIM.json, research/x4-joint-horner-seed29/EXPECTED.json, research/x4-joint-horner-seed29/PROOF.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/x4-joint-horner-seed29/CLAIM.json, research/x4-joint-horner-seed29/EXPECTED.json, research/x4-joint-horner-seed29/PROOF.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/945-manifest.json", "sha256": "8f9d933405c5f7f07872956d737d75ba0f91d9c2f489f8832933b7d89b1c1832" }, { "file": "remaining-record-audit/artifacts/945/priority-manifest.json", "sha256": "3c119cd6dd4807042604b5f0e0bf31a448ae2c3f1e907fb028603395a7e4140e" } ], "source_head": "a3245bf22fa2a2eb778b11128cbc605b130d737f" } }, { "pr": 947, "title": "Scoped negative result: exact constant-row center shear optimum (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/947", "author": "RossRichardson", "created_at": "2026-10-13T14:15:02Z", "accepted_at": "2026-10-13T15:57:09Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661957774647029", "kappa_fraction": "1661957774647029/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain the actual component/interface/constant improvement with its construction targets. A distinct whole multiplier endpoint requires its own authenticated complete selected native, owner/invoice, recursive, precision and whole-integer implementation; no title or unchanged-kappa exclusion is used." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/947/priority-manifest.json", "sha256": "88cf7e301c1668c7e337fbdbd572b991e09eebe8ec546f57d7318a141027dd87" } ], "source_head": "b6f6418bdcae748b267cea72a5949d551feb7bb2" } }, { "pr": 949, "title": "Scoped negative result: exact 73-primitive factory scale optimum (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/949", "author": "RossRichardson", "created_at": "2026-10-13T14:21:00Z", "accepted_at": "2026-10-13T15:57:09Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661957774647029", "kappa_fraction": "1661957774647029/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/949-manifest.json", "sha256": "e092f1a66765225db597d3f3a11e7b2a4c43390041929a49d6d483c7ea755e8e" }, { "file": "remaining-record-audit/artifacts/949/priority-manifest.json", "sha256": "da55e854963b136004fa087a8fae816dc538dac37dd9ce66fccbc24d640038db" } ], "source_head": "102ddfb47d11c8ad66121350907d4a2cc04cea8c" } }, { "pr": 954, "title": "Scoped negative result: classify E8's first decoder rank drop (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/954", "author": "RossRichardson", "created_at": "2026-10-13T14:28:45Z", "accepted_at": "2026-10-13T15:57:09Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661957774647029", "kappa_fraction": "1661957774647029/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "scoped_obstruction_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/954/priority-manifest.json", "sha256": "551bfcb62e545874bb7032e0613342ba32031bdfda328260c58ec7723bc46b73" } ], "source_head": "a98219aa708e1bd2ae4ca90e720e66569f7f0147" } }, { "pr": 958, "title": "Scoped negative result: five-port quadratic decoder cost ceiling (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/958", "author": "RossRichardson", "created_at": "2026-10-13T14:38:52Z", "accepted_at": "2026-10-13T15:57:09Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661957774647029", "kappa_fraction": "1661957774647029/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "scoped_obstruction_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/958/priority-manifest.json", "sha256": "ee004a24a367c916542497baeae4d24a753b7a54626795605c310ee6d26a26e3" } ], "source_head": "28d68c88f0184835d8c8a7266ab8d0dad3f18a8a" } }, { "pr": 968, "title": "Research: frame-pair decoders and the exact 8-term complex copy-cost floor (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/968", "author": "themilkman216", "created_at": "2026-10-13T15:17:41Z", "accepted_at": "2026-10-13T15:57:09Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661960547713947", "kappa_fraction": "1661960547713947/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "scoped_decoder_bound_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/968-manifest.json", "sha256": "2ed2ca9b568dfecbf21551c4ec094b47a1c8279ab300e5271ce3387fa80ee9dd" }, { "file": "remaining-record-audit/artifacts/968/priority-manifest.json", "sha256": "d8b531d2c38e37aa60b12af8e0e923c2dfd9d6d9569db14a71cb28609a415c52" } ], "source_head": "6a99e7240b961ac5e115ae6aa0301ec7c4a45d77" } }, { "pr": 828, "title": "Research consolidation: reconcile PR279 target-prefix sources and replay", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/828", "author": "mihir-s-05", "created_at": "2026-10-13T06:34:17Z", "accepted_at": "2026-10-13T16:15:01Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.000724098741932703", "kappa_fraction": "724098741932703/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "supporting_reconstruction_requires_target_cost_binding", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "If a cutoff for a referenced earlier construction is sought, separately bind its complete selected program, physical invoice and parameters; no numerical cutoff transfers from this scope audit." ], "source_manifest": [ { "file": "individual-primary-interface-source/828-manifest.json", "sha256": "54a9406384e6c0773f23f6521a8f0eb016b36addc94813877467192e3bb2aeea" }, { "file": "remaining-record-audit/artifacts/828/priority-manifest.json", "sha256": "9607256d93d42139d86a880df31f9461bc1985650af306aa63c0a941ca1893c7" } ], "source_head": "2e43537c0e8ed1c9f9ef21cab0ef9cddb5d79976" } }, { "pr": 930, "title": "Research consolidation: reconcile and replay PR210's parity/fusion update (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/930", "author": "RossRichardson", "created_at": "2026-10-13T13:12:35Z", "accepted_at": "2026-10-13T16:15:01Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.000710069340338651", "kappa_fraction": "710069340338651/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "supporting_reconstruction_requires_target_cost_binding", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 22, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "If a cutoff for a referenced earlier construction is sought, separately bind its complete selected program, physical invoice and parameters; no numerical cutoff transfers from this scope audit." ], "source_manifest": [ { "file": "finite-bridge-source-expansion/930-manifest.json", "sha256": "4c33dacadd46a1de0d972a4b9e4e729067f620f7377ed784aaf20e02ab66d5c7" } ], "source_head": "222fb22c0ae2d13c25674cb8c18d168d8518cef5" } }, { "pr": 943, "title": "Research: sharp four/five-source dirty-connector boundary (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/943", "author": "RossRichardson", "created_at": "2026-10-13T13:51:34Z", "accepted_at": "2026-10-13T16:15:01Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661957774647029", "kappa_fraction": "1661957774647029/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "A numerical whole-multiplier comparison must separately identify an actual complete selected native/caller/owner/recursive work-height-stock interface and precision/analytic/outer realization. This source-scope disposition neither supplies nor transfers that bound, and does not extend a restricted negative result beyond its stated family." ], "source_manifest": [ { "file": "individual-primary-interface-source/943-manifest.json", "sha256": "41bee6549ce34846860ed6a716c4fba8178fe22608ecac94f7839010171452ed" }, { "file": "remaining-record-audit/artifacts/943/priority-manifest.json", "sha256": "269e7084e1011d27749566db170cef5b8c0fbd808994469caa2eace482114f0e" } ], "source_head": "cf360b4b09b7d0419decdd6ac85421fefed55bdd" } }, { "pr": 939, "title": "Scoped negative result: E8 star-copy ratio cannot improve through 55 punctures (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/939", "author": "RossRichardson", "created_at": "2026-10-13T13:43:12Z", "accepted_at": "2026-10-13T17:29:47Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661957774647029", "kappa_fraction": "1661957774647029/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "scoped_obstruction_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/939/priority-manifest.json", "sha256": "875559922362d2d67bf74f3088a4a9546b435da2439e362a223485b4bd14bcc9" } ], "source_head": "3a8ec54d62fb8824c658dc7ed356f99423cac8cf" } }, { "pr": 992, "title": "Research audit: sharp T37 integrality penalties (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/992", "author": "woklerx", "created_at": "2026-10-13T16:07:23Z", "accepted_at": "2026-10-13T17:29:47Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661960547713947", "kappa_fraction": "1661960547713947/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "supporting_relaxation_audit_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "If a cutoff for a referenced earlier construction is sought, separately bind its complete selected program, physical invoice and parameters; no numerical cutoff transfers from this scope audit." ], "source_manifest": [ { "file": "individual-primary-interface-source/992-manifest.json", "sha256": "43b10ea6277bdd269e91122300eb4c587009a011297d2c8a2c50be0ca38ebc83" }, { "file": "remaining-record-audit/artifacts/992/priority-manifest.json", "sha256": "6e8f97cad7daeda145e63b2fba19e1c3bc2d95477265ac32a2ac004ac11f973b" } ], "source_head": "0efdfc28b1eb71c91c012ca1e1945baeeebce7bb" } }, { "pr": 1009, "title": "Audit selected T37 bootstrap depth: six levels suffice and five cannot", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1009", "author": "woklerx", "created_at": "2026-10-13T16:26:22Z", "accepted_at": "2026-10-13T17:29:47Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661960547713947", "kappa_fraction": "1661960547713947/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1009-selected-t37-gaussian-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "The source exact absolute-phase/normalized-wrapper and whole Gaussian endpoint contracts, together with common-label/mutable-source and all-size unequal-child realization interfaces, remain explicit hypotheses of the fixed comparison protocol.", "Actual selected native scalar/frame columns were replayed; own whole-owner physical windows/charts, padded parent banks and complete numeric invoices were checked afresh. Original full phase engines are not claimed rerun.", "The numeric PLAN is a newly checked source-equivalent realization with identical selected program/owner/order/window/profile semantics. It does not claim historical parent-template or PLAN provenance-string byte identity.", "Completed exact Gaussian children have semantic norm one under the source endpoint interface; own finite literal inequalities fund C0=2^210000 and the full own 512/1024 payload charges.", "Same direct Gaussian/fine-prime/finite-section/boundary/recovery analytic conditions, exact candidate-only Fermat helper, fixed XAG tariff and repaired unlimited optimized-GMP correctness/halting assumptions.", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "This new direct Gaussian/Fermat realization uses the exact own explicitly selected942 T37 core. It does not execute or quantify the original six-/seven-level affine bootstrap algorithm; no cost benefit of the source bootstrap-depth improvement is inferred.", "Exact identity imports the named native/owner/invoice component only; own source arithmetic replay scope remains as recorded, with no new full native/phase or876-source verifier execution." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "The source exact absolute-phase/normalized-wrapper and whole Gaussian endpoint contracts, together with common-label/mutable-source and all-size unequal-child realization interfaces, remain explicit hypotheses of the fixed comparison protocol.", "Actual selected native scalar/frame columns were replayed; own whole-owner physical windows/charts, padded parent banks and complete numeric invoices were checked afresh. Original full phase engines are not claimed rerun.", "The numeric PLAN is a newly checked source-equivalent realization with identical selected program/owner/order/window/profile semantics. It does not claim historical parent-template or PLAN provenance-string byte identity.", "Completed exact Gaussian children have semantic norm one under the source endpoint interface; own finite literal inequalities fund C0=2^210000 and the full own 512/1024 payload charges.", "Same direct Gaussian/fine-prime/finite-section/boundary/recovery analytic conditions, exact candidate-only Fermat helper, fixed XAG tariff and repaired unlimited optimized-GMP correctness/halting assumptions.", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "This new direct Gaussian/Fermat realization uses the exact own explicitly selected942 T37 core. It does not execute or quantify the original six-/seven-level affine bootstrap algorithm; no cost benefit of the source bootstrap-depth improvement is inferred.", "Exact identity imports the named native/owner/invoice component only; own source arithmetic replay scope remains as recorded, with no new full native/phase or876-source verifier execution." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1009-selected-t37-gaussian-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/1009-manifest.json", "sha256": "6c709b69bf238e54abac132208b836b1b6af7caa380bdfd66762296708626ce7" }, { "file": "remaining-record-audit/artifacts/1009/priority-manifest.json", "sha256": "41384ee58de86b78b43d6aec48a258522dd0049ed9a167fa33653c0f4a8f1ccd" } ], "source_head": "4740dc74a2ee2fb7aeaa0e0013cf8f997558d101" } }, { "pr": 1001, "title": "Finite bit construction: R439 frame 506 uses 21 ADDs (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1001", "author": "ToikY", "created_at": "2026-10-13T16:17:27Z", "accepted_at": "2026-10-13T17:33:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661960547713947", "kappa_fraction": "1661960547713947/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/r439-frame506-two-factor/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/r439-frame506-two-factor/CERTIFICATE.json, research/r439-frame506-two-factor/CLAIM.json, research/r439-frame506-two-factor/NATIVE.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/r439-frame506-two-factor/CERTIFICATE.json#/candidate/invoice and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/1001-manifest.json", "sha256": "5407c5cd20a79880abb2c2c5e7e2562c987335029e6f330cab6a923aaa3b3cce" }, { "file": "remaining-record-audit/artifacts/1001/priority-manifest.json", "sha256": "470fd6581994e588d278c0a918d54707fec3f6b7b0b35f1398cb00393fbddd2d" } ], "source_head": "fbf54e6c95c47a3891eb7e8ed063b5198e920f3f" } }, { "pr": 1004, "title": "Conditional \u03ba = 0.001664233607446043: mutable-leaver all-K cells, U8 hybrids and frame re-optimisation on PR799's word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1004", "author": "jeremykothe2", "created_at": "2026-10-13T16:20:01Z", "accepted_at": "2026-10-13T18:05:23Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001664233607446043", "kappa_fraction": "1664233607446043/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 115, "source_index": 165, "at": "2026-10-13T16:20:01Z", "until": "2026-10-13T16:20:33Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001664233607446043", "dashboard_float_text": "0.001664233607446043", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1004", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 132, "source_index": null, "at": "2026-10-13T16:20:01Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001664233607446043", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1004", "evidence_excerpt": "Conditional \u03ba = **0.001664233607446043** (conservative 0.001664233604589014). That is +2.27\u00d710\u207b\u2076 over the merged #942 (0.001661960547713947) and +2.28\u00d710\u207b\u2076 over our #870. The complex side binds; PR589's bit supplier is unchanged.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 418, "source_index": null, "at": "2026-10-13T16:20:01Z", "until": null, "date_basis": "body-version", "fraction": "1664233607446043/1000000000000000000", "value_decimal": "0.001664233607446043", "dashboard_float_text": null, "expression": "0.001664233607446043", "historical_title": "Conditional \u03ba = 0.001664233607446043: mutable-leaver all-K cells, U8 hybrids and frame re-optimisation on PR799's word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1004", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001664233607446043 (conservative 0.001664233604589014). That is +2.27*10^-6 over the merged #942 (0.001661960547713947) and +2.28*10^-6 over our #870. The complex side binds; PR589's bit supplier is", "automated_comparable": true, "body_sha256": "180b71e918805211a3679ec435444ec0aa8a437f2c7d1c74aa4d9dd6e51a225c" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/87db776d70ad1d28a27e9f7906237e5a279414f3/certificates/selected-result.json", "path": null, "commit": "87db776d70ad1d28a27e9f7906237e5a279414f3", "at": "2026-10-13T18:05:11Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_selected_full_program_bytes_missing; gauge44; required full program 7c463c53c0bf883a84f3d1df691a01c32b8c415ca3380fce809b48957d009478; both orientations {\"backward\": \"b8de98f996a99fdc477c126faba7f7e47297679f313e8a831d5ea9dda3de3260\", \"forward\": \"e4ee794f189c84c473cf48df8a9ff198feefa0940dbcbf99163a8e9118c9176c\"}; Recover exact actual complete selected program bytes, by own immutable primary source or deterministic pinned constructor/recipe with mandatory complete semantic and orientation commitments. A matching profile, scalar saving or another provider does not fill this gap. Missing canonical catalogue may remain a separately stated endpoint premise only after the actual selected program and complete own physical/invoice are bound." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1004/priority-manifest.json", "sha256": "4ba01e4cd800c5c517b0c45ab5ea0f5287254f04469a36c3377178ccea4c54c9" } ], "source_head": "1974578f82a30158dd5fcdcdf226b83df8e7196f" } }, { "pr": 1005, "title": "Conditional \u03ba = 0.001671387264390146: all eight mutable-leaver all-K cells, U8 hybrids and frame re-optimisation on PR799's word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1005", "author": "jeremykothe2", "created_at": "2026-10-13T16:20:33Z", "accepted_at": "2026-10-13T18:05:23Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001671387264390146", "kappa_fraction": "835693632195073/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 116, "source_index": 166, "at": "2026-10-13T16:20:33Z", "until": "2026-10-13T16:38:58Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001671387264390146", "dashboard_float_text": "0.001671387264390146", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1005", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 133, "source_index": null, "at": "2026-10-13T16:20:33Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001671387264390146", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1005", "evidence_excerpt": "Conditional \u03ba = **0.001671387264390146** (conservative 0.001671387261540186). That is +9.43\u00d710\u207b\u2076 over the merged #942 (0.001661960547713947) and +7.15\u00d710\u207b\u2076 over #1004. The complex side binds; PR589's bit supplier is unchanged.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 419, "source_index": null, "at": "2026-10-13T16:20:33Z", "until": null, "date_basis": "opening-title", "fraction": "835693632195073/500000000000000000", "value_decimal": "0.001671387264390146", "dashboard_float_text": null, "expression": "0.001671387264390146", "historical_title": "Conditional \u03ba = 0.001671387264390146: all eight mutable-leaver all-K cells, U8 hybrids and frame re-optimisation on PR799's word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1005", "evidence_excerpt": "Conditional \u03ba = 0.001671387264390146: all eight mutable-leaver all-K cells, U8 hybrids and frame re-optimisation on PR799's word", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/87db776d70ad1d28a27e9f7906237e5a279414f3/certificates/selected-result.json", "path": null, "commit": "87db776d70ad1d28a27e9f7906237e5a279414f3", "at": "2026-10-13T18:05:11Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_selected_full_program_bytes_missing; gauge44; required full program ad9ce1708474b8b4790b8a1908b47fde0e182d319b3baac4180dd6d928bcfab5; both orientations {\"backward\": \"2d184e4d9d48aa4d5e3679368ee0eca7e0388b1966eb05e0fd17d22d00d36293\", \"forward\": \"683f83231d4d4890a7fc3d18f30d4ac7bfbd7bbdf4e7ff57ad0eb09e8a5f571c\"}; Recover exact actual complete selected program bytes, by own immutable primary source or deterministic pinned constructor/recipe with mandatory complete semantic and orientation commitments. A matching profile, scalar saving or another provider does not fill this gap. Missing canonical catalogue may remain a separately stated endpoint premise only after the actual selected program and complete own physical/invoice are bound." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1005/priority-manifest.json", "sha256": "9d33c9bf8549e114a3dcadcedf9b2158c1d85f97fbc873a88256974b987ce5fe" } ], "source_head": "779e80aef469bc3a28b19f1adde199871a9a22e3" } }, { "pr": 1018, "title": "Conditional \u03ba = 0.00167166528321877: seven triangle-hybrid slots (PR987 search) on the k8 leaver word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1018", "author": "jeremykothe2", "created_at": "2026-10-13T16:38:58Z", "accepted_at": "2026-10-13T18:05:23Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00167166528321877", "kappa_fraction": "167166528321877/100000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1018-dispatched-finite-controller-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 117, "source_index": 167, "at": "2026-10-13T16:38:58Z", "until": "2026-10-13T16:39:06Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.00167166528321877", "dashboard_float_text": "0.00167166528321877", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1018", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 134, "source_index": null, "at": "2026-10-13T16:38:58Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00167166528321877", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1018", "evidence_excerpt": "Conditional \u03ba = **0.00167166528321877**. That is +2.78\u00d710\u207b\u2077 over #1005 (0.001671387264390146) and +9.70\u00d710\u207b\u2076 over the merged #942. The complex side binds; PR589's bit supplier is unchanged.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 420, "source_index": null, "at": "2026-10-13T16:38:58Z", "until": null, "date_basis": "body-version", "fraction": "167166528321877/100000000000000000", "value_decimal": "0.00167166528321877", "dashboard_float_text": null, "expression": "0.00167166528321877", "historical_title": "Conditional \u03ba = 0.00167166528321877: seven triangle-hybrid slots (PR987 search) on the k8 leaver word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1018", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.00167166528321877. That is +2.78*10^-7 over #1005 (0.001671387264390146) and +9.70*10^-6 over the merged #942. The complex side binds; PR589's bit supplier is unchanged.\n\nChange: seven more triangl", "automated_comparable": true, "body_sha256": "36fa48c346c4eb86edc10ae8031a7418edf9a15ddcbc289b572888331e38dd15" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/87db776d70ad1d28a27e9f7906237e5a279414f3/certificates/selected-result.json", "path": null, "commit": "87db776d70ad1d28a27e9f7906237e5a279414f3", "at": "2026-10-13T18:05:11Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1018-dispatched-finite-controller-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 7, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1018/priority-manifest.json", "sha256": "1184d584002296f58a3d289e30585b1e6e5463c69a83ab76f48b1b9e081f156d" } ], "source_head": "eac7547cb191f875d5f5ea5f9bbb1d2b8c51c4ef" } }, { "pr": 1019, "title": "Conditional \u03ba = 0.001661960547713947858091 by exact T37 grid refinement", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1019", "author": "1337isnot1337", "created_at": "2026-10-13T16:39:06Z", "accepted_at": "2026-10-13T18:05:23Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661960547713947858091", "kappa_fraction": "1661960547713947858091/1000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1019-selected-t37-gaussian-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "The source exact absolute-phase/normalized-wrapper and whole Gaussian endpoint contracts, together with common-label/mutable-source and all-size unequal-child realization interfaces, remain explicit hypotheses of the fixed comparison protocol.", "Actual selected native scalar/frame columns were replayed; own whole-owner physical windows/charts, padded parent banks and complete numeric invoices were checked afresh. Original full phase engines are not claimed rerun.", "The numeric PLAN is a newly checked source-equivalent realization with identical selected program/owner/order/window/profile semantics. It does not claim historical parent-template or PLAN provenance-string byte identity.", "Completed exact Gaussian children have semantic norm one under the source endpoint interface; own finite literal inequalities fund C0=2^210000 and the full own 512/1024 payload charges.", "Same direct Gaussian/fine-prime/finite-section/boundary/recovery analytic conditions, exact candidate-only Fermat helper, fixed XAG tariff and repaired unlimited optimized-GMP correctness/halting assumptions.", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "This new direct Gaussian/Fermat realization uses the exact own explicitly selected942 T37 core. It does not execute or quantify the original six-/seven-level affine bootstrap algorithm; no cost benefit of the source bootstrap-depth improvement is inferred.", "Exact identity imports the named native/owner/invoice component only; own source arithmetic replay scope remains as recorded, with no new full native/phase or876-source verifier execution." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "The source exact absolute-phase/normalized-wrapper and whole Gaussian endpoint contracts, together with common-label/mutable-source and all-size unequal-child realization interfaces, remain explicit hypotheses of the fixed comparison protocol.", "Actual selected native scalar/frame columns were replayed; own whole-owner physical windows/charts, padded parent banks and complete numeric invoices were checked afresh. Original full phase engines are not claimed rerun.", "The numeric PLAN is a newly checked source-equivalent realization with identical selected program/owner/order/window/profile semantics. It does not claim historical parent-template or PLAN provenance-string byte identity.", "Completed exact Gaussian children have semantic norm one under the source endpoint interface; own finite literal inequalities fund C0=2^210000 and the full own 512/1024 payload charges.", "Same direct Gaussian/fine-prime/finite-section/boundary/recovery analytic conditions, exact candidate-only Fermat helper, fixed XAG tariff and repaired unlimited optimized-GMP correctness/halting assumptions.", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "This new direct Gaussian/Fermat realization uses the exact own explicitly selected942 T37 core. It does not execute or quantify the original six-/seven-level affine bootstrap algorithm; no cost benefit of the source bootstrap-depth improvement is inferred.", "Exact identity imports the named native/owner/invoice component only; own source arithmetic replay scope remains as recorded, with no new full native/phase or876-source verifier execution." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1019-selected-t37-gaussian-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 7, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/1019-manifest.json", "sha256": "3b3147885c9cd4cae483c804dd0a93f018305052ae970e6d7dbf6bf745455ab7" }, { "file": "remaining-record-audit/artifacts/1019/priority-manifest.json", "sha256": "ca72ccf0699ad198b038ff5b8d767f690adac79a7979ccf3755ece5ef1d529f1" } ], "source_head": "eff657644137971f6e31ac3c825950c770471349" } }, { "pr": 1022, "title": "Conditional \u03ba = 0.001672081255752945: sixteen-replica owner controller on the seven-slot k8 word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1022", "author": "jeremykothe2", "created_at": "2026-10-13T16:48:43Z", "accepted_at": "2026-10-13T18:05:23Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672081255752945", "kappa_fraction": "334416251150589/200000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1022-recovered-t16-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 118, "source_index": 169, "at": "2026-10-13T16:48:43Z", "until": "2026-10-13T16:56:23Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001672081255752945", "dashboard_float_text": "0.001672081255752945", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1022", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 135, "source_index": null, "at": "2026-10-13T16:48:43Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001672081255752945", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1022", "evidence_excerpt": "Conditional \u03ba = **0.001672081255752945** (conservative 0.001672081252901961). That is +4.16\u00d710\u207b\u2077 over #1018 (0.00167166528321877). The complex side binds; PR589's bit supplier is unchanged.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 421, "source_index": null, "at": "2026-10-13T16:48:43Z", "until": null, "date_basis": "body-version", "fraction": "334416251150589/200000000000000000", "value_decimal": "0.001672081255752945", "dashboard_float_text": null, "expression": "0.001672081255752945", "historical_title": "Conditional \u03ba = 0.001672081255752945: sixteen-replica owner controller on the seven-slot k8 word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1022", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001672081255752945 (conservative 0.001672081252901961). That is +4.16*10^-7 over #1018 (0.00167166528321877). The complex side binds; PR589's bit supplier is unchanged.\n\nChange: FanPUYen's #858 sixt", "automated_comparable": true, "body_sha256": "daf36cfdb9fcf9df0f52520912d5eb97d122233aa7c107e117de5f0b4ef4b526" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/87db776d70ad1d28a27e9f7906237e5a279414f3/certificates/selected-result.json", "path": null, "commit": "87db776d70ad1d28a27e9f7906237e5a279414f3", "at": "2026-10-13T18:05:11Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1022-recovered-t16-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1022/priority-manifest.json", "sha256": "7b5a7b78b9d2d12322815b3c31abdf003444481ad7ec43c12cead2660caf73c2" } ], "source_head": "58618bcbfe88a252467755fc283c04c3db5ca4fd" } }, { "pr": 1028, "title": "Conditional \u03ba = 0.001672166670891177: improved T16 owner packing on the seven-slot k8 word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1028", "author": "jeremykothe2", "created_at": "2026-10-13T16:56:23Z", "accepted_at": "2026-10-13T18:05:23Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672166670891177", "kappa_fraction": "1672166670891177/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1028-recovered-t16-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 119, "source_index": 170, "at": "2026-10-13T16:56:23Z", "until": "2026-10-13T16:57:42Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001672166670891177", "dashboard_float_text": "0.001672166670891177", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1028", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 136, "source_index": null, "at": "2026-10-13T16:56:23Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001672166670891177", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1028", "evidence_excerpt": "Conditional \u03ba = **0.001672166670891177**, +8.54\u00d710\u207b\u2078 over #1022 (0.001672081255752945). It uses the same construction and code as #1022; only the T16 owner map changes (an exact LNS repack on the actual T16 windows). The files that differ from #1022 are `data/{OWNERS,PLAN,SPEC}`, README, RESULT and MANIFEST.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 422, "source_index": null, "at": "2026-10-13T16:56:23Z", "until": null, "date_basis": "body-version", "fraction": "1672166670891177/1000000000000000000", "value_decimal": "0.001672166670891177", "dashboard_float_text": null, "expression": "0.001672166670891177", "historical_title": "Conditional \u03ba = 0.001672166670891177: improved T16 owner packing on the seven-slot k8 word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1028", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001672166670891177, +8.54*10^-8 over #1022 (0.001672081255752945). It uses the same construction and code as #1022; only the T16 owner map changes (an exact LNS repack on the actual T16 windows). Th", "automated_comparable": true, "body_sha256": "9c46bffbc98b7690c34646bb44f28c3b7e790c6eca6d5dfe23f3d4c185e82423" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/87db776d70ad1d28a27e9f7906237e5a279414f3/certificates/selected-result.json", "path": null, "commit": "87db776d70ad1d28a27e9f7906237e5a279414f3", "at": "2026-10-13T18:05:11Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1028-recovered-t16-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1028/priority-manifest.json", "sha256": "d083ca4ac053f175ecfc9214dfd2fcfa2fdb4bcf857ef3f3d0341d0c5e5ef156" } ], "source_head": "be4bd89cb4483dcee43257200cd27601f938f13d" } }, { "pr": 1030, "title": "Conditional \u03ba = 0.00166202617947539: U8 with two rank-seven helper ends", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1030", "author": "AlexS-scale", "created_at": "2026-10-13T16:57:42Z", "accepted_at": "2026-10-13T18:05:23Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00166202617947539", "kappa_fraction": "166202617947539/100000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/complex-rank7-end-pair/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Recompute the complete own productive/paid histogram from research/complex-rank7-end-pair/SEARCH.json#/packing_search and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/complex-rank7-end-pair/data/EXPECTED.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/1030-manifest.json", "sha256": "0c79176c83f50179c1a366b2c6af722c0b7619473d8ab78a1f40b2947aeba983" }, { "file": "remaining-record-audit/artifacts/1030/priority-manifest.json", "sha256": "452d7f04a6e03fb1029897c04cde9bd02f5be647761210df018466c88080f10a" } ], "source_head": "d71857cd0ae7824e935aac17327e4ec27f66322b" } }, { "pr": 1031, "title": "Conditional \u03ba = 0.001672167430672016: improved T16 owner packing on the seven-slot k8 word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1031", "author": "jeremykothe2", "created_at": "2026-10-13T16:58:06Z", "accepted_at": "2026-10-13T18:05:23Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672167430672016", "kappa_fraction": "104510464417001/62500000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1031-recovered-t16-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 120, "source_index": 172, "at": "2026-10-13T16:58:06Z", "until": "2026-10-13T17:07:01Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001672167430672016", "dashboard_float_text": "0.001672167430672016", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1031", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 137, "source_index": null, "at": "2026-10-13T16:58:06Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001672167430672016", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1031", "evidence_excerpt": "Conditional \u03ba = **0.001672167430672016**, +7.6\u00d710\u207b\u00b9\u2070 over #1028 (0.001672166670891177). Same construction and code as #1022/#1028; only the T16 owner map changes (exact LNS repack). Differs from #1028 only in `data/{OWNERS,PLAN,SPEC}`, README, RESULT and MANIFEST.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 423, "source_index": null, "at": "2026-10-13T16:58:06Z", "until": null, "date_basis": "body-version", "fraction": "104510464417001/62500000000000000", "value_decimal": "0.001672167430672016", "dashboard_float_text": null, "expression": "0.001672167430672016", "historical_title": "Conditional \u03ba = 0.001672167430672016: improved T16 owner packing on the seven-slot k8 word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1031", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001672167430672016, +7.6*10^-10 over #1028 (0.001672166670891177). Same construction and code as #1022/#1028; only the T16 owner map changes (exact LNS repack). Differs from #1028 only in data/{OWNE", "automated_comparable": true, "body_sha256": "d0387536cbdd78b1ad0fe5af84a246dcf24a33cec769c9e17f907d95366b6c3f" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/87db776d70ad1d28a27e9f7906237e5a279414f3/certificates/selected-result.json", "path": null, "commit": "87db776d70ad1d28a27e9f7906237e5a279414f3", "at": "2026-10-13T18:05:11Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1031-recovered-t16-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1031/priority-manifest.json", "sha256": "d3d30f54d62693282fd91f1ee6ca1e6c11898e90c40c5b668081bdb178b4cd74" } ], "source_head": "e900534f0beda892c726723524203b97471fb9a3" } }, { "pr": 991, "title": "Independent T37 schedule and targeted payload/binding verification (same \u03ba as #942)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/991", "author": "tekuuu", "created_at": "2026-10-13T16:06:46Z", "accepted_at": "2026-10-13T18:05:24Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661960547713947", "kappa_fraction": "1661960547713947/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr991-generated-U8-t37-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr991-generated-U8-t37-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/991/priority-manifest.json", "sha256": "19057b14824a43aae491847b1b4236d8d6307d3d9887e45a3b495ac15662565e" } ], "source_head": "69f989511a3f0c6f7a26da1c1608b265fbb1668a" } }, { "pr": 1042, "title": "Conditional \u03ba = 0.001672188119205421: improved T16 owner packing on the seven-slot k8 word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1042", "author": "jeremykothe2", "created_at": "2026-10-13T17:07:01Z", "accepted_at": "2026-10-13T18:05:24Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672188119205421", "kappa_fraction": "1672188119205421/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1042-r480-finite-controller-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own exact arbitrary-input phase/normalized-wrapper, common-label/mutable-source and all-size unequal-child realization interfaces remain explicit fixed-protocol hypotheses.", "Exact earlier own-SPEC canonical/program hashes are recovered from a later archive; only identical earlier selected bytes are reused. No later owner/profile or rank supplier is substituted.", "All704 native scalar input columns, private clears, actual wrapper sweeps, dyadic Horner/prefix counts and each own whole T16 role/window/chart/profile were freshly checked; no full phase or Lean replay is claimed.", "The parent numeric realization uses an independently window-matched primary geometry fixture and source direct-sum lift. Own historical PLAN, call order, windows, profile and owner bytes are bound; historical parent provenance metadata byte identity is not claimed.", "Completed Gaussian children have semantic norm one under the endpoint contract. Own finite router/literal/C0 inequalities,512-bit payload and16469 row allowance fund the typed precision interface.", "Same direct Gaussian/fine-prime/finite-section/boundary/recovery analytic contracts, exact candidate-only Fermat helper and repaired unlimited optimized-GMP correctness/halting assumptions." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "historical_selected_or_reviewed_conditional_checkpoint_source", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 121, "source_index": 173, "at": "2026-10-13T17:07:01Z", "until": "2026-10-13T17:13:22Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001672188119205421", "dashboard_float_text": "0.001672188119205421", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1042", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 138, "source_index": null, "at": "2026-10-13T17:07:01Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001672188119205421", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1042", "evidence_excerpt": "Conditional \u03ba = **0.001672188119205421**. Same construction and code as #1022; only the T16 owner map changes (exact LNS repack). Differs from the previous record only in `data/{OWNERS,PLAN,SPEC}`, README, RESULT and MANIFEST.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 424, "source_index": null, "at": "2026-10-13T17:07:01Z", "until": null, "date_basis": "body-version", "fraction": "1672188119205421/1000000000000000000", "value_decimal": "0.001672188119205421", "dashboard_float_text": null, "expression": "0.001672188119205421", "historical_title": "Conditional \u03ba = 0.001672188119205421: improved T16 owner packing on the seven-slot k8 word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1042", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001672188119205421. Same construction and code as #1022; only the T16 owner map changes (exact LNS repack). Differs from the previous record only in data/{OWNERS,PLAN,SPEC}, README, RESULT and MANIF", "automated_comparable": true, "body_sha256": "1498016217f4e40ab79290a2af99c922cecd67b814f0598154f22d23c74cd74b" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "first_listed_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "first_listed_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/87db776d70ad1d28a27e9f7906237e5a279414f3/certificates/selected-result.json", "path": null, "commit": "87db776d70ad1d28a27e9f7906237e5a279414f3", "at": "2026-10-13T18:05:11Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own exact arbitrary-input phase/normalized-wrapper, common-label/mutable-source and all-size unequal-child realization interfaces remain explicit fixed-protocol hypotheses.", "Exact earlier own-SPEC canonical/program hashes are recovered from a later archive; only identical earlier selected bytes are reused. No later owner/profile or rank supplier is substituted.", "All704 native scalar input columns, private clears, actual wrapper sweeps, dyadic Horner/prefix counts and each own whole T16 role/window/chart/profile were freshly checked; no full phase or Lean replay is claimed.", "The parent numeric realization uses an independently window-matched primary geometry fixture and source direct-sum lift. Own historical PLAN, call order, windows, profile and owner bytes are bound; historical parent provenance metadata byte identity is not claimed.", "Completed Gaussian children have semantic norm one under the endpoint contract. Own finite router/literal/C0 inequalities,512-bit payload and16469 row allowance fund the typed precision interface.", "Same direct Gaussian/fine-prime/finite-section/boundary/recovery analytic contracts, exact candidate-only Fermat helper and repaired unlimited optimized-GMP correctness/halting assumptions." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1042-r480-finite-controller-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1042/priority-manifest.json", "sha256": "5a4d55bafb7486122cf8569c8b3b18d4b736dccaddb2f5cbf5f8a90760ee814f" } ], "source_head": "7e8ef087c02a77038a28a337a7ee3a77039cac0d" } }, { "pr": 1074, "title": "Conditional \u03ba = 0.001672651218919025: improved T16 owner packing on the seven-slot k8 word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1074", "author": "jeremykothe2", "created_at": "2026-10-13T17:42:58Z", "accepted_at": "2026-10-13T18:47:07Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672651218919025", "kappa_fraction": "66906048756761/40000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1074-recovered-t16-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 129, "source_index": 183, "at": "2026-10-13T17:42:58Z", "until": "2026-10-13T17:49:04Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001672651218919025", "dashboard_float_text": "0.001672651218919025", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1074", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 146, "source_index": null, "at": "2026-10-13T17:42:58Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001672651218919025", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1074", "evidence_excerpt": "Conditional \u03ba = **0.001672651218919025**. Same construction and code as #1022; only the T16 owner map changes (exact LNS repack). Differs from the previous record only in `data/{OWNERS,PLAN,SPEC}`, README, RESULT and MANIFEST.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 432, "source_index": null, "at": "2026-10-13T17:42:58Z", "until": null, "date_basis": "body-version", "fraction": "66906048756761/40000000000000000", "value_decimal": "0.001672651218919025", "dashboard_float_text": null, "expression": "0.001672651218919025", "historical_title": "Conditional \u03ba = 0.001672651218919025: improved T16 owner packing on the seven-slot k8 word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1074", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001672651218919025. Same construction and code as #1022; only the T16 owner map changes (exact LNS repack). Differs from the previous record only in data/{OWNERS,PLAN,SPEC}, README, RESULT and MANIF", "automated_comparable": true, "body_sha256": "b7c6295f77c2d5cdc01b81ed0c708f456151579726e3b4acbcbe444968e6517e" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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A twelve-bin whole-helper repacking moves idle ranks 2 and 3 into a rank-5 remainder while preserving the scalar word, role wid", "automated_comparable": true, "body_sha256": "d041fe7cc611493d8eaf43cf568c33bec35fa023c593195a95f5c26567bbb9a4" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1082-dispatched-finite-controller-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 4, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1082/priority-manifest.json", "sha256": "e3fc0ca617632882303d5af05071a223aff5ce9fe14bd119ee9edb55f29432f9" } ], "source_head": "0c2e294ec204e83846d27344f829d15ed9ee7cc6" } }, { "pr": 1087, "title": "Conditional \u03ba = 0.001672654541898561: improved T16 owner packing on the seven-slot k8 word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1087", "author": "jeremykothe2", "created_at": "2026-10-13T17:53:01Z", "accepted_at": "2026-10-13T18:47:07Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672654541898561", "kappa_fraction": "1672654541898561/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1087-recovered-t16-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 131, "source_index": 185, "at": "2026-10-13T17:53:01Z", "until": "2026-10-13T17:55:47Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001672654541898561", "dashboard_float_text": "0.001672654541898561", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1087", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 148, "source_index": null, "at": "2026-10-13T17:53:01Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001672654541898561", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1087", "evidence_excerpt": "Conditional \u03ba = **0.001672654541898561**. Same construction and code as #1022; only the T16 owner map changes (exact LNS repack). Differs from the previous record only in `data/{OWNERS,PLAN,SPEC}`, README, RESULT and MANIFEST.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 434, "source_index": null, "at": "2026-10-13T17:53:01Z", "until": null, "date_basis": "body-version", "fraction": "1672654541898561/1000000000000000000", "value_decimal": "0.001672654541898561", "dashboard_float_text": null, "expression": "0.001672654541898561", "historical_title": "Conditional \u03ba = 0.001672654541898561: improved T16 owner packing on the seven-slot k8 word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1087", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001672654541898561. Same construction and code as #1022; only the T16 owner map changes (exact LNS repack). Differs from the previous record only in data/{OWNERS,PLAN,SPEC}, README, RESULT and MANIF", "automated_comparable": true, "body_sha256": "84caef900926a9f7cabd4890d55257e3615cc1d40a009affd2aae04f994b64d8" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1087-recovered-t16-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1087/priority-manifest.json", "sha256": "d2a5bb5f4a2306a256ca6a307aeb3bd1a7b17b0c15a3c45e98fcddd55bd60a55" } ], "source_head": "589d1cedf5ef5f231182f4ec86408616311a8af0" } }, { "pr": 1088, "title": "Research: exact weighted optimum for signed 3x3 connector repairs (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1088", "author": "martinxxx9", "created_at": "2026-10-13T17:55:12Z", "accepted_at": "2026-10-13T18:47:07Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661960547713947", "kappa_fraction": "1661960547713947/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "A numerical whole-multiplier comparison must separately identify an actual complete selected native/caller/owner/recursive work-height-stock interface and precision/analytic/outer realization. This source-scope disposition neither supplies nor transfers that bound, and does not extend a restricted negative result beyond its stated family." ], "source_manifest": [ { "file": "individual-primary-interface-source/1088-manifest.json", "sha256": "e0c199ede84a70f0d418a9adb924e518aed91aafedfeb52a89c945053873f5e2" }, { "file": "remaining-record-audit/artifacts/1088/priority-manifest.json", "sha256": "1a79edf550d2f116d2103c5a0c82c6e0bb9dad87588ae522f14f9c19d6ef3f40" } ], "source_head": "b0396aad724fec58630fbd4d13a809c562f18d9e" } }, { "pr": 1090, "title": "Conditional \u03ba = 0.001672404744903063: rank-seven helper ends on the k8 word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1090", "author": "1337isnot1337", "created_at": "2026-10-13T17:55:47Z", "accepted_at": "2026-10-13T18:47:07Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672404744903063", "kappa_fraction": "1672404744903063/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/k8-rank7-composition/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/k8-rank7-composition/CERTIFICATE.json, research/k8-rank7-composition/CLAIM.json, research/k8-rank7-composition/MANIFEST.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/k8-rank7-composition/CERTIFICATE.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/k8-rank7-composition/CERTIFICATE.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/1090-manifest.json", "sha256": "9fa09ed6d611153a933774d047093acc0e638ee53f371f3b0eca6db73004e782" }, { "file": "remaining-record-audit/artifacts/1090/priority-manifest.json", "sha256": "dd12a82230f05181eadb1137ef8d91b09b40643a4ae20b64d4dbdd60c3a1468a" } ], "source_head": "b535975a5948afafda984e73c301183a634ff8c8" } }, { "pr": 1091, "title": "Research audit: independent owner-map check of all 15 open T16 claims on the seven-slot k8 word (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1091", "author": "JosieElliston", "created_at": "2026-10-13T17:57:50Z", "accepted_at": "2026-10-13T18:47:07Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672", "kappa_fraction": "209/125000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1091/priority-manifest.json", "sha256": "70c739c319c8c434e9685c4d6dbd51384efd997d220c686a45ed456102389253" } ], "source_head": "b4c13a228acb80f74c682b7097f0ce9bbf51bc4e" } }, { "pr": 1094, "title": "Conditional kappa 0.001672660197076918: rare-pattern T16 exchanges", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1094", "author": "rohanarun", "created_at": "2026-10-13T18:00:40Z", "accepted_at": "2026-10-13T18:47:07Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1094-r480-finite-controller-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own exact arbitrary-input phase/normalized-wrapper, common-label/mutable-source and all-size unequal-child realization interfaces remain explicit fixed-protocol hypotheses.", "Exact earlier own-SPEC canonical/program hashes are recovered from a later archive; only identical earlier selected bytes are reused. No later owner/profile or rank supplier is substituted.", "All704 native scalar input columns, private clears, actual wrapper sweeps, dyadic Horner/prefix counts and each own whole T16 role/window/chart/profile were freshly checked; no full phase or Lean replay is claimed.", "The parent numeric realization uses an independently window-matched primary geometry fixture and source direct-sum lift. Own historical PLAN, call order, windows, profile and owner bytes are bound; historical parent provenance metadata byte identity is not claimed.", "Completed Gaussian children have semantic norm one under the endpoint contract. Own finite router/literal/C0 inequalities,512-bit payload and16469 row allowance fund the typed precision interface.", "Same direct Gaussian/fine-prime/finite-section/boundary/recovery analytic contracts, exact candidate-only Fermat helper and repaired unlimited optimized-GMP correctness/halting assumptions." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "historical_selected_or_reviewed_conditional_checkpoint_source", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 132, "source_index": 187, "at": "2026-10-13T18:05:04.741306Z", "until": "2026-10-13T18:15:35Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001672660197076918", "dashboard_float_text": "0.001672660197076918", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1094", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 149, "source_index": null, "at": "2026-10-13T18:05:04.741306+00:00", "until": null, "date_basis": "observed_revision", "fraction": null, "value_decimal": "0.001672660197076918", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1094", "evidence_excerpt": "Conditional candidate kappa **0.001672660197076918**, **+0.000338096%** over PR1087 (0.001672654541898561). Repeated sixteen-bin whole-helper repacking, seeded through rare full-bin patterns, improves the idle-rank profile. The scalar word, role widths and source-event times are unchanged.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 435, "source_index": null, "at": "2026-10-13T18:00:40Z", "until": null, "date_basis": "body-version", "fraction": "33453121246973/20000000000000000", "value_decimal": "0.001672660197076918", "dashboard_float_text": null, "expression": "0.00167265606234865", "historical_title": "Draft conditional kappa 0.00167265606234865: rare-pattern T16 exchanges", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1094", "evidence_excerpt": "Conditional candidate kappa 0.00167265606234865, +0.000090900% over PR1087 (0.001672654541898561). Sampling rare full-bin patterns enables a sixteen-bin whole-helper repacking: four rank-one idle remainders become two rank-two ", "automated_comparable": true, "body_sha256": "8af975d47ce0827332670dfbb3c9512af60ab136093c1a31ada13b375fb9a90b" }, { "stream": "recovered_literal_highwater", "stream_row": 436, "source_index": null, "at": "2026-10-13T18:02:53Z", "until": null, "date_basis": "body-version", "fraction": "836328952466699/500000000000000000", "value_decimal": "0.001672660197076918", "dashboard_float_text": null, "expression": "0.001672657904933398", "historical_title": "Draft conditional kappa 0.001672657904933398: rare-pattern T16 exchanges", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1094", "evidence_excerpt": "Conditional candidate kappa 0.001672657904933398, +0.000201060% over PR1087 (0.001672654541898561). Sampling rare full-bin patterns enables a sixteen-bin whole-helper repacking: four rank-one idle remainders become two rank-two ", "automated_comparable": true, "body_sha256": "2fbebbb726d69e9b140b3dd7981c9a4e70ee4470389d36f8e4ee162ea5456c7f" }, { "stream": "recovered_literal_highwater", "stream_row": 437, "source_index": null, "at": "2026-10-13T18:03:53Z", "until": null, "date_basis": "body-version", "fraction": "836329312582229/500000000000000000", "value_decimal": "0.001672660197076918", "dashboard_float_text": null, "expression": "0.001672658625164458", "historical_title": "Draft conditional kappa 0.001672658625164458: rare-pattern T16 exchanges", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1094", "evidence_excerpt": "Conditional candidate kappa 0.001672658625164458, +0.000244119% over PR1087 (0.001672654541898561). Repeated sixteen-bin whole-helper repacking, seeded through rare full-bin patterns, improves the idle-rank profile. The scalar w", "automated_comparable": true, "body_sha256": "ba5386142f63d098b6ee6331e327f204f995e1fcee6385d2f103b4034770a65f" }, { "stream": "recovered_literal_highwater", "stream_row": 438, "source_index": null, "at": "2026-10-13T18:04:26Z", "until": null, "date_basis": "body-version", "fraction": "836330098538459/500000000000000000", "value_decimal": "0.001672660197076918", "dashboard_float_text": null, "expression": "0.001672660197076918", "historical_title": "Draft conditional kappa 0.001672660197076918: rare-pattern T16 exchanges", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1094", "evidence_excerpt": "Conditional candidate kappa 0.001672660197076918, +0.000338096% over PR1087 (0.001672654541898561). Repeated sixteen-bin whole-helper repacking, seeded through rare full-bin patterns, improves the idle-rank profile. The scalar w", "automated_comparable": true, "body_sha256": "ea8d65848fead7bedf680f4af0d2d83346d70e2efcce73657a771ae3e474e7b6" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "first_listed_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "first_listed_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "first_listed_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own exact arbitrary-input phase/normalized-wrapper, common-label/mutable-source and all-size unequal-child realization interfaces remain explicit fixed-protocol hypotheses.", "Exact earlier own-SPEC canonical/program hashes are recovered from a later archive; only identical earlier selected bytes are reused. No later owner/profile or rank supplier is substituted.", "All704 native scalar input columns, private clears, actual wrapper sweeps, dyadic Horner/prefix counts and each own whole T16 role/window/chart/profile were freshly checked; no full phase or Lean replay is claimed.", "The parent numeric realization uses an independently window-matched primary geometry fixture and source direct-sum lift. Own historical PLAN, call order, windows, profile and owner bytes are bound; historical parent provenance metadata byte identity is not claimed.", "Completed Gaussian children have semantic norm one under the endpoint contract. Own finite router/literal/C0 inequalities,512-bit payload and16469 row allowance fund the typed precision interface.", "Same direct Gaussian/fine-prime/finite-section/boundary/recovery analytic contracts, exact candidate-only Fermat helper and repaired unlimited optimized-GMP correctness/halting assumptions." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1094-r480-finite-controller-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 4, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1094/priority-manifest.json", "sha256": "ca39f4761ff670a95257011ef01bbe0e8e3885f951de9a139d0a077ab21b7a11" } ], "source_head": "0fc329d0bec93ca7cd288eaea1295172e8789810" } }, { "pr": 1050, "title": "Conditional \u03ba = 0.001672241870811633: improved T16 owner packing on the seven-slot k8 word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1050", "author": "jeremykothe2", "created_at": "2026-10-13T17:13:22Z", "accepted_at": "2026-10-13T18:47:08Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672241870811633", "kappa_fraction": "1672241870811633/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1050-recovered-t16-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 122, "source_index": 174, "at": "2026-10-13T17:13:22Z", "until": "2026-10-13T17:17:55Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001672241870811633", "dashboard_float_text": "0.001672241870811633", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1050", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 139, "source_index": null, "at": "2026-10-13T17:13:22Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001672241870811633", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1050", "evidence_excerpt": "Conditional \u03ba = **0.001672241870811633**. Same construction and code as #1022; only the T16 owner map changes (exact LNS repack). Differs from the previous record only in `data/{OWNERS,PLAN,SPEC}`, README, RESULT and MANIFEST.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 425, "source_index": null, "at": "2026-10-13T17:13:22Z", "until": null, "date_basis": "body-version", "fraction": "1672241870811633/1000000000000000000", "value_decimal": "0.001672241870811633", "dashboard_float_text": null, "expression": "0.001672241870811633", "historical_title": "Conditional \u03ba = 0.001672241870811633: improved T16 owner packing on the seven-slot k8 word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1050", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001672241870811633. Same construction and code as #1022; only the T16 owner map changes (exact LNS repack). Differs from the previous record only in data/{OWNERS,PLAN,SPEC}, README, RESULT and MANIF", "automated_comparable": true, "body_sha256": "0867d5c643cb7440374c27cb945e9b483054a649fa1ef569382d2353a32a7841" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1050-recovered-t16-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1050/priority-manifest.json", "sha256": "34b1f0b9527029aad37edf75b26ec6cad5604b9155c4a8460287447e8b0729f6" } ], "source_head": "c87242f846cfab8c0b97fd889b5fecb0eacef939" } }, { "pr": 1051, "title": "Independent verification: code-disjoint T37 moment endpoints and kappa reduction (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1051", "author": "thakrarsagar", "created_at": "2026-10-13T17:13:34Z", "accepted_at": "2026-10-13T18:47:08Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661960547713947", "kappa_fraction": "1661960547713947/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "individual-primary-interface-source/1051-manifest.json", "sha256": "63eff57821d4c773c58e2b10147a1aae23b922e27ed43801c00ea447977404c2" }, { "file": "remaining-record-audit/artifacts/1051/priority-manifest.json", "sha256": "d3725a6c0d8075eeb9591bf7c2eaa6536ace30997eb5303315b2a834294a9c7e" } ], "source_head": "3b8fab9b48d54160d0765c316eed45078f32aa5e" } }, { "pr": 1052, "title": "Independent verification: T37 positive-binomial moments, all-T lemma, and 1024-bit reduction (seed 78, no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1052", "author": "steph4n-gh", "created_at": "2026-10-13T17:17:39Z", "accepted_at": "2026-10-13T18:47:08Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661960547713947", "kappa_fraction": "1661960547713947/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "individual-primary-interface-source/1052-manifest.json", "sha256": "8ecef1fb06cc7a46dbcb75be1e361d837d6ded933c207c86d9f047aac27ca4a9" }, { "file": "remaining-record-audit/artifacts/1052/priority-manifest.json", "sha256": "1505a35151f6baacf64db10c357ce665f3cb32e68befa98e74dbfa7484e2cf5a" } ], "source_head": "e7f0319b7a7b4e8e1958ae523affdc123e3ea597" } }, { "pr": 1053, "title": "Conditional \u03ba = 0.001672245809535804: improved T16 owner packing on the seven-slot k8 word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1053", "author": "jeremykothe2", "created_at": "2026-10-13T17:17:55Z", "accepted_at": "2026-10-13T18:47:08Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672245809535804", "kappa_fraction": "418061452383951/250000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1053-recovered-t16-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 123, "source_index": 175, "at": "2026-10-13T17:17:55Z", "until": "2026-10-13T17:20:29Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001672245809535804", "dashboard_float_text": "0.001672245809535804", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1053", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 140, "source_index": null, "at": "2026-10-13T17:17:55Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001672245809535804", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1053", "evidence_excerpt": "Conditional \u03ba = **0.001672245809535804**. Same construction and code as #1022; only the T16 owner map changes (exact LNS repack). Differs from the previous record only in `data/{OWNERS,PLAN,SPEC}`, README, RESULT and MANIFEST.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 426, "source_index": null, "at": "2026-10-13T17:17:55Z", "until": null, "date_basis": "body-version", "fraction": "418061452383951/250000000000000000", "value_decimal": "0.001672245809535804", "dashboard_float_text": null, "expression": "0.001672245809535804", "historical_title": "Conditional \u03ba = 0.001672245809535804: improved T16 owner packing on the seven-slot k8 word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1053", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001672245809535804. Same construction and code as #1022; only the T16 owner map changes (exact LNS repack). Differs from the previous record only in data/{OWNERS,PLAN,SPEC}, README, RESULT and MANIF", "automated_comparable": true, "body_sha256": "54232708cba987c9abce84acecb382f5d4188e3a64898fb7bd830be3004be7d7" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1053-recovered-t16-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1053/priority-manifest.json", "sha256": "d0a235dd18de6fbd4f8098baa9a604ff5f28ad5e672d3e8f9b37aedf1ae65e00" } ], "source_head": "6f92ce8884929c9fd4730c86a28e2e3735de02af" } }, { "pr": 1055, "title": "Conditional \u03ba = 0.001672251604432734: improved T16 owner packing on the seven-slot k8 word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1055", "author": "jeremykothe2", "created_at": "2026-10-13T17:20:29Z", "accepted_at": "2026-10-13T18:47:08Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672251604432734", "kappa_fraction": "836125802216367/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1055-recovered-t16-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 124, "source_index": 176, "at": "2026-10-13T17:20:29Z", "until": "2026-10-13T17:21:35Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001672251604432734", "dashboard_float_text": "0.001672251604432734", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1055", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 141, "source_index": null, "at": "2026-10-13T17:20:29Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001672251604432734", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1055", "evidence_excerpt": "Conditional \u03ba = **0.001672251604432734**. Same construction and code as #1022; only the T16 owner map changes (exact LNS repack). Differs from the previous record only in `data/{OWNERS,PLAN,SPEC}`, README, RESULT and MANIFEST.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 427, "source_index": null, "at": "2026-10-13T17:20:29Z", "until": null, "date_basis": "body-version", "fraction": "836125802216367/500000000000000000", "value_decimal": "0.001672251604432734", "dashboard_float_text": null, "expression": "0.001672251604432734", "historical_title": "Conditional \u03ba = 0.001672251604432734: improved T16 owner packing on the seven-slot k8 word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1055", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001672251604432734. Same construction and code as #1022; only the T16 owner map changes (exact LNS repack). Differs from the previous record only in data/{OWNERS,PLAN,SPEC}, README, RESULT and MANIF", "automated_comparable": true, "body_sha256": "df3375fd3dad20e84aa4283c664a45c1ab16756cd02fb63fc18848e323f48bf5" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1055-recovered-t16-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1055/priority-manifest.json", "sha256": "ff3a5293e3b5aa2aadba5c8f7c89192972b19050cdbce69c244ec9e9e0690a45" } ], "source_head": "a8ea308976f1709eef0a328463f010cf51469277" } }, { "pr": 1056, "title": "Conditional kappa 0.001672267698427438: whole-helper exchanges on the T16 owner map", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1056", "author": "rohanarun", "created_at": "2026-10-13T17:21:35Z", "accepted_at": "2026-10-13T18:47:08Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672267698427438", "kappa_fraction": "836133849213719/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1056-gaussian-only-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 125, "source_index": 177, "at": "2026-10-13T17:21:35Z", "until": "2026-10-13T17:26:20Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001672267698427438", "dashboard_float_text": "0.001672267698427438", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1056", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 142, "source_index": null, "at": "2026-10-13T17:21:35Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001672267698427438", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1056", "evidence_excerpt": "Conditional kappa **0.001672267698427438**, **+0.00154449%** over the PR1050 parent (0.001672241870811633). It also exceeds the later PR1055 claim by **0.00096241%**. Repeated whole-helper exchanges improve the exact T16 owner map while preserving the local word, widths, call order and source-event times.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 428, "source_index": null, "at": "2026-10-13T17:21:35Z", "until": null, "date_basis": "body-version", "fraction": "836133849213719/500000000000000000", "value_decimal": "0.001672267698427438", "dashboard_float_text": null, "expression": "0.001672267698427438", "historical_title": "Conditional kappa 0.001672267698427438: whole-helper exchanges on the T16 owner map", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1056", "evidence_excerpt": "Conditional kappa 0.001672267698427438, +0.00154449% over PR1050 (0.001672241870811633), using whole-helper owner exchanges on its exact T16 map. Local word, widths, call order and source-event times remain unchanged. ", "automated_comparable": true, "body_sha256": "2acb618e08dcacd4453fc92e31757f950bcd37072a451a813917fe79426e8ad3" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1056-gaussian-only-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 5, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1056/priority-manifest.json", "sha256": "9c4c7d5738511ed7b298b1007c0ad85da181038e4a1ccfc0dfd811264818d23a" } ], "source_head": "d0201efbd68c4acc9832b84bcc986c8781b83c4f" } }, { "pr": 1061, "title": "Conditional \u03ba = 0.00167259071506618: improved T16 owner packing on the seven-slot k8 word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1061", "author": "jeremykothe2", "created_at": "2026-10-13T17:26:20Z", "accepted_at": "2026-10-13T18:47:08Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00167259071506618", "kappa_fraction": "83629535753309/50000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1061-recovered-t16-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 126, "source_index": 178, "at": "2026-10-13T17:26:20Z", "until": "2026-10-13T17:28:50Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.00167259071506618", "dashboard_float_text": "0.00167259071506618", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1061", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 143, "source_index": null, "at": "2026-10-13T17:26:20Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00167259071506618", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1061", "evidence_excerpt": "Conditional \u03ba = **0.00167259071506618**. Same construction and code as #1022; only the T16 owner map changes (exact LNS repack). Differs from the previous record only in `data/{OWNERS,PLAN,SPEC}`, README, RESULT and MANIFEST.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 429, "source_index": null, "at": "2026-10-13T17:26:20Z", "until": null, "date_basis": "body-version", "fraction": "83629535753309/50000000000000000", "value_decimal": "0.00167259071506618", "dashboard_float_text": null, "expression": "0.00167259071506618", "historical_title": "Conditional \u03ba = 0.00167259071506618: improved T16 owner packing on the seven-slot k8 word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1061", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.00167259071506618. Same construction and code as #1022; only the T16 owner map changes (exact LNS repack). Differs from the previous record only in data/{OWNERS,PLAN,SPEC}, README, RESULT and MANIF", "automated_comparable": true, "body_sha256": "60406d811b3f2b167042c54874b3d3e12cd033b49132df65c84f133b10eb23c5" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1061-recovered-t16-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1061/priority-manifest.json", "sha256": "ff9182b35f6582de8dae40790d320546cc538856fd0ff1b7762f1b0929b9b7d9" } ], "source_head": "223f581afb1d63d5f8476a69040617e11bcd50e4" } }, { "pr": 1063, "title": "Conditional kappa 0.001672285678298543: neutral T16 reshuffles and whole-helper exchanges", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1063", "author": "rohanarun", "created_at": "2026-10-13T17:28:50Z", "accepted_at": "2026-10-13T18:47:08Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672285678298543", "kappa_fraction": "1672285678298543/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1063-dispatched-finite-controller-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1063-dispatched-finite-controller-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 5, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1063/priority-manifest.json", "sha256": "c26e4c03bcd97afdd8a19ecd7ad905639446ae46dffb5d8c9747ee26a02a6ccc" } ], "source_head": "d9377d32e0c97e41338e704c3960fd6f2fa73806" } }, { "pr": 1065, "title": "Conditional \u03ba = 0.001672644568760139: improved T16 owner packing on the seven-slot k8 word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1065", "author": "jeremykothe2", "created_at": "2026-10-13T17:31:47Z", "accepted_at": "2026-10-13T18:47:08Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672644568760139", "kappa_fraction": "1672644568760139/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1065-recovered-t16-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 127, "source_index": 180, "at": "2026-10-13T17:31:47Z", "until": "2026-10-13T17:35:22Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001672644568760139", "dashboard_float_text": "0.001672644568760139", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1065", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 144, "source_index": null, "at": "2026-10-13T17:31:47Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001672644568760139", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1065", "evidence_excerpt": "Conditional \u03ba = **0.001672644568760139**. Same construction and code as #1022; only the T16 owner map changes (exact LNS repack). Differs from the previous record only in `data/{OWNERS,PLAN,SPEC}`, README, RESULT and MANIFEST.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 430, "source_index": null, "at": "2026-10-13T17:31:47Z", "until": null, "date_basis": "body-version", "fraction": "1672644568760139/1000000000000000000", "value_decimal": "0.001672644568760139", "dashboard_float_text": null, "expression": "0.001672644568760139", "historical_title": "Conditional \u03ba = 0.001672644568760139: improved T16 owner packing on the seven-slot k8 word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1065", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001672644568760139. Same construction and code as #1022; only the T16 owner map changes (exact LNS repack). Differs from the previous record only in data/{OWNERS,PLAN,SPEC}, README, RESULT and MANIF", "automated_comparable": true, "body_sha256": "f35c0679b44924ed31932464643be3684bf70253205454cc7d95f80a1c5dd70e" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1065-recovered-t16-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1065/priority-manifest.json", "sha256": "8070cf6124f40e782763818f035cca69ec3a3247864892d4b3961cb868ce8bde" } ], "source_head": "387d935e354a931d636e2c5e6ee63a6910f78a1b" } }, { "pr": 1068, "title": "Conditional \u03ba = 0.001672650458698046: improved T16 owner packing on the seven-slot k8 word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1068", "author": "jeremykothe2", "created_at": "2026-10-13T17:35:22Z", "accepted_at": "2026-10-13T18:47:08Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672650458698046", "kappa_fraction": "836325229349023/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1068-recovered-t16-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 128, "source_index": 181, "at": "2026-10-13T17:35:22Z", "until": "2026-10-13T17:40:24Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001672650458698046", "dashboard_float_text": "0.001672650458698046", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1068", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 145, "source_index": null, "at": "2026-10-13T17:35:22Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001672650458698046", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1068", "evidence_excerpt": "Conditional \u03ba = **0.001672650458698046**. Same construction and code as #1022; only the T16 owner map changes (exact LNS repack). Differs from the previous record only in `data/{OWNERS,PLAN,SPEC}`, README, RESULT and MANIFEST.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 431, "source_index": null, "at": "2026-10-13T17:35:22Z", "until": null, "date_basis": "body-version", "fraction": "836325229349023/500000000000000000", "value_decimal": "0.001672650458698046", "dashboard_float_text": null, "expression": "0.001672650458698046", "historical_title": "Conditional \u03ba = 0.001672650458698046: improved T16 owner packing on the seven-slot k8 word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1068", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001672650458698046. Same construction and code as #1022; only the T16 owner map changes (exact LNS repack). Differs from the previous record only in data/{OWNERS,PLAN,SPEC}, README, RESULT and MANIF", "automated_comparable": true, "body_sha256": "3dde2b3acf8c45bfb4bad8d6da3cab9a0ba6b2e4b01f105f6826369a5b715375" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1068-recovered-t16-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1068/priority-manifest.json", "sha256": "7191c29f8cebca42de59030ea7be5b116ebc0bb314b5744a966c9275f2f6254a" } ], "source_head": "cc71375eae4e8754da0f5d940cb519d66625fb2e" } }, { "pr": 1072, "title": "Conditional \u03ba = 0.001661961039655941: one E4 call fills four T37 gaps", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1072", "author": "davidNbreslauer", "created_at": "2026-10-13T17:40:24Z", "accepted_at": "2026-10-13T18:47:08Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661961039655941", "kappa_fraction": "1661961039655941/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/u8-e4-gap-fill/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/u8-e4-gap-fill/CLAIM.json, research/u8-e4-gap-fill/README.md, research/u8-e4-gap-fill/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/u8-e4-gap-fill/CLAIM.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/u8-e4-gap-fill/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/1072-manifest.json", "sha256": "6be6b4f6a5caf684936a080795006db506400cbb95bee8379b46860e1f867c0c" }, { "file": "remaining-record-audit/artifacts/1072/priority-manifest.json", "sha256": "09774adbe7001ceb82c4be72e51d0581d8e4abb4dba33d2fe73aa6e875c45f3f" } ], "source_head": "6c1504cd75aae9b255ba16bf8e28d3f38af34c14" } }, { "pr": 987, "title": "Conditional \u03ba = 0.001662039077758742 \u2014 U10 (two new triangle-hybrid slots) on PR942's T37 owners", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/987", "author": "rohanarun", "created_at": "2026-10-13T16:03:48Z", "accepted_at": "2026-10-13T18:47:09Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001662039077758742", "kappa_fraction": "831019538879371/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 114, "source_index": 164, "at": "2026-10-13T16:14:50.724665Z", "until": "2026-10-13T16:20:01Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001662039077758742", "dashboard_float_text": "0.001662039077758742", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/987", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 131, "source_index": null, "at": "2026-10-13T16:14:50.724665+00:00", "until": null, "date_basis": "observed_revision", "fraction": null, "value_decimal": "0.001662039077758742", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/987", "evidence_excerpt": "## Conditional \u03ba = 0.001662039077758742: U10 (two new triangle-hybrid slots) on PR942's T37 owners", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 416, "source_index": null, "at": "2026-10-13T16:03:48Z", "until": null, "date_basis": "body-version", "fraction": "207754538053721/125000000000000000", "value_decimal": "0.001662039077758742", "dashboard_float_text": null, "expression": "0.001662036304429768", "historical_title": "Draft: conditional \u03ba = 0.001662036304429768 \u2014 two new triangle-hybrid slots on U8 (U10) with T21 owners", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/987", "evidence_excerpt": "## Draft: conditional \u03ba = 0.001662036304429768 (pending strict cold replay)\n\nThis adds +7.8529657*10^-8 over the selected PR890 result (0.001661957774647029). It is also above the open #942. The complex side still binds; the b", "automated_comparable": true, "body_sha256": "7689363e4d6796ea0ea6594f7e6705fc1be17bb9d23bf77aaba86334e472b4a1" }, { "stream": "recovered_literal_highwater", "stream_row": 417, "source_index": null, "at": "2026-10-13T16:14:23Z", "until": null, "date_basis": "title-edit", "fraction": "831019538879371/500000000000000000", "value_decimal": "0.001662039077758742", "dashboard_float_text": null, "expression": "0.001662039077758742", "historical_title": "Draft: conditional \u03ba = 0.001662039077758742 \u2014 U10 (two new triangle-hybrid slots) on PR942's T37 owners", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/987", "evidence_excerpt": "Draft: conditional \u03ba = 0.001662039077758742 \u2014 U10 (two new triangle-hybrid slots) on PR942's T37 owners", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/87db776d70ad1d28a27e9f7906237e5a279414f3/certificates/selected-result.json", "path": null, "commit": "87db776d70ad1d28a27e9f7906237e5a279414f3", "at": "2026-10-13T18:05:11Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/complex-u10-t37/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/complex-u10-t37/CLAIM.json, research/complex-u10-t37/MANIFEST.json, research/complex-u10-t37/PROOF.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/complex-u10-t37/CLAIM.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/complex-u10-t37/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/987-manifest.json", "sha256": "bff15950014cb10f495794dad55da805337b2b47b26cc480dd70e137efee1406" }, { "file": "remaining-record-audit/artifacts/987/priority-manifest.json", "sha256": "d61576e1b5123543214ace649caea9d5c556d29a80529d249afe895133db1747" } ], "source_head": "5142511af0437572aca71b35d1987cd2b47bb5e3" } }, { "pr": 3, "title": "Compress the complex network for a conditional 59/10^11 > 2^-31 bound", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3", "author": "eumemic", "created_at": "2026-10-08T02:23:07Z", "accepted_at": "2026-10-13T20:45:33Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "5.9E-10", "kappa_fraction": "59/100000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^1717986918404294967288)", "log2log2_input_bits": "1717986918404294967288", "plot_triple_log": { "exact_log2log2_integer": "1717986918404294967288" }, "source": "data/operation-audit/pr3-earliest-selected-gaussian-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own selected full all-role physical input/output Gaussian operator identities, required absolute phases and arbitrary dirty auxiliaries restored. Finite scalar/binary-frame checks alone do not prove the universal operator claim.", "Own common-label/all-column/whole-call/all-size compiler and normalized completed Gaussian endpoint identities.", "New fixed-wiring complete-row realization, complete native scalar/basis/phase/clear work and once-only row padding; only public-size address routing is free.", "Exact dyadic augmented-grid native arithmetic and nonlinear source path guard; completed Gaussian-integer H returns discard only proven-zero fractional guard bits.", "The separately closed nonlinear whole proof pays exact incoming-grid arithmetic, proven-zero guard-bit discard only at complete Gaussian-integer H returns, disjoint complete coefficient-block direct sums and full C0*d^C1 transient height,33p stored words/66p exact products.", "Concrete normalized Gaussian accretivity, bounded scale-aware Schur/finite-LDU, convolution/rounding/boundary/recovery and repaired optimized-reference correctness/halting remain explicit; no false arbitrary-scale theorem or historical BIT expense is used." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 1, "source_index": 1, "at": "2026-10-08T02:28:12Z", "until": "2026-10-08T03:45:41Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "5.9E-10", "dashboard_float_text": "5.9e-10", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 1, "source_index": null, "at": "2026-10-08T02:28:12Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "5.9E-10", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3", "evidence_excerpt": "**`kappa = 59/10^11 > 2^-31`**, a factor `590/83 \u2248 7.11` above `83/10^12`.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 2, "source_index": null, "at": "2026-10-08T02:23:07Z", "until": null, "date_basis": "body-version", "fraction": "59/100000000000", "value_decimal": "5.9E-10", "dashboard_float_text": null, "expression": "59/10^11", "historical_title": "Compress the complex network for a conditional 59/10^11 > 2^-31 bound", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3", "evidence_excerpt": "ding motif, and the unchanged compact-control recurrence and assembly give the conditional witness\n\nkappa = 59/10^11 > 2^-31, a factor 590/83 \u2248 7.11 above 83/10^12.\n\nBit network, compact-control movement/reservations/repair, generalized guard, Gaussian setup and assembly are all unchanged. This ", "automated_comparable": true, "body_sha256": "197965d5ca5e21b324fa42b60d43caf426c7825c4be7284d0dfecea45ebf577d" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/1000000000", "own_source_scope": [ "Own selected full all-role physical input/output Gaussian operator identities, required absolute phases and arbitrary dirty auxiliaries restored. Finite scalar/binary-frame checks alone do not prove the universal operator claim.", "Own common-label/all-column/whole-call/all-size compiler and normalized completed Gaussian endpoint identities.", "New fixed-wiring complete-row realization, complete native scalar/basis/phase/clear work and once-only row padding; only public-size address routing is free.", "Exact dyadic augmented-grid native arithmetic and nonlinear source path guard; completed Gaussian-integer H returns discard only proven-zero fractional guard bits.", "The separately closed nonlinear whole proof pays exact incoming-grid arithmetic, proven-zero guard-bit discard only at complete Gaussian-integer H returns, disjoint complete coefficient-block direct sums and full C0*d^C1 transient height,33p stored words/66p exact products.", "Concrete normalized Gaussian accretivity, bounded scale-aware Schur/finite-LDU, convolution/rounding/boundary/recovery and repaired optimized-reference correctness/halting remain explicit; no false arbitrary-scale theorem or historical BIT expense is used." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr3-earliest-selected-gaussian-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 5, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/3-manifest.json", "sha256": "9c09a6a8124166a1078848f380c903928f8de9ad246c3494d82175e29bcf1ff8" }, { "file": "remaining-record-audit/artifacts/3/priority-manifest.json", "sha256": "c0875da4c549a680b8aa1590ee7fcc0753b4b1601220da3c9858b6a548fb6fdd" } ], "source_head": "dfe5b818aad4d386cb5dd7d76df108088107765d" } }, { "pr": 4, "title": "Combine PR #3 shared exclusions with retained totals and stage sharing", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4", "author": "dleen", "created_at": "2026-10-08T02:53:18Z", "accepted_at": "2026-10-13T21:02:35Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "5.91E-10", "kappa_fraction": "591/1000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^1717986918404294967288)", "log2log2_input_bits": "1717986918404294967288", "plot_triple_log": { "exact_log2log2_integer": "1717986918404294967288" }, "source": "data/operation-audit/pr4-earliest-selected-gaussian-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own selected full all-role physical input/output Gaussian operator identities, required absolute phases and arbitrary dirty auxiliaries restored. Finite scalar/binary-frame checks alone do not prove the universal operator claim.", "Own common-label/all-column/whole-call/all-size compiler and normalized completed Gaussian endpoint identities.", "New fixed-wiring complete-row realization, complete native scalar/basis/phase/clear work and once-only row padding; only public-size address routing is free.", "Exact dyadic augmented-grid native arithmetic and nonlinear source path guard; completed Gaussian-integer H returns discard only proven-zero fractional guard bits.", "The separately closed nonlinear whole proof pays exact incoming-grid arithmetic, proven-zero guard-bit discard only at complete Gaussian-integer H returns, disjoint complete coefficient-block direct sums and full C0*d^C1 transient height,33p stored words/66p exact products.", "Concrete normalized Gaussian accretivity, bounded scale-aware Schur/finite-LDU, convolution/rounding/boundary/recovery and repaired optimized-reference correctness/halting remain explicit; no false arbitrary-scale theorem or historical BIT expense is used." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 2, "source_index": 2, "at": "2026-10-08T03:45:41Z", "until": "2026-10-08T08:22:26Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "5.91E-10", "dashboard_float_text": "5.91e-10", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 2, "source_index": null, "at": "2026-10-08T03:45:41Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "5.91E-10", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4", "evidence_excerpt": "Combine the shared-exclusion producer from #3 with retained exclusion totals and stage-1/3 bank sharing. At h=24, this reduces auxiliary roles to **90,950** and certifies complex saving **2.97e-8**, about **2.12\u00d7** #3's 1.4e-8. The bit producer remains unchanged, so the conditional headline stays **\u03ba = 591/10\u00b9\u00b2 > 2\u207b\u00b3\u00b9**; the combination supplies additional complex headroom.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 3, "source_index": null, "at": "2026-10-08T02:53:18Z", "until": null, "date_basis": "body-version", "fraction": "591/1000000000000", "value_decimal": "5.91E-10", "dashboard_float_text": null, "expression": "591/10^12", "historical_title": "Combine complex rectangles and retained totals for conditional 2^-31 bound", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4", "evidence_excerpt": "th frame directions, stage sharing and endpoint corrections.\n\nThe exact conditional witness becomes \u03ba = 591/10^12 = 5.91e-10 > 2^-31, versus 83/10^12 > 2^-34 (591/83 \u2248 7.12 times the exact saving). The paired-bit producer and compact-control movement are unchanged. The bit compiler's proposed", "automated_comparable": true, "body_sha256": "2c00efb9e60a404eb431b51ecd26fe6f62d2036d88b17f96293693df9e424335" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/1000000000", "own_source_scope": [ "Own selected full all-role physical input/output Gaussian operator identities, required absolute phases and arbitrary dirty auxiliaries restored. Finite scalar/binary-frame checks alone do not prove the universal operator claim.", "Own common-label/all-column/whole-call/all-size compiler and normalized completed Gaussian endpoint identities.", "New fixed-wiring complete-row realization, complete native scalar/basis/phase/clear work and once-only row padding; only public-size address routing is free.", "Exact dyadic augmented-grid native arithmetic and nonlinear source path guard; completed Gaussian-integer H returns discard only proven-zero fractional guard bits.", "The separately closed nonlinear whole proof pays exact incoming-grid arithmetic, proven-zero guard-bit discard only at complete Gaussian-integer H returns, disjoint complete coefficient-block direct sums and full C0*d^C1 transient height,33p stored words/66p exact products.", "Concrete normalized Gaussian accretivity, bounded scale-aware Schur/finite-LDU, convolution/rounding/boundary/recovery and repaired optimized-reference correctness/halting remain explicit; no false arbitrary-scale theorem or historical BIT expense is used." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr4-earliest-selected-gaussian-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 5, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/4-manifest.json", "sha256": "76981379ae9ba466122b19a66f753d45bd78617108e93614ac595341440fad5e" }, { "file": "remaining-record-audit/artifacts/4/priority-manifest.json", "sha256": "9a087a62a8ece3bbd3b6c5d6987355430a40e58cc43e038c050d3ad5a9ba4910" } ], "source_head": "8c225e619168c0141dcfcba3b68a65bbed6a8729" } }, { "pr": 2, "title": "Preserve aligned pairing and its conditional 17*2^-63 witness", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2", "author": "Bortlesboat", "created_at": "2026-10-07T22:20:00Z", "accepted_at": "2026-10-13T21:02:36Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "1.843143693225357537812669761478900909423828125E-18", "kappa_fraction": "17/9223372036854775808", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^274877906944000068719476728)", "log2log2_input_bits": "274877906944000068719476728", "plot_triple_log": { "exact_log2log2_integer": "274877906944000068719476728" }, "source": "data/operation-audit/pr2-earliest-selected-gaussian-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own selected full all-role physical input/output Gaussian operator identities, required absolute phases and arbitrary dirty auxiliaries restored. Finite scalar/binary-frame checks alone do not prove the universal operator claim.", "Own common-label/all-column/whole-call/all-size compiler and normalized completed Gaussian endpoint identities.", "New fixed-wiring complete-row realization, complete native scalar/basis/phase/clear work and once-only row padding; only public-size address routing is free.", "Exact dyadic augmented-grid native arithmetic and nonlinear source path guard; completed Gaussian-integer H returns discard only proven-zero fractional guard bits.", "The separately closed nonlinear whole proof pays exact incoming-grid arithmetic, proven-zero guard-bit discard only at complete Gaussian-integer H returns, disjoint complete coefficient-block direct sums and full C0*d^C1 transient height,33p stored words/66p exact products.", "Concrete normalized Gaussian accretivity, bounded scale-aware Schur/finite-LDU, convolution/rounding/boundary/recovery and repaired optimized-reference correctness/halting remain explicit; no false arbitrary-scale theorem or historical BIT expense is used." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "recovered_literal_highwater", "stream_row": 1, "source_index": null, "at": "2026-10-07T22:20:00Z", "until": null, "date_basis": "body-version", "fraction": "17/9223372036854775808", "value_decimal": "1.8431999999999999E-18", "dashboard_float_text": null, "expression": "17*2^-63", "historical_title": "Align pair groups for a conditional 17*2^-63 bound", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2", "evidence_excerpt": "etained analytic recipe and upstream theorem, the exact bit saving supports a conditional target of \u03ba = 17*2^-63, 6.25% above the current headline target 2^-59.\n\nFor common point i, put its global pair partner i ^ 1 last in the local point order and leave all other complete pairs together. R", "automated_comparable": true, "body_sha256": "a03fa730489e96e4ff01ac6f29ea4f3c97d47d07db4b0d15a7c8bdef80e26587" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/10000000000000", "own_source_scope": [ "Own selected full all-role physical input/output Gaussian operator identities, required absolute phases and arbitrary dirty auxiliaries restored. Finite scalar/binary-frame checks alone do not prove the universal operator claim.", "Own common-label/all-column/whole-call/all-size compiler and normalized completed Gaussian endpoint identities.", "New fixed-wiring complete-row realization, complete native scalar/basis/phase/clear work and once-only row padding; only public-size address routing is free.", "Exact dyadic augmented-grid native arithmetic and nonlinear source path guard; completed Gaussian-integer H returns discard only proven-zero fractional guard bits.", "The separately closed nonlinear whole proof pays exact incoming-grid arithmetic, proven-zero guard-bit discard only at complete Gaussian-integer H returns, disjoint complete coefficient-block direct sums and full C0*d^C1 transient height,33p stored words/66p exact products.", "Concrete normalized Gaussian accretivity, bounded scale-aware Schur/finite-LDU, convolution/rounding/boundary/recovery and repaired optimized-reference correctness/halting remain explicit; no false arbitrary-scale theorem or historical BIT expense is used." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr2-earliest-selected-gaussian-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 5, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/2-manifest.json", "sha256": "5b304d1d5fa41bc087e00ded201222846a8203e9300192437f26b62da9279b0f" }, { "file": "remaining-record-audit/artifacts/2/priority-manifest.json", "sha256": "4e92ab17455596c15f32c4de0d208f5d4c84babecd5edafceaf332d418ce6e7f" } ], "source_head": "8bb07d55f6898bc8ec919222cf7596e987e9b69f" } }, { "pr": 8, "title": "Review conditional geometric complex-network candidate with kappa = 5.9e-10", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/8", "author": "rohanarun", "created_at": "2026-10-08T07:33:25Z", "accepted_at": "2026-10-13T21:02:36Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "5.9E-10", "kappa_fraction": "59/100000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (README.md, research/geometric-complex/README.md, research/geometric-complex/certificate.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (README.md, research/geometric-complex/README.md, research/geometric-complex/certificate.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "Bind/recompute the source finite work, scalar coefficient grammar, denominator/precision/guard and all-size row-stock from research/geometric-complex/certificate.json#/guard before using the stopped recurrence or compiled uniform supplier.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/geometric-complex/certificate.json#/assembly after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/8-manifest.json", "sha256": "561375960d3e7d17291908d873a79b1c25467653804d447fec06f53c25593eb4" }, { "file": "remaining-record-audit/artifacts/8/priority-manifest.json", "sha256": "f3f5fb45c75b8d95b1d017653e4f0989016891a88e1eda8e62639683ca0894e1" } ], "source_head": "4920e44843512014f742d685e01341f6787bbd5f" } }, { "pr": 9, "title": "Refine PR #7 ternary star templates for conditional kappa = 3.8e-9", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/9", "author": "rohanarun", "created_at": "2026-10-08T08:07:17Z", "accepted_at": "2026-10-13T21:02:36Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "3.8E-9", "kappa_fraction": "19/5000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^1717986918404294967288)", "log2log2_input_bits": "1717986918404294967288", "plot_triple_log": { "exact_log2log2_integer": "1717986918404294967288" }, "source": "data/operation-audit/pr9-nonlinear-native-gaussian-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own explicit original PR7 complete complex native map and physical input/output/absolute-phase/all-column/arbitrary-dirty/common-label contracts.", "New application of the named arbitrary-rank complete-row coefficient lemma to the exact own finite core, not execution of an original PR9 mixed-row schedule.", "Distinct nonlinear C1=5\u22124theta+zeta semantic-depth induction and all unproved source analytic/all-size interfaces; parameter screens alone are not whole runtime bounds.", "Own bounded dyadic coefficient grammar and full1024Ew scalar/phase/clear tariff must satisfy the separate own-source grammar supplement.", "Exact augmented-grid native arithmetic and completed Gaussian-integer H return, nonlinear C0*d^C1, coefficient-block direct sums and full outer amplitude/rounding/33p/66p guards are those of the separately closed nonlinear whole proof, specialized with native theta.76.", "Concrete normalized Gaussian accretivity/finite-LDU/narrow/cyclic-boundary/prime/recovery and repaired-reference correctness/halting remain explicit; no false arbitrary-scale analytic assertion or original historical ternary BIT cost is used." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 3, "source_index": 3, "at": "2026-10-08T08:22:26Z", "until": "2026-10-08T08:47:03Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "3.8E-9", "dashboard_float_text": "3.8e-09", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/9", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 3, "source_index": null, "at": "2026-10-08T08:22:26Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "3.8E-9", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/9", "evidence_excerpt": "Under #7's retained general interfaces, the exact witness becomes **kappa = 19/5,000,000,000 = 3.8e-9 > 2^-28**, approximately **1.88% above #7's 3.73e-9 headline**. This is a modest circuit refinement and an asymptotic exponent comparison, not a runtime benchmark or a global optimality claim.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 7, "source_index": null, "at": "2026-10-08T08:07:17Z", "until": null, "date_basis": "opening-title", "fraction": "19/5000000000", "value_decimal": "3.8E-9", "dashboard_float_text": null, "expression": "3.8e-9", "historical_title": "Refine PR #7 ternary star templates for conditional kappa = 3.8e-9", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/9", "evidence_excerpt": "Refine PR #7 ternary star templates for conditional kappa = 3.8e-9", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/1000000000", "own_source_scope": [ "Own explicit original PR7 complete complex native map and physical input/output/absolute-phase/all-column/arbitrary-dirty/common-label contracts.", "New application of the named arbitrary-rank complete-row coefficient lemma to the exact own finite core, not execution of an original PR9 mixed-row schedule.", "Distinct nonlinear C1=5\u22124theta+zeta semantic-depth induction and all unproved source analytic/all-size interfaces; parameter screens alone are not whole runtime bounds.", "Own bounded dyadic coefficient grammar and full1024Ew scalar/phase/clear tariff must satisfy the separate own-source grammar supplement.", "Exact augmented-grid native arithmetic and completed Gaussian-integer H return, nonlinear C0*d^C1, coefficient-block direct sums and full outer amplitude/rounding/33p/66p guards are those of the separately closed nonlinear whole proof, specialized with native theta.76.", "Concrete normalized Gaussian accretivity/finite-LDU/narrow/cyclic-boundary/prime/recovery and repaired-reference correctness/halting remain explicit; no false arbitrary-scale analytic assertion or original historical ternary BIT cost is used." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr9-nonlinear-native-gaussian-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 6, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/9-manifest.json", "sha256": "71e6bc7ec13ac5d2eed6774b15356f2fffc7d0dd55941a7262e913937084ca97" }, { "file": "remaining-record-audit/artifacts/9/priority-manifest.json", "sha256": "7c703f8e19d99a45c27a1b24a86b04301c0da0568fcea09ef332ab3126b9f248" } ], "source_head": "cfd6a2baded9dba990b987934474a7721d6ca3fb" } }, { "pr": 12, "title": "Use dimension-30 geometry for conditional kappa = 1.2649e-7", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/12", "author": "rohanarun", "created_at": "2026-10-08T08:40:12Z", "accepted_at": "2026-10-13T21:02:36Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "1.2649E-7", "kappa_fraction": "12649/100000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^2361183242025118417206705651704)", "log2log2_input_bits": "2361183242025118417206705651704", "plot_triple_log": { "exact_log2log2_integer": "2361183242025118417206705651704" }, "source": "data/operation-audit/pr12-nonlinear-native-gaussian-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own complete all-role native circuit, physical entry/output frames and absolute phases on arbitrary dirty data.", "Own nondegenerate binary residual normal forms, normalized completed Gaussian endpoint and all-column/common-label/whole-helper restoration.", "Source complete-row volume and spectator identity, with once-only padding; fixed nonuniform routing replaces compact address descriptors only.", "Named Gaussian analytic/boundary/recovery interfaces and separate nonlinear C1>1 global precision/count proof; no whole-integer upper admitted by this component.", "Concrete normalized Gaussian shifted-kernel accretivity/finite-LDU, narrow/cyclic boundary recovery and complete integer convolution/carry interfaces from the closed direct Gaussian construction remain explicit. The false arbitrary-scale accretive theorem is not used.", "The nonlinear source height C0*d^C1, not completed norm1, is paid in full at every native invocation, including the synchronized factors and outer-transform normalization.", "This new direct Gaussian/Fermat coefficient circuit does not execute the historical source BIT supplier or compact address-descriptor routing. Full native operator/absolute-phase/common-label/owned/complete-row identities remain premises.", "The repaired unlimited optimized-GMP source model and finite-kernel halting are retained; numerical bounds concern this declared source-derived family, not every implementation." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 4, "source_index": 4, "at": "2026-10-08T08:47:03Z", "until": "2026-10-08T10:57:04Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "1.2649E-7", "dashboard_float_text": "1.2649e-07", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/12", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 4, "source_index": null, "at": "2026-10-08T08:47:03Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "1.2649E-7", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/12", "evidence_excerpt": "This follow-up supports the unreviewed conditional witness **kappa = 12649/100000000000 = 1.2649e-7**, about **2.84% above PR #10's 1.2299998e-7**, in `T(n) = O(n (log n)^(1-kappa))`.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 9, "source_index": null, "at": "2026-10-08T08:40:12Z", "until": null, "date_basis": "body-version", "fraction": "12649/100000000000", "value_decimal": "1.2649E-7", "dashboard_float_text": null, "expression": "12649/100000000000", "historical_title": "Use dimension-30 geometry for conditional kappa = 1.2649e-7", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/12", "evidence_excerpt": "This follow-up supports the unreviewed conditional witness kappa = 12649/100000000000 = 1.2649e-7, about 2.84% above PR #10's 1.2299998e-7, in T(n) = O(n (log n)^(1-kappa)).\n\nThe change uses the five-subset bit network at dimension 30, the selected star rules of #9", "automated_comparable": true, "body_sha256": "cb5250617ddc827e2679e3ee7d86bedbf92943f730defcb8ab08ef356aa30a4e" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/10000000", "own_source_scope": [ "Own complete all-role native circuit, physical entry/output frames and absolute phases on arbitrary dirty data.", "Own nondegenerate binary residual normal forms, normalized completed Gaussian endpoint and all-column/common-label/whole-helper restoration.", "Source complete-row volume and spectator identity, with once-only padding; fixed nonuniform routing replaces compact address descriptors only.", "Named Gaussian analytic/boundary/recovery interfaces and separate nonlinear C1>1 global precision/count proof; no whole-integer upper admitted by this component.", "Concrete normalized Gaussian shifted-kernel accretivity/finite-LDU, narrow/cyclic boundary recovery and complete integer convolution/carry interfaces from the closed direct Gaussian construction remain explicit. The false arbitrary-scale accretive theorem is not used.", "The nonlinear source height C0*d^C1, not completed norm1, is paid in full at every native invocation, including the synchronized factors and outer-transform normalization.", "This new direct Gaussian/Fermat coefficient circuit does not execute the historical source BIT supplier or compact address-descriptor routing. Full native operator/absolute-phase/common-label/owned/complete-row identities remain premises.", "The repaired unlimited optimized-GMP source model and finite-kernel halting are retained; numerical bounds concern this declared source-derived family, not every implementation." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr12-nonlinear-native-gaussian-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 10, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/12-manifest.json", "sha256": "96fb2320ee7876b020cbdb502f4353265b3381b883ee9e05672c2d59d57088e0" }, { "file": "remaining-record-audit/artifacts/12/priority-manifest.json", "sha256": "6046821bb6fc1af3777d19dbfa660bee3b3e4e9f4ce2d0d2ea58f7bc0629d1b2" } ], "source_head": "35d31e30f28bc5da0ae6a88e7b03d75ebc855534" } }, { "pr": 1272, "title": "Director: priority revision 3 \u2014 aim effort at centre path, rank shape and coverage law (stacked on #1240)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1272", "author": "Mister-Meeseeks", "created_at": "2026-10-13T21:33:05Z", "accepted_at": "2026-10-14T03:38:45Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0016873", "kappa_fraction": "16873/10000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "not-indexed-in-canonical-ledger", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "A numerical whole-multiplier comparison must separately identify an actual complete selected native/caller/owner/recursive work-height-stock interface and precision/analytic/outer realization. This source-scope disposition neither supplies nor transfers that bound, and does not extend a restricted negative result beyond its stated family." ], "source_manifest": [ { "file": "individual-primary-interface-source/1272-manifest.json", "sha256": "676ff20c59f22f62e312cebbf5b07ecd374b48cfc0b121db6615914f1b37b314" }, { "file": "remaining-record-audit/artifacts/1272/priority-manifest.json", "sha256": "39561ba1e0d11ae24244310458947546a8cf48e5e695251263a90d1035751a8c" } ], "source_head": "e7ba787e5a2ab430dd054901fe1a3feb72ef5ba5" } }, { "pr": 716, "title": "Research: optimal disjoint R420 target pairs save 3,250 XORs (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/716", "author": "thakrarsagar", "created_at": "2026-10-13T04:41:45Z", "accepted_at": "2026-10-14T04:29:12Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001635527380375392", "kappa_fraction": "51110230636731/31250000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/r420-target-pairs/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/r420-target-pairs/README.md, research/r420-target-pairs/certificate.json, research/r420-target-pairs/verify.py). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/r420-target-pairs/certificate.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/716-manifest.json", "sha256": "8a52cdb1d4d01533ddad44c17e6c8a7a586ea8ef5fe74ac7304263614f3ba9b2" }, { "file": "remaining-record-audit/artifacts/716/priority-manifest.json", "sha256": "14d561a831c57381777b00cc3bb49b455e0287354bc8410e444e46a1bcda3100" } ], "source_head": "afeb452f58ff0cbf109172335e2ba282aac3dcde" } }, { "pr": 742, "title": "Research: shared target donors save 3,288 R420 XORs (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/742", "author": "ellipsi2", "created_at": "2026-10-13T05:01:26Z", "accepted_at": "2026-10-14T04:29:55Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001635527380375392", "kappa_fraction": "51110230636731/31250000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/r420-target-star/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/r420-target-star/CERTIFICATE.json, research/r420-target-star/CLAIM.json, research/r420-target-star/NATIVE.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/r420-target-star/CERTIFICATE.json#/original and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/742/priority-manifest.json", "sha256": "fa771f33c8c6f584ab56cba62f44587da197be0010469b6ba8e8fdb9006f6ce8" } ], "source_head": "6e7a5d271a123886dc7b54ca3180d0b9f9beda5a" } }, { "pr": 765, "title": "Scoped negative result: tensor E8 basis mixing cannot lower 72^d copy rank", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/765", "author": "Mister-Meeseeks", "created_at": "2026-10-13T05:18:29Z", "accepted_at": "2026-10-14T04:30:13Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001635527380375392", "kappa_fraction": "51110230636731/31250000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep the actual named multiplier/changedprogram as a distinct costing target. This contribution is validation, a restricted theorem or an unimplementedtarget; it defines no new fullruntime point. Its target-specific scope/negative controls/constant qualifications must be checked when a complete supplier is priced." ], "source_manifest": [ { "file": "individual-primary-interface-source/765-manifest.json", "sha256": "666a337819fef7ef43b340fc52edda10f7593554bccdfc7b8afea568dc877dbd" }, { "file": "remaining-record-audit/artifacts/765/priority-manifest.json", "sha256": "173e3897fcefecb556b5e77ba591c5ae3889a6626dccf5a8e4f48c5629889f56" } ], "source_head": "d8eaa3db32f76111b39db9b930f347ef30118a28" } }, { "pr": 792, "title": "Finite circuit construction: interleaved R439 mini-nodes save 32 XORs (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/792", "author": "Ryan-Haines", "created_at": "2026-10-13T05:39:20Z", "accepted_at": "2026-10-14T04:30:27Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001635527380375392", "kappa_fraction": "51110230636731/31250000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/p111-interleaved-mini-nodes/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/p111-interleaved-mini-nodes/CERTIFICATE.json, research/p111-interleaved-mini-nodes/EXPECTED.json, research/p111-interleaved-mini-nodes/NATIVE.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/p111-interleaved-mini-nodes/EXPECTED.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/792-manifest.json", "sha256": "4591ea08704c921a752e8a2b73e1e249a2f1a77e90650e2bcac5da5fc16a2b0a" }, { "file": "remaining-record-audit/artifacts/792/priority-manifest.json", "sha256": "4f2bf51c25f33fbce9da7a2609ea790025b930f70a6fcd3023626698fcee9c6b" } ], "source_head": "6a17fb0925c3d3bce770c90bc5c3ff0295b0f3d3" } }, { "pr": 802, "title": "Audit: independent replay confirms #681's 1,484-operation raw factory saving (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/802", "author": "Rohansguliani", "created_at": "2026-10-13T05:56:42Z", "accepted_at": "2026-10-14T04:30:27Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001635527380375392", "kappa_fraction": "51110230636731/31250000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "supporting_native_audit_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 2, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "If a cutoff for a referenced earlier construction is sought, separately bind its complete selected program, physical invoice and parameters; no numerical cutoff transfers from this scope audit." ], "source_manifest": [ { "file": "individual-primary-interface-source/802-manifest.json", "sha256": "b0793afe11b76fc12a88118eb4cce945ef9db592527cfa3338e8769536c5bf5b" }, { "file": "remaining-record-audit/artifacts/802/priority-manifest.json", "sha256": "34a983043a4dab4f8eb6fd3c4ea7ae1d067390ce5b5c1df9492d3e4b2d4f0c6b" } ], "source_head": "0957b70fc2ed1ac7592467e7a24d6d0788ff6758" } }, { "pr": 811, "title": "Research: JP8 additive coefficient routes save 2,784 beyond rescaling (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/811", "author": "Ryan-Haines", "created_at": "2026-10-13T06:10:06Z", "accepted_at": "2026-10-14T04:30:34Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661202643272239", "kappa_fraction": "1661202643272239/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 9, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/jp8-additive-coefficient-routes/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/jp8-additive-coefficient-routes/CERTIFICATE.json, research/jp8-additive-coefficient-routes/EXPECTED.json, research/jp8-additive-coefficient-routes/NATIVE.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/jp8-additive-coefficient-routes/CERTIFICATE.json, research/jp8-additive-coefficient-routes/EXPECTED.json, research/jp8-additive-coefficient-routes/NATIVE.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/811-manifest.json", "sha256": "b9be1b75ba6fd9c95eecd5bb10b8d65bc755a295ccd73a53011fe99be75c51b6" }, { "file": "remaining-record-audit/artifacts/811/priority-manifest.json", "sha256": "a03d76f7e64eb11b76fc2096bcfd08f10811c158d04e706042ded69f709d15a4" } ], "source_head": "b5c244c916dd0b30957332edad7ae7ae22b0eb9d" } }, { "pr": 814, "title": "Research: Eisenstein nonlinear message copy floor 22b under explicit width pricing", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/814", "author": "shiftybitshiftr", "created_at": "2026-10-13T06:15:53Z", "accepted_at": "2026-10-14T04:30:34Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661202643272239", "kappa_fraction": "1661202643272239/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "scoped_information_bound_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/814-manifest.json", "sha256": "12a9e0cacb969abbae73497e3f9beef17598e5cd3b0ae35a8a5e5e5fc6244b29" }, { "file": "remaining-record-audit/artifacts/814/priority-manifest.json", "sha256": "dd8d42e706d7e27e15f48e9af9017b8144e70f91cf732da22b53abb2db4ee5f0" } ], "source_head": "d91c5152b314391406b0ec792b6765a5cf0af2f1" } }, { "pr": 820, "title": "Independent verification: algebraic radix-9 coefficient and factor audit", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/820", "author": "WilliamLawyer", "created_at": "2026-10-13T06:22:22Z", "accepted_at": "2026-10-14T04:52:56Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661202643272239", "kappa_fraction": "1661202643272239/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain the exact stated lemma, finite-audit scope, correction or provenance with its actual selected target. A numerical runtime bound requires an actual source-selected full native/owner/recursive invoice/precision/outer realization and exact own commitments. No cutoff follows from unchanged kappa, a scalar lemma or an audit pass." ], "source_manifest": [ { "file": "individual-primary-interface-source/820-manifest.json", "sha256": "54452fb3b0b17539bde7dec6d0d74416caced4a046c7f64cd79b2d9b1d992257" }, { "file": "remaining-record-audit/artifacts/820/priority-manifest.json", "sha256": "b585923bc33cbf1df3cf8ccd300429bdce31380c68dbb3bcd80adba61e95aab7" } ], "source_head": "00f326845c0614366bef11ee6901ae6295af4999" } }, { "pr": 821, "title": "Research audit: 286-to-160-bit prefix estimate for pinned #626 (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/821", "author": "Brodee042", "created_at": "2026-10-13T06:25:21Z", "accepted_at": "2026-10-14T04:52:56Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661202643272239", "kappa_fraction": "1661202643272239/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/replica-prefix-audit/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/replica-prefix-audit/EXPECTED.json, research/replica-prefix-audit/PROOF.md, research/replica-prefix-audit/README.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/replica-prefix-audit/EXPECTED.json, research/replica-prefix-audit/PROOF.md, research/replica-prefix-audit/README.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/821-manifest.json", "sha256": "f4c4e2028d9690c90270ee29053e402961928277b704fdec33cefee780d75472" }, { "file": "remaining-record-audit/artifacts/821/priority-manifest.json", "sha256": "abb74875b0649bae5d127c6ca2838833d6eac5aad3b390d7341eeeda087dd723" } ], "source_head": "6b832a6ba4dce8dd6e2fb0897dd4543364b932f8" } }, { "pr": 823, "title": "Research construction: shorten historical R480 quad 1 by 12 XORs (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/823", "author": "FanPUYen", "created_at": "2026-10-13T06:27:43Z", "accepted_at": "2026-10-14T04:52:56Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661202643272239", "kappa_fraction": "1661202643272239/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/r480-quad-seed1/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/r480-quad-seed1/CLAIM.json, research/r480-quad-seed1/EXPECTED.json, research/r480-quad-seed1/NATIVE-EXPECTED.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/r480-quad-seed1/EXPECTED.json#/candidate/cost and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/r480-quad-seed1/SOURCES.json#/base_selected_record_context after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/823-manifest.json", "sha256": "b0a23f02493b5303f3dd9495be79a2bd2b969dd356766a74a02debd7914bba8d" }, { "file": "remaining-record-audit/artifacts/823/priority-manifest.json", "sha256": "9dbf0bf1a927152d51e893f90962c0cc26fedf68bf8ff42641a9b107b71b0b91" } ], "source_head": "83d547e30fed98682ffc6eacbeeaafa96cfb42fb" } }, { "pr": 843, "title": "Research construction: reuse R439 source sum for 2,880 fewer hosted instructions (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/843", "author": "anudeepadi", "created_at": "2026-10-13T07:18:06Z", "accepted_at": "2026-10-14T04:52:56Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661634653669567", "kappa_fraction": "1661634653669567/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/p111-dirty-block509/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Recompute the complete own productive/paid histogram from research/p111-dirty-block509/NATIVE.json#/hosted/candidate/hosted_audit and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/p111-dirty-block509/SOURCES.json#/selected_at_base after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/843-manifest.json", "sha256": "e3e70e00ebb34b132467f1e6e5eb53181a990eb8c815af7f3dc8e5830684934f" }, { "file": "remaining-record-audit/artifacts/843/priority-manifest.json", "sha256": "c21153f03d52ff4b9ced03988447d2c3aac519bbd171c87f9e770a40615617fc" } ], "source_head": "c99f4478156906c323b1a041f0443f76139d6b6c" } }, { "pr": 938, "title": "Independent verification: complete minimum-word census for dirty fanout stars (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/938", "author": "RossRichardson", "created_at": "2026-10-13T13:42:42Z", "accepted_at": "2026-10-14T04:53:26Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661957774647029", "kappa_fraction": "1661957774647029/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "supporting_local_identity_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "If a cutoff for a referenced earlier construction is sought, separately bind its complete selected program, physical invoice and parameters; no numerical cutoff transfers from this scope audit." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/938/priority-manifest.json", "sha256": "5b81cec09cbd7104ef8d71c937a7227680fa930acfac594603dcfe650d3fd0a7" } ], "source_head": "df645942469e6a739ec94010a6068c398f4a6c86" } }, { "pr": 940, "title": "Research audit: exact scope of retained Fourier layout cancellation (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/940", "author": "RossRichardson", "created_at": "2026-10-13T13:46:28Z", "accepted_at": "2026-10-14T04:53:26Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661957774647029", "kappa_fraction": "1661957774647029/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/940-manifest.json", "sha256": "539c77204252f14bd6aea65c104e9ffa87ef99a2ed43496b1ec3f25b84447cdf" }, { "file": "remaining-record-audit/artifacts/940/priority-manifest.json", "sha256": "5dcafb17e62def458300a150b280d1c9ece120059f884cc749a0dd6d12972eed" } ], "source_head": "fccac36fa9bcc063c4fda733299a22349ce10e56" } }, { "pr": 955, "title": "Research: close the eight register words left open by PR800 (no kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/955", "author": "littleBro", "created_at": "2026-10-13T14:31:28Z", "accepted_at": "2026-10-14T04:53:26Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661957774647029", "kappa_fraction": "1661957774647029/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No independent whole-multiplier cutoff is defined by this supplied contribution. Price the explicitly referenced complete algorithm only after binding its actual native/operator, ownership, recursive invoice, precision and outer parameters. Relevant local constants, guards and negative hypotheses remain attached to that target; they are not discarded." ], "source_manifest": [ { "file": "individual-primary-interface-source/955-manifest.json", "sha256": "4187effbb59fb195441caf6aa2e66e7993fad4fca0dc55def871eccfeab54d25" }, { "file": "remaining-record-audit/artifacts/955/priority-manifest.json", "sha256": "7bee750172b8d899102bd49e10b0e5c9fce688c4d2792b79535d73e4619c20b5" } ], "source_head": "df668be6f75e76e12d25da5e03eb22ff656aaf86" } }, { "pr": 975, "title": "Finite construction: four-source Horner saves 8,976 beyond X4 pairs (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/975", "author": "ToikY", "created_at": "2026-10-13T15:32:56Z", "accepted_at": "2026-10-14T04:53:26Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661960547713947", "kappa_fraction": "1661960547713947/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/x4-four-source-horner/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/x4-four-source-horner/EXPECTED.json, research/x4-four-source-horner/PROOF.md, research/x4-four-source-horner/README.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/x4-four-source-horner/EXPECTED.json, research/x4-four-source-horner/PROOF.md, research/x4-four-source-horner/README.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/x4-four-source-horner/SOURCES.json#/selection_context after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/975-manifest.json", "sha256": "a362f13998069a38d3305e5b3a777049a1bf7f063a9357e422d578ac93a2e9ea" }, { "file": "remaining-record-audit/artifacts/975/priority-manifest.json", "sha256": "f2275a7fc13a6c83247ea99f08fe57d11e760ab3535370ae7e08f10e5547f854" } ], "source_head": "4b40489c3e0f5819d00251de179a9ea7b1acfba8" } }, { "pr": 982, "title": "Research: output-borrowed fanout with an exact scratch/work tradeoff (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/982", "author": "RossRichardson", "created_at": "2026-10-13T15:49:17Z", "accepted_at": "2026-10-14T04:53:26Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661960547713947", "kappa_fraction": "1661960547713947/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 9, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/output-borrowed-fanout/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/output-borrowed-fanout/CERTIFICATE.json.gz, research/output-borrowed-fanout/EXPECTED.json, research/output-borrowed-fanout/PROOF.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/output-borrowed-fanout/CERTIFICATE.json.gz, research/output-borrowed-fanout/EXPECTED.json, research/output-borrowed-fanout/PROOF.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/982-manifest.json", "sha256": "6df21a149294b1d177ac404b15ebf4497add4e883d543532c2a1ea629b11b6e9" }, { "file": "remaining-record-audit/artifacts/982/priority-manifest.json", "sha256": "6ac2748fc1791e2d6a85346eb030fca40f0c07c64575fc005836d7549fbf63d1" } ], "source_head": "5eca5b435d2ce172edf6ffb85694c7efa31bf114" } }, { "pr": 1057, "title": "Research: exact additive echoes with three dirty arrays at any depth (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1057", "author": "bitplane", "created_at": "2026-10-13T17:22:19Z", "accepted_at": "2026-10-14T04:53:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661960547713947", "kappa_fraction": "1661960547713947/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 9, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/linear-port-borrowing/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/linear-port-borrowing/CLAIM.json, research/linear-port-borrowing/EXPECTED.json, research/linear-port-borrowing/PROOF.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/linear-port-borrowing/CLAIM.json, research/linear-port-borrowing/EXPECTED.json, research/linear-port-borrowing/PROOF.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/1057-manifest.json", "sha256": "7d2103f6f81cd34b852d32f38f11ec7da4021e509ea4f4798bbd4bdfedfbe3fb" }, { "file": "remaining-record-audit/artifacts/1057/priority-manifest.json", "sha256": "6483534b6f8d3ba71b6fdc12bf5aa5a20b99e311c0324507d259522eeca4a782" } ], "source_head": "78a062df1dcab2bffea5ff4d8243f3da6e465414" } }, { "pr": 974, "title": "Research: T21/T37 interface budget and bit-binding headroom (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/974", "author": "avirazza", "created_at": "2026-10-13T15:29:02Z", "accepted_at": "2026-10-14T04:54:12Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001730427469823602", "kappa_fraction": "865213734911801/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/974-manifest.json", "sha256": "1541c187317421bdadd3d1c8f8f613784a00b80bced2ba30637e2105f7b07cbe" }, { "file": "remaining-record-audit/artifacts/974/priority-manifest.json", "sha256": "b474a94855fdfb055284a0a45b9e78e0bfc13dc8e481880188e5c9bf9e3a1dcf" } ], "source_head": "f40cd20a8c257bcfee17508c7de68fee24df0568" } }, { "pr": 1012, "title": "Research note: restoration deferral is mass-neutral in the hosted T37 recurrence (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1012", "author": "thakrarsagar", "created_at": "2026-10-13T16:28:44Z", "accepted_at": "2026-10-14T04:54:19Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661960547713947", "kappa_fraction": "1661960547713947/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/1012-manifest.json", "sha256": "aa6b6f86586e4efee209c5a3c0e5bb988677f79d273e1931e02b33fdee56b900" }, { "file": "remaining-record-audit/artifacts/1012/priority-manifest.json", "sha256": "b721d43ff8d71136751655cac9a2fed15006bd46271aeb22fe70a1c5b9af3dd2" } ], "source_head": "4ceaf380ed41b28dadcc41d2f974f025ac4d8c03" } }, { "pr": 1071, "title": "Research: delivery lower bounds for #968's frame-pair centers (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1071", "author": "JosieElliston", "created_at": "2026-10-13T17:39:28Z", "accepted_at": "2026-10-14T04:56:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661960547713947", "kappa_fraction": "1661960547713947/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "scoped_obstruction_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "If a cutoff for a referenced earlier construction is sought, separately bind its complete selected program, physical invoice and parameters; no numerical cutoff transfers from this scope audit." ], "source_manifest": [ { "file": "individual-primary-interface-source/1071-manifest.json", "sha256": "450f1bb967065319c0fbac8ee26988c84e07c0a3c81604bdcdd80ca4e9d61aaf" }, { "file": "remaining-record-audit/artifacts/1071/priority-manifest.json", "sha256": "2333fd1328ca3078f943389e9d3b88b853d1eb18ab21a8a5687cd98fec4c229b" } ], "source_head": "ce9531beba1ce115fdcdc44925ded995a29b8bac" } }, { "pr": 1079, "title": "Scoped negative result: R439 source-substitution census has one known survivor", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1079", "author": "bbMisk", "created_at": "2026-10-13T17:46:30Z", "accepted_at": "2026-10-14T04:56:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661960547713947", "kappa_fraction": "1661960547713947/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "scoped_obstruction_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "If a cutoff for a referenced earlier construction is sought, separately bind its complete selected program, physical invoice and parameters; no numerical cutoff transfers from this scope audit." ], "source_manifest": [ { "file": "individual-primary-interface-source/1079-manifest.json", "sha256": "f8b0d19a64d290484b8f628f1cfb468029b2506c91d29451f09585aed785851d" }, { "file": "remaining-record-audit/artifacts/1079/priority-manifest.json", "sha256": "1c7ff77d9bef084083c82d957fad37e02617329f5b1f4ad28c021706f096c0f7" } ], "source_head": "bb20dab261884412f2d2a7955cdb2fd8e2e64a16" } }, { "pr": 1080, "title": "Construction: two-sided signed bi-forest U8 compensation saving 53,596 real primitives (seed 35, no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1080", "author": "steph4n-gh", "created_at": "2026-10-13T17:46:45Z", "accepted_at": "2026-10-14T04:56:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661960547713947", "kappa_fraction": "1661960547713947/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/u8-two-sided-biforest-seed35/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/u8-two-sided-biforest-seed35/EXPECTED.json, research/u8-two-sided-biforest-seed35/PROOF.md, research/u8-two-sided-biforest-seed35/README.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/1080-manifest.json", "sha256": "fbc3b7cf9348ec98162856aa8e03e73599c658c2554cfff972255995d4d99bab" }, { "file": "remaining-record-audit/artifacts/1080/priority-manifest.json", "sha256": "8cbfd2df5bfb6ff19c02983d4a141afb403c2420abeb8f112b0127f7a4770e84" } ], "source_head": "803e080e181229a3af2196b7a13615c9d81ae10d" } }, { "pr": 1108, "title": "Research: exact compact-control boundary cancellation obstruction (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1108", "author": "martinxxx9", "created_at": "2026-10-13T18:21:07Z", "accepted_at": "2026-10-14T05:18:48Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672188119205421", "kappa_fraction": "1672188119205421/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "scoped_obstruction_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/1108-manifest.json", "sha256": "4ea566a4ca5afc33517b39b9b5625f786d7bf04d322649730146bf45d9c0c4ee" }, { "file": "remaining-record-audit/artifacts/1108/priority-manifest.json", "sha256": "fd5202281adcf90afbd1384f0c52c701f49632f73f8176723161210f3b4d8ea1" } ], "source_head": "b76bb2853be4e7001508582b10913e32ad7aba9f" } }, { "pr": 1111, "title": "Conditional \u03ba = 0.001672780159952542: reverse one entrance promotion to fill T16 gaps", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1111", "author": "seslly", "created_at": "2026-10-13T18:23:15Z", "accepted_at": "2026-10-14T05:18:48Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672780159952542", "kappa_fraction": "836390079976271/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 135, "source_index": 190, "at": "2026-10-13T18:23:15Z", "until": "2026-10-13T18:31:49Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001672780159952542", "dashboard_float_text": "0.001672780159952542", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1111", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 152, "source_index": null, "at": "2026-10-13T18:23:15Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001672780159952542", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1111", "evidence_excerpt": "This construction certifies conditional **\u03ba = 0.001672780159952542** (`836390079976271/500000000000000000`). It improves pinned #1087 by `0.000000125618053981` and exceeds the subsequently reported #1107 result `0.001672765980186726`.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 441, "source_index": null, "at": "2026-10-13T18:23:15Z", "until": null, "date_basis": "body-version", "fraction": "836390079976271/500000000000000000", "value_decimal": "0.001672780159952542", "dashboard_float_text": null, "expression": "0.001672780159952542", "historical_title": "Conditional \u03ba = 0.001672780159952542: reverse one entrance promotion to fill T16 gaps", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1111", "evidence_excerpt": "This construction certifies conditional \u03ba = 0.001672780159952542 (836390079976271/500000000000000000). It improves pinned #1087 by 0.000000125618053981 and exceeds the subsequently reported #1107 result 0.001672765980186726.\n\nThe k8 supplier re", "automated_comparable": true, "body_sha256": "e207c43ed63330ee9316ad588419792e05fa0b98ced83a5ce49a3ced066ba921" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_selected_full_program_bytes_missing; demote635; required full program 95b4b824cad700f58e06b1fcfdec7db76a7ba44724d0db25f9ab805ebf284450; both orientations {\"backward\": \"3d5aa446df31c39c961632a2d2776de745e1fa6d26b3821b77bf4d4826304851\", \"forward\": \"6a54115bda570250418fb648712d80c7514170261616c60a3517f6ba0308c992\"}; Recover exact actual complete selected program bytes, by own immutable primary source or deterministic pinned constructor/recipe with mandatory complete semantic and orientation commitments. A matching profile, scalar saving or another provider does not fill this gap. Missing canonical catalogue may remain a separately stated endpoint premise only after the actual selected program and complete own physical/invoice are bound.", "Source-specific frozen V10 discovery snapshot: actual_selected_physical_input_unresolved; PLAN; expected f9347c64fa73033818aaae8ef1cb9838931d9ee87b42e5fb1300164da56662aa; Bind the actual complete own PLAN/OWNERS bytes or reconstruct a source-equivalent complete physical realization with explicit changed-parent provenance, actual role/program/windows/stock checks and fresh full invoice. A404 under conventional local paths is not proof that an explicitly pinned parent archive is absent.", "Source-specific frozen V10 discovery snapshot: actual_selected_physical_input_unresolved; OWNERS; expected c62240c99943735e3e35535e7ac95de2889c6da5da243c5e5871ed1716fdf365; Bind the actual complete own PLAN/OWNERS bytes or reconstruct a source-equivalent complete physical realization with explicit changed-parent provenance, actual role/program/windows/stock checks and fresh full invoice. A404 under conventional local paths is not proof that an explicitly pinned parent archive is absent." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1111/priority-manifest.json", "sha256": "8f5d872a5265f230d67ffb34b1025174246911f8904cf46375438b828e5f44df" } ], "source_head": "381831ea554ea983e16224dabed8921b7d0ffdbc" } }, { "pr": 1114, "title": "Research audit: exact two-choice classification of six frame coalescences (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1114", "author": "adamgall", "created_at": "2026-10-13T18:27:28Z", "accepted_at": "2026-10-14T05:18:48Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672188119205421", "kappa_fraction": "1672188119205421/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "supporting_local_classification_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "If a cutoff for a referenced earlier construction is sought, separately bind its complete selected program, physical invoice and parameters; no numerical cutoff transfers from this scope audit." ], "source_manifest": [ { "file": "individual-primary-interface-source/1114-manifest.json", "sha256": "0b828c0e789e2af318da05240409cb816109588138c970727a9e79a0fa8a8770" }, { "file": "remaining-record-audit/artifacts/1114/priority-manifest.json", "sha256": "28049e5a47491d262a280036423a3dcd643b0707242fe16d87c8508e5574d3da" } ], "source_head": "1d6b61aeb268b1f918f16ff76a4bec57aa39eaa1" } }, { "pr": 1118, "title": "Finite complex construction: CK grid-preserving circuits save 1,310 per orientation (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1118", "author": "ToikY", "created_at": "2026-10-13T18:32:26Z", "accepted_at": "2026-10-14T05:18:48Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672188119205421", "kappa_fraction": "1672188119205421/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/ck-grid-synthesis-seed24/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/ck-grid-synthesis-seed24/CLAIM.json, research/ck-grid-synthesis-seed24/EXPECTED.json, research/ck-grid-synthesis-seed24/PROOF.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/ck-grid-synthesis-seed24/CLAIM.json, research/ck-grid-synthesis-seed24/EXPECTED.json, research/ck-grid-synthesis-seed24/PROOF.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/1118-manifest.json", "sha256": "2c4a67d0b24575673898b57d32c2892f0182a2e236751b86103460a00f3447e3" }, { "file": "remaining-record-audit/artifacts/1118/priority-manifest.json", "sha256": "c92fe27a64cfdbc891513ed995efa51fce1af3cc8992942307c21dafc144181d" } ], "source_head": "82575f429d817f1730c28537e669e56a8016e3a7" } }, { "pr": 1119, "title": "Finite complex construction: two-sided Markowitz LPR cleanup refactorization on U8 (-2,580 macros, -37,320 real prims per orientation, seed 30, no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1119", "author": "steph4n-gh", "created_at": "2026-10-13T18:32:44Z", "accepted_at": "2026-10-14T05:18:48Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661960547713947", "kappa_fraction": "1661960547713947/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/u8-cleanup-markowitz-lpr-seed30/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/u8-cleanup-markowitz-lpr-seed30/CLAIM.json, research/u8-cleanup-markowitz-lpr-seed30/EXPECTED.json, research/u8-cleanup-markowitz-lpr-seed30/PROOF.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/u8-cleanup-markowitz-lpr-seed30/CLAIM.json#/selected_frontier_certificate after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/1119-manifest.json", "sha256": "107c563f755437659bd93ffed0f430f0cba6528c5524b7065736bf87538543f3" }, { "file": "remaining-record-audit/artifacts/1119/priority-manifest.json", "sha256": "e821924de46c12bece2f24922aba7189700c291ec4d45137094e3fe7d912ad6a" } ], "source_head": "bc0140e016bd865fffc7fdf64e12158183d52339" } }, { "pr": 1129, "title": "Conditional \u03ba = 0.001674097969905390: an attaining T37 construction and fixed R480 owner optimum", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1129", "author": "aliromman", "created_at": "2026-10-13T18:47:16Z", "accepted_at": "2026-10-14T05:18:48Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00167409796990539", "kappa_fraction": "167409796990539/100000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1129-gaussian-only-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 139, "source_index": 194, "at": "2026-10-13T18:47:16Z", "until": "2026-10-13T18:47:31Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001674097969905390", "dashboard_float_text": "0.00167409796990539", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1129", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 156, "source_index": null, "at": "2026-10-13T18:47:16Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001674097969905390", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1129", "evidence_excerpt": "Conditional \u03ba = 0.001674097969905390: an attaining T37 construction and fixed R480 owner optimum", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 445, "source_index": null, "at": "2026-10-13T18:47:16Z", "until": null, "date_basis": "body-version", "fraction": "167409796990539/100000000000000000", "value_decimal": "0.001674097969905390", "dashboard_float_text": null, "expression": "0.001674097969905390", "historical_title": "Conditional \u03ba = 0.001674097969905390: an attaining T37 construction and fixed R480 owner optimum", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1129", "evidence_excerpt": "ge proves that bound and gives a physical 37-replica construction that attains it, with conditional \u03ba = 0.001674097969905390. It changes only the owner assignment and its finite admission. The local word, bit supplier, and selected-result pointers are unchanged.\n\nThe signed bin inequality covers all 1,1", "automated_comparable": true, "body_sha256": "3280e922c0edc41a06841704f289f8c1d15864a5245e04e438b6bc80e52aa521" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1129-gaussian-only-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1129/priority-manifest.json", "sha256": "d46eb1ecc9e738c426a59fc58d70cbb85a342ea75970e0f6f347be7fd1b422fd" } ], "source_head": "a007dc2e1cc7ae7e8f7ec1343e8883fe43259f21" } }, { "pr": 1101, "title": "Tooling: overlap bit589 and complex741 in the #741 ancestry replay, 17% (50% with --complex-jobs 3) less wall time (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1101", "author": "rcfc-jreed", "created_at": "2026-10-13T18:11:28Z", "accepted_at": "2026-10-14T05:18:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661202643272239", "kappa_fraction": "1661202643272239/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "verification_tooling_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 3, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No distinct numerical point should be fabricated for this support artifact. Bind a referenced implementation separately if displaying its inherited cutoff." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1101/priority-manifest.json", "sha256": "ba46878a0c4454180761229a719075e4f9b10280c7cee1226be7add49e64b993" } ], "source_head": "4d45bef9bd0b52cc4989f195cd2dd4597f4a6d08" } }, { "pr": 1135, "title": "Research: exact restoration contracts and resource bounds for rounded borrowing", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1135", "author": "aliromman", "created_at": "2026-10-13T18:53:46Z", "accepted_at": "2026-10-14T05:19:03Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672188119205421", "kappa_fraction": "1672188119205421/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 9, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No independent whole-multiplier cutoff is defined by this supplied contribution. Price the explicitly referenced complete algorithm only after binding its actual native/operator, ownership, recursive invoice, precision and outer parameters. Relevant local constants, guards and negative hypotheses remain attached to that target; they are not discarded." ], "source_manifest": [ { "file": "individual-primary-interface-source/1135-manifest.json", "sha256": "4a0075af53352676132031f22e31bb47b947f1e2952d422d05d0ef049595a40f" }, { "file": "remaining-record-audit/artifacts/1135/priority-manifest.json", "sha256": "3a344c79121c0c7685e347e12da1d0751c0d14c6b2e6502a69504b7881e2e533" } ], "source_head": "4c35687d7c0da8e6cf33f17e418ecf31c95ff3ad" } }, { "pr": 1153, "title": "Finite construction: PR1042 R480 sign normalization saves 408 primitives per orientation (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1153", "author": "Scratch-net", "created_at": "2026-10-13T19:13:50Z", "accepted_at": "2026-10-14T05:19:03Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672188119205421", "kappa_fraction": "1672188119205421/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/selected-k8-sign-seed38/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/selected-k8-sign-seed38/CLAIM.json, research/selected-k8-sign-seed38/EXPECTED.json, research/selected-k8-sign-seed38/PROOF.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/selected-k8-sign-seed38/CLAIM.json, research/selected-k8-sign-seed38/EXPECTED.json, research/selected-k8-sign-seed38/PROOF.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/selected-k8-sign-seed38/CLAIM.json#/result after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/1153-manifest.json", "sha256": "8fa56c4ec07de4bedbfd9fad5cf99081dc08b72356e2152172a6b054e7b52436" }, { "file": "remaining-record-audit/artifacts/1153/priority-manifest.json", "sha256": "92d43af118bcab2eb5c58a58c3ea35d816f6653b77262edbb5dd383ebbc2b5fa" } ], "source_head": "c744b52d839c52312bc70f90c0530543a5fb205f" } }, { "pr": 1198, "title": "Independent verification: R480 private-center erasure and 40 CLEAR/COPY omissions (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1198", "author": "Scratch-net", "created_at": "2026-10-13T19:57:18Z", "accepted_at": "2026-10-14T05:19:17Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "supporting_native_fault_audit_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "If a cutoff for a referenced earlier construction is sought, separately bind its complete selected program, physical invoice and parameters; no numerical cutoff transfers from this scope audit." ], "source_manifest": [ { "file": "individual-primary-interface-source/1198-manifest.json", "sha256": "26af6636eae0141cc0efb0d4007543b1f14b84409b2dab17af30843254e9054f" }, { "file": "remaining-record-audit/artifacts/1198/priority-manifest.json", "sha256": "e27a1a2f626b1e792d02fd8d869204d350f777d012769b60e110032517b218ea" } ], "source_head": "2abd7e92b7ad3cd769376244ce32dc7b3501c2b3" } }, { "pr": 1206, "title": "Finite bit construction: ordered R420 decoder chains save 142 ADDs (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1206", "author": "adamgall", "created_at": "2026-10-13T20:07:38Z", "accepted_at": "2026-10-14T05:19:23Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672188119205421", "kappa_fraction": "1672188119205421/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/r420-decoder-chain/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/r420-decoder-chain/CERTIFICATE.json, research/r420-decoder-chain/CLAIM.json, research/r420-decoder-chain/NATIVE.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/r420-decoder-chain/NATIVE.json#/words/candidate and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/1206-manifest.json", "sha256": "a3fa094621724d5287b0337af9193419132a5192df8151b1a9304190f3e05858" }, { "file": "remaining-record-audit/artifacts/1206/priority-manifest.json", "sha256": "d8cd6ffe0d88bb5625cebceed935c0f72b44d71bbd2e4eac6105ca00c2d34cd7" } ], "source_head": "3c0a3240035f1c71ef09251b7be7c4791da8157d" } }, { "pr": 1112, "title": "Independent verification: selected PR1042 finite invoice, 9 guards, 14 bootstrap steps and 94 outer slacks (seed 81, no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1112", "author": "Wronskode", "created_at": "2026-10-13T18:24:51Z", "accepted_at": "2026-10-14T05:19:41Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672188119205421", "kappa_fraction": "1672188119205421/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "supporting_invoice_audit_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "If a cutoff for a referenced earlier construction is sought, separately bind its complete selected program, physical invoice and parameters; no numerical cutoff transfers from this scope audit." ], "source_manifest": [ { "file": "individual-primary-interface-source/1112-manifest.json", "sha256": "d4be71710f2bd8f1b338da9fab21478b9cae26066890dbf287f1f1cdda799311" }, { "file": "remaining-record-audit/artifacts/1112/priority-manifest.json", "sha256": "7df4fcf07fcacd22973a0f1863bd29496e0aa71eb9de449e4dcb4af5ad8c1707" } ], "source_head": "3a6a13cf4fbda16e1d191553f8b08cb6a3d5ed27" } }, { "pr": 1212, "title": "Research: rank-8 complex decoders are gauge-rigid; E-graph eight-term floor (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1212", "author": "burntout76", "created_at": "2026-10-13T20:14:05Z", "accepted_at": "2026-10-14T05:57:05Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain the exact stated lemma, finite-audit scope, correction or provenance with its actual selected target. A numerical runtime bound requires an actual source-selected full native/owner/recursive invoice/precision/outer realization and exact own commitments. No cutoff follows from unchanged kappa, a scalar lemma or an audit pass." ], "source_manifest": [ { "file": "individual-primary-interface-source/1212-manifest.json", "sha256": "6663aefcc83352bfeeb24fe0393f5287c8116ce06bfbcdf9d89a28538941cf44" }, { "file": "remaining-record-audit/artifacts/1212/priority-manifest.json", "sha256": "8108c6becbe58f4a0cc768d71fea5951c9eceab601d060dbca964397ede21167" } ], "source_head": "57099cb5684f38877f31d149d598801671a633db" } }, { "pr": 1226, "title": "Research: masked root-star trimmed-star census on P112; exact covering bound 784/13, 64 falsified for beta-7 atoms (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1226", "author": "navinor", "created_at": "2026-10-13T20:29:08Z", "accepted_at": "2026-10-14T05:57:05Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/1226-manifest.json", "sha256": "3174f5980d105ff71588dafcca875fbbe983371d5b93d465308f29dc74b30cce" }, { "file": "remaining-record-audit/artifacts/1226/priority-manifest.json", "sha256": "7d68cad3eb9825deda9754fbe62c30cce6de4171ec0a685b9ce119c7bbfd3874" } ], "source_head": "8b10989e4e45f0f9ce41004d7898a21a32f87e11" } }, { "pr": 1232, "title": "Consolidation: stop historical status sections from claiming to be current (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1232", "author": "Mister-Meeseeks", "created_at": "2026-10-13T20:45:28Z", "accepted_at": "2026-10-14T05:57:05Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672188", "kappa_fraction": "418047/250000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "documentation_maintenance_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 2, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No distinct numerical point should be fabricated for this support artifact. Bind a referenced implementation separately if displaying its inherited cutoff." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1232/priority-manifest.json", "sha256": "bd7141fd07ddb3ab11d9137f0b848698efbf9091be103b7b81fd95bb7b7ac032" } ], "source_head": "1a0ecf7f534a67a910b7b5a7e0abe46be074c609" } }, { "pr": 1277, "title": "Research audit: the selected #1094 reuse replay discards its ancestry recheck; binding certified from committed archives (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1277", "author": "thakrarsagar", "created_at": "2026-10-13T21:36:35Z", "accepted_at": "2026-10-14T06:04:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain the exact stated lemma, finite-audit scope, correction or provenance with its actual selected target. A numerical runtime bound requires an actual source-selected full native/owner/recursive invoice/precision/outer realization and exact own commitments. No cutoff follows from unchanged kappa, a scalar lemma or an audit pass." ], "source_manifest": [ { "file": "individual-primary-interface-source/1277-manifest.json", "sha256": "b6326a3fb0f967869e1df131a546fdfde3434d1f52a84e19c3460a040449c29a" }, { "file": "remaining-record-audit/artifacts/1277/priority-manifest.json", "sha256": "c7a5b45edd5b8a3e8beac3b1bb0de4de0a82af004e233dd40e1d9d5af1da719e" } ], "source_head": "02d279515ff1fc468ab99a19d89461f1b6391507" } }, { "pr": 1292, "title": "Research: masked rank-8 complex decoders are locally rigid on all P104 frame-pair punctures (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1292", "author": "navinor", "created_at": "2026-10-13T21:49:44Z", "accepted_at": "2026-10-14T06:04:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain the exact stated lemma, finite-audit scope, correction or provenance with its actual selected target. A numerical runtime bound requires an actual source-selected full native/owner/recursive invoice/precision/outer realization and exact own commitments. No cutoff follows from unchanged kappa, a scalar lemma or an audit pass." ], "source_manifest": [ { "file": "individual-primary-interface-source/1292-manifest.json", "sha256": "7383ac8276191543910fc202fec644af47ac242e3782bd9ee3423797a4dfbb53" }, { "file": "remaining-record-audit/artifacts/1292/priority-manifest.json", "sha256": "5992284e5afe7e307cc69e2126764f9b5b352d4bec781f347e7e9581bc78162b" } ], "source_head": "7a8325f6c8e5a6830ce919965a2959ac459e010a" } }, { "pr": 1341, "title": "Scoped negative result: R439 quad17 minimizes positive ADDs and reverse envelope", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1341", "author": "1337isnot1337", "created_at": "2026-10-13T23:07:53Z", "accepted_at": "2026-10-14T06:08:54Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No independent whole-multiplier cutoff is defined by this supplied contribution. Price the explicitly referenced complete algorithm only after binding its actual native/operator, ownership, recursive invoice, precision and outer parameters. Relevant local constants, guards and negative hypotheses remain attached to that target; they are not discarded." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1341/priority-manifest.json", "sha256": "555f3e181b93fcc5fbb18f865de0c8fe5d4afa8261859c50c24ad17612db357c" } ], "source_head": "becd4a2b6fad711914fe80f4344aef0008b30a28" } }, { "pr": 1346, "title": "Research/jp8 diagonal gauge seed35", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1346", "author": "mythrilium", "created_at": "2026-10-13T23:10:41Z", "accepted_at": "2026-10-14T06:27:46Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/complex-jp8-diagonal-gauge/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/complex-jp8-diagonal-gauge/CERTIFICATE.json, research/complex-jp8-diagonal-gauge/CLAIM.json, research/complex-jp8-diagonal-gauge/EXPECTED.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/complex-jp8-diagonal-gauge/CERTIFICATE.json, research/complex-jp8-diagonal-gauge/CLAIM.json, research/complex-jp8-diagonal-gauge/EXPECTED.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/1346-manifest.json", "sha256": "795008fe91fcaa7cefa8af2f5a6ae21be4f789d44a36cf3c5e18e6668a2a2c8b" }, { "file": "remaining-record-audit/artifacts/1346/priority-manifest.json", "sha256": "f0d072d21de8610eca7ccefba6ff8144018b6103088cca245583e2bf5b1bf9a4" } ], "source_head": "fd33c640407dda0867604722b612e6c68b7cd6e2" } }, { "pr": 1351, "title": "Research: exact one-family physical host realization for selected PR589 (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1351", "author": "1337isnot1337", "created_at": "2026-10-13T23:16:08Z", "accepted_at": "2026-10-14T06:27:46Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain the exact stated lemma, finite-audit scope, correction or provenance with its actual selected target. A numerical runtime bound requires an actual source-selected full native/owner/recursive invoice/precision/outer realization and exact own commitments. No cutoff follows from unchanged kappa, a scalar lemma or an audit pass." ], "source_manifest": [ { "file": "individual-primary-interface-source/1351-manifest.json", "sha256": "c77cbc0798a2b85c1d79380b8728bb625a88ad10e2a5fbe8b2b648054a0bf53b" }, { "file": "remaining-record-audit/artifacts/1351/priority-manifest.json", "sha256": "b0b6d5a0ed2e61c223bedb14a260ba34328dfed83027530d6b65ef05b059f648" } ], "source_head": "c2ede7d2fcf8b1d812521fa1a65064946b0de5a6" } }, { "pr": 1358, "title": "Scoped negative result: no extra singleton 4-to-6 B-frame in selected k8 word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1358", "author": "1337isnot1337", "created_at": "2026-10-13T23:23:18Z", "accepted_at": "2026-10-14T06:27:46Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/1358-manifest.json", "sha256": "066273368236fc0ccc952d8e6d4f2ed9c80fad65ae3b4e31a694823968c408ab" }, { "file": "remaining-record-audit/artifacts/1358/priority-manifest.json", "sha256": "6eeeb18950b2d7cb802d956d6b40cf5ba0ff6d02278cd8ccc2dcc85a2233c55c" } ], "source_head": "381d4a48b3cab8c204d437627b4e76cfc0c17164" } }, { "pr": 1359, "title": "Scoped proof: exact 3-ADD minimum for PR1221's R439 frame-509 endpoint", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1359", "author": "1337isnot1337", "created_at": "2026-10-13T23:24:42Z", "accepted_at": "2026-10-14T06:27:46Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No independent whole-multiplier cutoff is defined by this supplied contribution. Price the explicitly referenced complete algorithm only after binding its actual native/operator, ownership, recursive invoice, precision and outer parameters. Relevant local constants, guards and negative hypotheses remain attached to that target; they are not discarded." ], "source_manifest": [ { "file": "individual-primary-interface-source/1359-manifest.json", "sha256": "11a52591397fca3ee6b2ef055acb1190cd63c4be0ed522b2c72ea475ba65fc15" }, { "file": "remaining-record-audit/artifacts/1359/priority-manifest.json", "sha256": "7f280b7fbbcd6c46913af2c78db4643fc944b709402d950b3ec4bef07f4b3132" } ], "source_head": "6a10c0eaa7e896bb5c6d297a0b9c6bbe46143498" } }, { "pr": 1371, "title": "Independent verification: PR589 family map by exact projector algebra", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1371", "author": "1337isnot1337", "created_at": "2026-10-13T23:36:53Z", "accepted_at": "2026-10-14T06:27:46Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain the exact stated lemma, finite-audit scope, correction or provenance with its actual selected target. A numerical runtime bound requires an actual source-selected full native/owner/recursive invoice/precision/outer realization and exact own commitments. No cutoff follows from unchanged kappa, a scalar lemma or an audit pass." ], "source_manifest": [ { "file": "individual-primary-interface-source/1371-manifest.json", "sha256": "6076b8bfdaecc0a39337e974a7470d8ecea875d82f62ef7999bf8805c093caa9" }, { "file": "remaining-record-audit/artifacts/1371/priority-manifest.json", "sha256": "393df9ac4b034aa417110e211705cf21ed3e8bf94d28c96785f54deee1fa0bc6" } ], "source_head": "680e382e208c07adc011fe155d9fab9f1ff02148" } }, { "pr": 1390, "title": "Research: Pareto-selected R420 block 6 circuit saves 14 ADDs (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1390", "author": "1337isnot1337", "created_at": "2026-10-13T23:59:09Z", "accepted_at": "2026-10-14T06:31:14Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/r420-block6-budgeted-lu/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/r420-block6-budgeted-lu/PROOF.md, research/r420-block6-budgeted-lu/README.md, research/r420-block6-budgeted-lu/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/r420-block6-budgeted-lu/VALIDATION.json#/finite_word and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/r420-block6-budgeted-lu/VALIDATION.json#/current_selection after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/1390-manifest.json", "sha256": "c24b2d40829a7284441b45ea1add8d9dbcd888968087d50d35be3596747e6831" }, { "file": "remaining-record-audit/artifacts/1390/priority-manifest.json", "sha256": "75b117abb9130caa28c473f47191e716cc42711d9f0420fa11158c6c0667c10a" } ], "source_head": "e43071a8470c7e2f62f1d4590337ef7f2ea347c3" } }, { "pr": 1408, "title": "Research: compose L248/L253/L259 schedules on PR1263 word (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1408", "author": "1337isnot1337", "created_at": "2026-10-14T00:22:48Z", "accepted_at": "2026-10-14T06:31:15Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/k8-l248-l253-l259-temporal-composition-seed27/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/k8-l248-l253-l259-temporal-composition-seed27/RESULT.json, research/k8-l248-l253-l259-temporal-composition-seed27/SOURCES.json, research/k8-l248-l253-l259-temporal-composition-seed27/verify.py). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/k8-l248-l253-l259-temporal-composition-seed27/RESULT.json, research/k8-l248-l253-l259-temporal-composition-seed27/SOURCES.json, research/k8-l248-l253-l259-temporal-composition-seed27/verify.py) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/1408-manifest.json", "sha256": "a41f59e5dc1e900c3e3b1157616ec1ee603b8be1098e7987c457a7b84fa5dddc" }, { "file": "remaining-record-audit/artifacts/1408/priority-manifest.json", "sha256": "49ba091480d30c6feaddba66dab509364b3c80e097059519aa1a3ca245ff389e" } ], "source_head": "3d251bcd8f6d243fd4e26b94f4b0e9287c2da79c" } }, { "pr": 1465, "title": "Prove a complete-cost obstruction for eight two-accumulator rewrites", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1465", "author": "aliromman", "created_at": "2026-10-14T01:06:13Z", "accepted_at": "2026-10-14T06:44:53Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00167409796990539", "kappa_fraction": "167409796990539/100000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "A numerical whole-multiplier comparison must separately identify an actual complete selected native/caller/owner/recursive work-height-stock interface and precision/analytic/outer realization. This source-scope disposition neither supplies nor transfers that bound, and does not extend a restricted negative result beyond its stated family." ], "source_manifest": [ { "file": "individual-primary-interface-source/1465-manifest.json", "sha256": "dd816e77e278dff20942a7ead62287115477be307d7a9caf5f0d8fdbef1efbaa" }, { "file": "remaining-record-audit/artifacts/1465/priority-manifest.json", "sha256": "e2dec4ecb548e00cc3ef9b6a6bcf65a58b4363cf53ee1640c2dd26173fb522c4" } ], "source_head": "bb7fc427c79c26669a9e8de06e55f31cadaa992d" } }, { "pr": 1532, "title": "Research note: paid quadratic-reader restoration and exact square-repair floor", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1532", "author": "theon199", "created_at": "2026-10-14T02:22:48Z", "accepted_at": "2026-10-14T15:14:10Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain the actual component/interface/constant improvement with its construction targets. A distinct whole multiplier endpoint requires its own authenticated complete selected native, owner/invoice, recursive, precision and whole-integer implementation; no title or unchanged-kappa exclusion is used." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1532/priority-manifest.json", "sha256": "677d06d1d382c0dc149590ac926ac4aafcd0c619fa765e936ff31950b886bb59" } ], "source_head": "aa54509994cb050174ff2ee1442af8caf8161670" } }, { "pr": 1499, "title": "Research construction: phase-typed two-source order-four echo (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1499", "author": "1337isnot1337", "created_at": "2026-10-14T01:53:29Z", "accepted_at": "2026-10-14T15:14:11Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/z4-distinct-source-seed55/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/z4-distinct-source-seed55/README.md, research/z4-distinct-source-seed55/RESULT.json, research/z4-distinct-source-seed55/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/z4-distinct-source-seed55/README.md, research/z4-distinct-source-seed55/RESULT.json, research/z4-distinct-source-seed55/SOURCES.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/1499-manifest.json", "sha256": "de32c4058c7419cf5c49b482a73e53fbdbe6963cd3976c8bc1f73bc1b9019f9b" }, { "file": "remaining-record-audit/artifacts/1499/priority-manifest.json", "sha256": "8a14b0eac10bfd5ab7d93ddb9e5ace05ac3894ff8fc838c28dc3072ffe940c5d" } ], "source_head": "3ff7f7922d879a810aecb24d6dca66546014198d" } }, { "pr": 1520, "title": "Finite bit construction: one extra XOR reaches the J3 positive-envelope floor (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1520", "author": "bbMisk", "created_at": "2026-10-14T02:10:16Z", "accepted_at": "2026-10-14T15:14:11Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/bit-j3-precision-seed11/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/bit-j3-precision-seed11/CERTIFICATE.json, research/bit-j3-precision-seed11/README.md, research/bit-j3-precision-seed11/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/bit-j3-precision-seed11/CERTIFICATE.json, research/bit-j3-precision-seed11/README.md, research/bit-j3-precision-seed11/SOURCES.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/1520-manifest.json", "sha256": "42258bd789047d33487aa3cb4a8e71aab5cbf592895e82ecb0e50b37489eda30" }, { "file": "remaining-record-audit/artifacts/1520/priority-manifest.json", "sha256": "db696f90b3a7a864234be0e1baa76dd9dfce641560c4b87b2d52063058b8576d" } ], "source_head": "69e353410ae1e6f0555b5add9720f3e691a762b9" } }, { "pr": 1648, "title": "Research: screen the queue-ceiling census's uncovered sixteen claims (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1648", "author": "navinor", "created_at": "2026-10-14T05:07:11Z", "accepted_at": "2026-10-14T15:43:58Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain the exact stated lemma, finite-audit scope, correction or provenance with its actual selected target. A numerical runtime bound requires an actual source-selected full native/owner/recursive invoice/precision/outer realization and exact own commitments. No cutoff follows from unchanged kappa, a scalar lemma or an audit pass." ], "source_manifest": [ { "file": "individual-primary-interface-source/1648-manifest.json", "sha256": "01fc7721296b3addd21fb680ba71dc4f00f3bea170115764458d548b09d25ce0" }, { "file": "remaining-record-audit/artifacts/1648/priority-manifest.json", "sha256": "5ce4d1d0f9e78925d93a91d97518917a5c657663db61c7d37e02f0884ebbf631" } ], "source_head": "9efe15ab79b669c99d1e95dcc4a50e2d3ad71a9c" } }, { "pr": 1689, "title": "Scoped negative result: 72/77 copy-cost lower bounds for two masked Walsh P112 totals", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1689", "author": "just-mn", "created_at": "2026-10-14T07:06:38Z", "accepted_at": "2026-10-14T15:49:50Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1689/priority-manifest.json", "sha256": "bb773192c14cccb2681f64d93963e63e138a392c5a5484f2bcbacbe3ca8bae8c" } ], "source_head": "f87724057cc5fc5192fe2904675a563273612851" } }, { "pr": 1746, "title": "Research: exact P104 port adapter for selected word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1746", "author": "1337isnot1337", "created_at": "2026-10-14T08:29:09Z", "accepted_at": "2026-10-14T16:13:22Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001730427469823602", "kappa_fraction": "865213734911801/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/selected-p104-port-adapter/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/selected-p104-port-adapter/CERTIFICATE.json, research/selected-p104-port-adapter/README.md, research/selected-p104-port-adapter/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/selected-p104-port-adapter/CERTIFICATE.json#/pricing/P112 and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/selected-p104-port-adapter/CERTIFICATE.json#/pricing/bit_cap after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/1746-manifest.json", "sha256": "249a659c8c6e120ce5d04274d9f8b59cae7e1a9823c9d20ea3b1468f8a3a871e" }, { "file": "remaining-record-audit/artifacts/1746/priority-manifest.json", "sha256": "2350b44e3f5e68f20967ada6b681dd8897fd7961fabbf712a61b6fb049f5950d" } ], "source_head": "23bae0f8d16246862524581b742c7a922514bfd5" } }, { "pr": 1749, "title": "Scoped S4 result: four roles do not compress noncommuting 3-cycles below four calls", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1749", "author": "1337isnot1337", "created_at": "2026-10-14T08:36:25Z", "accepted_at": "2026-10-14T16:13:22Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No independent whole-multiplier cutoff is defined by this supplied contribution. Price the explicitly referenced complete algorithm only after binding its actual native/operator, ownership, recursive invoice, precision and outer parameters. Relevant local constants, guards and negative hypotheses remain attached to that target; they are not discarded." ], "source_manifest": [ { "file": "individual-primary-interface-source/1749-manifest.json", "sha256": "0fa861464591e3f25d5a486ed6d8113836673b6596bbf5d9dbdb5f03985ef02d" }, { "file": "remaining-record-audit/artifacts/1749/priority-manifest.json", "sha256": "2a1a11c9816396b88de9d9e1f89aedcc417c703c59146a1875c1e8152fe0f262" } ], "source_head": "90405b9498e4abfdd7d0eececcf11c7e83c6d13b" } }, { "pr": 1790, "title": "Selected PR1094: complete two-role whole-helper swap census (no improving swap)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1790", "author": "navinor", "created_at": "2026-10-14T10:03:09Z", "accepted_at": "2026-10-14T16:18:33Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/1790-manifest.json", "sha256": "07287c65aae44a0da601d8bed8c36f02a3f624fbe0ddc483227ee2f84a982647" }, { "file": "remaining-record-audit/artifacts/1790/priority-manifest.json", "sha256": "4b461bfb710fe809e727c3ce058a236fd885f4cfa3d81e093c12c8022217530d" } ], "source_head": "48ee04ee708081c8713e8868a370bbbf5aa099e1" } }, { "pr": 1824, "title": "Tooling: selected final stage reruns byte-for-byte on CPython 3.10-3.14, reproducing the certificate bytes (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1824", "author": "JosieElliston", "created_at": "2026-10-14T10:59:05Z", "accepted_at": "2026-10-14T16:34:44Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain the exact stated lemma, finite-audit scope, correction or provenance with its actual selected target. A numerical runtime bound requires an actual source-selected full native/owner/recursive invoice/precision/outer realization and exact own commitments. No cutoff follows from unchanged kappa, a scalar lemma or an audit pass." ], "source_manifest": [ { "file": "individual-primary-interface-source/1824-manifest.json", "sha256": "6977b1b09f25a3879ba7103523b28ba57b51440a62b800fde69d15ac93843a75" }, { "file": "remaining-record-audit/artifacts/1824/priority-manifest.json", "sha256": "6aae53c9e734ab9d46c877aea798b4765fa865ab0bcabaace863ea97e1c499e7" } ], "source_head": "ad5b1248f25a71983b20617e2f3a80be22f03990" } }, { "pr": 1797, "title": "Audit: PR1786 fine-prime transfer lemmas checked exactly; outer headroom 1.68e-10 on the PR1699 supplier (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1797", "author": "JosieElliston", "created_at": "2026-10-14T10:16:00Z", "accepted_at": "2026-10-14T16:44:45Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001679754788150048", "kappa_fraction": "52492337129689/31250000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No independent whole-multiplier cutoff is defined by this supplied contribution. Price the explicitly referenced complete algorithm only after binding its actual native/operator, ownership, recursive invoice, precision and outer parameters. Relevant local constants, guards and negative hypotheses remain attached to that target; they are not discarded." ], "source_manifest": [ { "file": "individual-primary-interface-source/1797-manifest.json", "sha256": "b915f77e2beb36e1a2ef804e6a9755d3230f2b2ed8e7e974c2086974204f22b1" }, { "file": "remaining-record-audit/artifacts/1797/priority-manifest.json", "sha256": "373feb444e86f7fa3184966f6681f0aa6101c61c0c1985a94f5bf6728b4c122b" } ], "source_head": "4e8f77031b1a936d6739b2cd84f378dcf1eb5635" } }, { "pr": 2010, "title": "Research: exact five-call minimum for binary tetrahedral mixed triple (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2010", "author": "1337isnot1337", "created_at": "2026-10-14T16:59:44Z", "accepted_at": "2026-10-14T18:04:22Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No independent whole-multiplier cutoff is defined by this supplied contribution. Price the explicitly referenced complete algorithm only after binding its actual native/operator, ownership, recursive invoice, precision and outer parameters. Relevant local constants, guards and negative hypotheses remain attached to that target; they are not discarded." ], "source_manifest": [ { "file": "individual-primary-interface-source/2010-manifest.json", "sha256": "53bcb7f6f91ac02caa92299921ca67d7b6ca36e7ede2e30daf3aa853c4f4cc86" }, { "file": "remaining-record-audit/artifacts/2010/priority-manifest.json", "sha256": "3f6f1d2779d9e630a85e3d7e65dec95965a5f4c5fcaacab77ad9a11e5b6c0db7" } ], "source_head": "125ed77d114e0db0cb2c684494c7a5c90f559d60" } }, { "pr": 1348, "title": "Scoped thresholds: what a coverage-law change must deliver for the selected complex local word (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1348", "author": "navinor", "created_at": "2026-10-13T23:13:01Z", "accepted_at": "2026-10-15T16:56:27Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.01", "kappa_fraction": "1/100", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "A numerical whole-multiplier comparison must separately identify an actual complete selected native/caller/owner/recursive work-height-stock interface and precision/analytic/outer realization. This source-scope disposition neither supplies nor transfers that bound, and does not extend a restricted negative result beyond its stated family." ], "source_manifest": [ { "file": "individual-primary-interface-source/1348-manifest.json", "sha256": "e580d9bd11ef6fc78f2f42142a45dc431be13809c5f908ba227d1e3f6c74eed0" }, { "file": "remaining-record-audit/artifacts/1348/priority-manifest.json", "sha256": "84598b50de318b570b33cf2770de000179d10f1cd60e8608d6d42a6eaa12c4ba" } ], "source_head": "74768ab408b1ae2ce2c7094b49457a86fcb06e94" } }, { "pr": 1142, "title": "Independent verification: selected PR1042 replay-capsule closure (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1142", "author": "martinxxx9", "created_at": "2026-10-13T18:59:53Z", "accepted_at": "2026-10-15T17:18:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672188119205421", "kappa_fraction": "1672188119205421/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No independent whole-multiplier cutoff is defined by this supplied contribution. Price the explicitly referenced complete algorithm only after binding its actual native/operator, ownership, recursive invoice, precision and outer parameters. Relevant local constants, guards and negative hypotheses remain attached to that target; they are not discarded." ], "source_manifest": [ { "file": "individual-primary-interface-source/1142-manifest.json", "sha256": "d74cb054a1942909bddedc22ca3d3d2652949a83b9d5441f4d703c5324b4eae0" }, { "file": "remaining-record-audit/artifacts/1142/priority-manifest.json", "sha256": "f25117500710bca0ea0128265f45d9359d6b1726594dc5701b01211126ba172c" } ], "source_head": "c62ed26b1538e477f96b578f6d9d8a6b176ed363" } }, { "pr": 2169, "title": "Record candidate: T16 owner map from class-level re-solve and guided realisation on the selected supplier (\u03ba=0.001673614205725695), with a proved packing ceiling", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2169", "author": "philippeVV", "created_at": "2026-10-14T21:54:22Z", "accepted_at": "2026-10-15T17:59:16Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001673614205725695", "kappa_fraction": "334722841145139/200000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr2169-gaussian-only-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr2169-gaussian-only-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 7, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/2169/priority-manifest.json", "sha256": "8a52f0110957f18649306eab64b14a193d775a373a49fe9ddcd66c89dec57a19" } ], "source_head": "4452c98ce93b83e696fd285eeb024f6669c145c0" } }, { "pr": 2187, "title": "Research: C4 root-lift obstruction for four outputs (no kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2187", "author": "1337isnot1337", "created_at": "2026-10-14T22:49:54Z", "accepted_at": "2026-10-15T17:59:16Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No independent whole-multiplier cutoff is defined by this supplied contribution. Price the explicitly referenced complete algorithm only after binding its actual native/operator, ownership, recursive invoice, precision and outer parameters. Relevant local constants, guards and negative hypotheses remain attached to that target; they are not discarded." ], "source_manifest": [ { "file": "individual-primary-interface-source/2187-manifest.json", "sha256": "445031a231e849b9ae0486ef39cfc521f8800abedad7448d44df66e16cea9610" }, { "file": "remaining-record-audit/artifacts/2187/priority-manifest.json", "sha256": "23b2ac7cf5ba5b5c84da312bed09fc50d7c9fe190053848de3f1ce44eaaed9fe" } ], "source_head": "46ea5b300f334993972ccf9d9d4f9c19ac8d719d" } }, { "pr": 2217, "title": "Consolidation: PR #211 source-retention receipt and CONTRIBUTORS credit (seed a690c28b, no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2217", "author": "steph4n-gh", "created_at": "2026-10-15T00:12:37Z", "accepted_at": "2026-10-15T18:29:57Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.000683847872495777", "kappa_fraction": "683847872495777/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain exact local evidence and stated restrictions with the named target. A whole-input crossover needs its own source-selected complete native/owner/recursive/precision/outer invoice and all-size realization." ], "source_manifest": [ { "file": "individual-primary-interface-source/2217-manifest.json", "sha256": "7c2e34a17735b2a0e38f7c4701a01f6c0534c33c704c17930710322deb3238c3" }, { "file": "remaining-record-audit/artifacts/2217/priority-manifest.json", "sha256": "9dc5ea579421517a2dac80a4afe0536caf3f55134c8415af95ea62773faaa5a4" } ], "source_head": "0e9667d2bad73efca39a965bec25ebcd8c3762e1" } }, { "pr": 2286, "title": "Audit (no new \u03ba): side-condition coverage of the pending T74 outer at #2044 \u2014 554 written conditions, none load-bearing false; or-True and g\u00b2 review items resolved", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2286", "author": "thakrarsagar", "created_at": "2026-10-15T03:31:40Z", "accepted_at": "2026-10-15T21:18:21Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0016797549561255445", "kappa_fraction": "3359509912251089/2000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain exact local evidence and stated restrictions with the named target. A whole-input crossover needs its own source-selected complete native/owner/recursive/precision/outer invoice and all-size realization." ], "source_manifest": [ { "file": "individual-primary-interface-source/2286-manifest.json", "sha256": "7daa600b4a99c2294fe7f24a19e8af80867b510453895856a5747cf2f142b07d" }, { "file": "remaining-record-audit/artifacts/2286/priority-manifest.json", "sha256": "3b2a7fc6d41ad5a023d21e0e9d18e16e8bb8375a4b08d4269d788057b094a85f" } ], "source_head": "325601ad64b58f10c6fda659851e3acd43bb10b7" } }, { "pr": 2311, "title": "Independent verification: supplier-admission premises of the #2265 substitution traced into PR2260 (0 FALSE / 0 MISSING-PROOF; no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2311", "author": "thakrarsagar", "created_at": "2026-10-15T04:49:12Z", "accepted_at": "2026-10-15T21:18:21Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0016834", "kappa_fraction": "8417/5000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/2311-manifest.json", "sha256": "2b849e8a009a84e946f8a02280aef9b3a389c2064296df902f885973f849d391" }, { "file": "remaining-record-audit/artifacts/2311/priority-manifest.json", "sha256": "432004d0fc74e352ad8bb55216c83944833a3902b16ac09d21820dfc16c1fdc3" } ], "source_head": "00de1b48c3155846ee340993eeb9e9d7daf157af" } }, { "pr": 2315, "title": "Independent verification (no new \u03ba): record candidate #2269 T74 borrow43 \u2014 words, 437-helper fill and moment root reproduce; stale evidence, unpriced buffers, X2 open", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2315", "author": "thakrarsagar", "created_at": "2026-10-15T04:54:21Z", "accepted_at": "2026-10-15T21:54:48Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0016962471390584742", "kappa_fraction": "8481235695292371/5000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep the actual named multiplier/changedprogram as a distinct costing target. This contribution is validation, a restricted theorem or an unimplementedtarget; it defines no new fullruntime point. Its target-specific scope/negative controls/constant qualifications must be checked when a complete supplier is priced." ], "source_manifest": [ { "file": "individual-primary-interface-source/2315-manifest.json", "sha256": "1a369881995e2391b634b6bac90c9555e682b92c3cf5d5ddf9c1aeb777a9cb4a" }, { "file": "remaining-record-audit/artifacts/2315/priority-manifest.json", "sha256": "64867f9d763c42ea77b4e41369f54be624bb5a594d6f3e0af003e66de4798c88" } ], "source_head": "4a2f20ea339e30348448096ca789d0efe55df9bb" } }, { "pr": 1155, "title": "Research note: restoration coalescing across a recursion batch (read-free + composable-family boundary; no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1155", "author": "navinor", "created_at": "2026-10-13T19:16:20Z", "accepted_at": "2026-10-15T23:58:39Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "A numerical whole-multiplier comparison must separately identify an actual complete selected native/caller/owner/recursive work-height-stock interface and precision/analytic/outer realization. This source-scope disposition neither supplies nor transfers that bound, and does not extend a restricted negative result beyond its stated family." ], "source_manifest": [ { "file": "individual-primary-interface-source/1155-manifest.json", "sha256": "e2d1284449f7814c187d9a0f1129daed20861d3bc10c2588204487b2e7a44d32" }, { "file": "remaining-record-audit/artifacts/1155/priority-manifest.json", "sha256": "82baf78929df299ed3a89f11430787dcdd320c24e502db7a23aa3be23457b7a0" } ], "source_head": "02c9e171c98b1b4de4d2107b0134cee4446e10e0" } }, { "pr": 2406, "title": "Research: cap T74 scalar and handoff frame refits at b < 0.0016972", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2406", "author": "jeremydiviney", "created_at": "2026-10-15T07:45:52Z", "accepted_at": "2026-10-15T23:58:39Z", "acceptance_basis": "github_merged_at", "kappa_decimal": null, "kappa_fraction": null, "kappa_status": "no_selected_positive_source_kappa", "kappa_scope": "Documented projection, retraction, mechanism objection or scope exclusion; see flags.", "source_status": "scope-flagged", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater" ], "historical_status": "candidate_source_ambiguous_requires_primary_read", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 179, "source_index": 289, "at": "2026-10-15T07:45:52Z", "until": "2026-10-15T09:42:03Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.0016972", "dashboard_float_text": "0.0016972", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2406", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 212, "source_index": null, "at": "2026-10-15T07:45:52Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.0016972", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2406", "evidence_excerpt": "The leading PR2322/2374 T74 words leave a concrete question after owner optimization: can changing their intermediate frames, including the entry/exit charts of fixed logical handoffs, materially improve the primitive saving? This package proves **b < 0.0016972** for that broader model, with arbitrary fractional whole-helper packing on the unchanged T74 stock. **No higher \u03ba is claimed.**", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain exact local evidence and stated restrictions with the named target. A whole-input crossover needs its own source-selected complete native/owner/recursive/precision/outer invoice and all-size realization." ], "source_manifest": [ { "file": "individual-primary-interface-source/2406-manifest.json", "sha256": "cb323cf1c9aceebec67e884989b8804eb11f2a6d8aa115f6fabe25c922f08724" }, { "file": "remaining-record-audit/artifacts/2406/priority-manifest.json", "sha256": "240448511a3bb2e6342232bc20fb088358dd24818bd28f4e5af60a9890ff582b" } ], "source_head": "626ce8eddf5569d270a3422954f9a3ce90f16942" } }, { "pr": 2442, "title": "Audit (no \u03ba): exact owner-fill optima on the T74 handoff line \u2014 #2374's fill is optimal over all fills; #2435's fill leaves +5.8e-10 (pattern optimum certified)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2442", "author": "thakrarsagar", "created_at": "2026-10-15T10:07:09Z", "accepted_at": "2026-10-16T00:25:04Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0016971949509", "kappa_fraction": "16971949509/10000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep the actual named multiplier/changedprogram as a distinct costing target. This contribution is validation, a restricted theorem or an unimplementedtarget; it defines no new fullruntime point. Its target-specific scope/negative controls/constant qualifications must be checked when a complete supplier is priced." ], "source_manifest": [ { "file": "individual-primary-interface-source/2442-manifest.json", "sha256": "1c28bf9c47120e3dcc085609b65f1c8683b369c0a4836f7f36c90c4e0a4c033a" }, { "file": "remaining-record-audit/artifacts/2442/priority-manifest.json", "sha256": "c02c4bd28252fed1a2221f64a34e7c83a40558ade9ceafa214e33be3457dad0a" } ], "source_head": "435e5c412fcad664cef2b52cf6adf1c9f23ffc87" } }, { "pr": 2446, "title": "Independent verification (no \u03ba): #2435's words, 289,044-role owner map and endpoint reproduce; its change is frame-only (24 raised entrances), entrance delivery unchecked", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2446", "author": "thakrarsagar", "created_at": "2026-10-15T10:32:51Z", "accepted_at": "2026-10-16T00:25:04Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0016985113437", "kappa_fraction": "16985113437/10000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep the actual named multiplier/changedprogram as a distinct costing target. This contribution is validation, a restricted theorem or an unimplementedtarget; it defines no new fullruntime point. Its target-specific scope/negative controls/constant qualifications must be checked when a complete supplier is priced." ], "source_manifest": [ { "file": "individual-primary-interface-source/2446-manifest.json", "sha256": "e768d853463c7f112a2b879e9d0ad911767d7249d5fb081de47d1c357613308c" }, { "file": "remaining-record-audit/artifacts/2446/priority-manifest.json", "sha256": "c0fc4f01b86b113335bf73246818dddb35df6ddc232c0802abbc40d501dcebfc" } ], "source_head": "a3aabff9471dfdc3e85b065616e45a317f38882e" } }, { "pr": 2466, "title": "Independent verification (no \u03ba): #2447's owner fill is exactly the certified optimum for #2435's words; the same optimum in 4 role moves (fewer charts)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2466", "author": "thakrarsagar", "created_at": "2026-10-15T11:46:31Z", "accepted_at": "2026-10-16T00:25:04Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001698511924002761", "kappa_fraction": "1698511924002761/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t74-2435-optimal-owner-map/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/t74-2435-optimal-owner-map/README.md, research/t74-2435-optimal-owner-map/SOURCES.json, research/t74-2435-optimal-owner-map/TASK.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/t74-2435-optimal-owner-map/README.md, research/t74-2435-optimal-owner-map/SOURCES.json, research/t74-2435-optimal-owner-map/TASK.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/2466-manifest.json", "sha256": "14f947e2996d3cfee8e29a973113e267875de9f9c09166afc1486a803955513e" }, { "file": "remaining-record-audit/artifacts/2466/priority-manifest.json", "sha256": "d495736bf88663ba3847f57350a353470027e62df0832a629c0836c47f4d08af" } ], "source_head": "0804003fadf7779176d95f0da2c08a118b8884f0" } }, { "pr": 2423, "title": "Bit construction (no \u03ba; conditional on #1043): R438 + one transport + optimal window-respecting re-hosting \u2192 c = 0.0017348463 (+0.082% vs #589); fixes two #1345 atlas crashes", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2423", "author": "thakrarsagar", "created_at": "2026-10-15T09:03:43Z", "accepted_at": "2026-10-16T00:37:03Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0016726602", "kappa_fraction": "8363301/5000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/bit-r438-transport-rehost/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/bit-r438-transport-rehost/README.md, research/bit-r438-transport-rehost/SOURCES.json, research/bit-r438-transport-rehost/TASK.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/bit-r438-transport-rehost/README.md, research/bit-r438-transport-rehost/SOURCES.json, research/bit-r438-transport-rehost/TASK.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/2423-manifest.json", "sha256": "7d6817c43606259f9811cfae94cdbe9bfdd24958946b126c2c325294c0c89977" }, { "file": "remaining-record-audit/artifacts/2423/priority-manifest.json", "sha256": "5f0241903c55a445569ebd9e536c0dac6a7e9f605fbeef3674dfc2f45b5d72e9" } ], "source_head": "13cd273dc13c98244b1f9bcf588b6e828cbc0347" } }, { "pr": 2578, "title": "Independent review: PR1731 rectangular batching and radix-distributed union schedule (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2578", "author": "rtyu193-rgb", "created_at": "2026-10-15T15:06:15Z", "accepted_at": "2026-10-16T01:53:57Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001678123830633547", "kappa_fraction": "1678123830633547/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep the actual named multiplier/changedprogram as a distinct costing target. This contribution is validation, a restricted theorem or an unimplementedtarget; it defines no new fullruntime point. Its target-specific scope/negative controls/constant qualifications must be checked when a complete supplier is priced." ], "source_manifest": [ { "file": "individual-primary-interface-source/2578-manifest.json", "sha256": "8baa6b8cc6f8c9d612fec3ad3055a49c051ef0332f0839fa0929725da26e5481" }, { "file": "remaining-record-audit/artifacts/2578/priority-manifest.json", "sha256": "f93f23efd7755a563525e10e507f0b214b624368fdc0a4e99271e74c8e5cd60f" } ], "source_head": "9cbf085815c94ac1b72bef9703f64b23cdea71ce" } }, { "pr": 2705, "title": "KB1c: admission-ready evidence for the typed-window z4 typed-echo schedule (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2705", "author": "navinor", "created_at": "2026-10-15T17:54:35Z", "accepted_at": "2026-10-16T03:35:09Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672188119205421", "kappa_fraction": "1672188119205421/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep the actual named multiplier/changedprogram as a distinct costing target. This contribution is validation, a restricted theorem or an unimplementedtarget; it defines no new fullruntime point. Its target-specific scope/negative controls/constant qualifications must be checked when a complete supplier is priced." ], "source_manifest": [ { "file": "individual-primary-interface-source/2705-manifest.json", "sha256": "525416208c549454db5326a1a57363ce44dee76b320b6167ba66554ccbb7448c" }, { "file": "remaining-record-audit/artifacts/2705/priority-manifest.json", "sha256": "e10b6d046110b07ed8aa27540f3ef7e9008aff090662fd4cecd1092843f0f65d" } ], "source_head": "124cab4118e39d30c2c24b41d753dabf612c8a8c" } }, { "pr": 2847, "title": "Independent verification: #2802's seven-stage increment over #2751 (retired5 + retired7 stages) passes 28/28 rules and 20/20 controls; covers #2818's identical construction (no \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2847", "author": "thakrarsagar", "created_at": "2026-10-16T02:17:53Z", "accepted_at": "2026-10-16T08:06:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001714849224721887", "kappa_fraction": "1714849224721887/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Preserve the actual increment proof and named negative controls with2802/2818. Their full native/owner/invoice/precision/outer cost obligations must be audited at those own source entries; this verification report supplies no distinct runtime to plot." ], "source_manifest": [ { "file": "individual-primary-interface-source/2847-manifest.json", "sha256": "c023c1ed2103b489a12371d080060495c3903386bbb9f79864fb0010139834f5" }, { "file": "remaining-record-audit/artifacts/2847/priority-manifest.json", "sha256": "9aeeccee2541475828afaf57b5252f0e7f55885a762a52839813079bfb77e1df" } ], "source_head": "f3786fa5d7e28d643f0efaf7d75089cb2909b337" } }, { "pr": 801, "title": "Research: certified format ceilings for Eisenstein/Gaussian/Hurwitz E8 copy floors (no \u03ba claim)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/801", "author": "Rohansguliani", "created_at": "2026-10-13T05:55:43Z", "accepted_at": "2026-10-16T09:08:58Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.01", "kappa_fraction": "1/100", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 3, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No independent whole-multiplier cutoff is defined by this supplied contribution. Price the explicitly referenced complete algorithm only after binding its actual native/operator, ownership, recursive invoice, precision and outer parameters. Relevant local constants, guards and negative hypotheses remain attached to that target; they are not discarded." ], "source_manifest": [ { "file": "individual-primary-interface-source/801-manifest.json", "sha256": "2278845dc8bfc33fa940d0278dbfe4eb8a50cff5beed9b815147d4bbffe6a3b7" }, { "file": "remaining-record-audit/artifacts/801/priority-manifest.json", "sha256": "1a58d2e06319645f803f37310fe7080568f5883b945fb39a3f166eee4b898e52" } ], "source_head": "f0758653a5a1f72c3b59e58d6fe8d658db20b50b" } }, { "pr": 2537, "title": "Tooling improvement: output-identical fraction-free null_exact fast path for recycled-bit --all exact nesting", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2537", "author": "thakrarsagar", "created_at": "2026-10-15T13:53:57Z", "accepted_at": "2026-10-16T09:57:03Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.000472154791", "kappa_fraction": "472154791/1000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "supporting_verification_tooling_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Bind the separately referenced complete integer construction and its actual physical/invoice/parameter changes before assigning a numerical cutoff; this source interface/tooling result creates no independent runtime point." ], "source_manifest": [ { "file": "finite-bridge-source-expansion/2537-manifest.json", "sha256": "a7c48c8304f3d00d9cf748cb6f67c04350cb270cca652143bbc96c77fa019cab" } ], "source_head": "222063b96ec1a109a8c9f40e5d615498a737c6dd" } }, { "pr": 2219, "title": "Record P104 private descent fanout reuse construction", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2219", "author": "1337isnot1337", "created_at": "2026-10-15T00:25:20Z", "accepted_at": "2026-10-16T10:37:05Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/p104-private-descent-reuse-seed915fa969/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/p104-private-descent-reuse-seed915fa969/NATIVE-RESULT.json, research/p104-private-descent-reuse-seed915fa969/README.md, research/p104-private-descent-reuse-seed915fa969/TASK.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/p104-private-descent-reuse-seed915fa969/NATIVE-RESULT.json, research/p104-private-descent-reuse-seed915fa969/README.md, research/p104-private-descent-reuse-seed915fa969/TASK.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/p104-private-descent-reuse-seed915fa969/TASK.json#/selected_result after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2219-manifest.json", "sha256": "554b547c7d40747a61d28568221c2e6ff95782c19603418ad7b53124c5bca906" }, { "file": "remaining-record-audit/artifacts/2219/priority-manifest.json", "sha256": "0f6d94d4ceac5e72c066d7216fe6fd7788dc150c5de4c1ff2e424eaeb055fdfc" } ], "source_head": "3f913bc17276b68f0c9008a1202b6ce588e77ff6" } }, { "pr": 2904, "title": "Research: T185 dirty-entry and frame-refit screens on the #2863/#2894 words (negative result, no \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2904", "author": "digitalis-p", "created_at": "2026-10-16T09:19:06Z", "accepted_at": "2026-10-16T12:05:57Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001720100805416885927943999999999999999999999900000000000", "kappa_fraction": "17201008054168859279439999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep the actual named multiplier/changedprogram as a distinct costing target. This contribution is validation, a restricted theorem or an unimplementedtarget; it defines no new fullruntime point. Its target-specific scope/negative controls/constant qualifications must be checked when a complete supplier is priced." ], "source_manifest": [ { "file": "individual-primary-interface-source/2904-manifest.json", "sha256": "f84ec5003ccb5625544989de4ac3982d086fc6236577d5fc84c26ae20a779f2a" }, { "file": "remaining-record-audit/artifacts/2904/priority-manifest.json", "sha256": "4a51445aa2242859199f2f88c10e5ac0ae66e0464fcc9f8038d96b8e0be7aa27" } ], "source_head": "c291ad5cc6c0f4bd7a3319855202d2f753bebb17" } }, { "pr": 2464, "title": "KB1 supplier instantiation of the certified z4 typed echo: priced whole construction, exact moments and a < D/E, one hosting obstruction (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2464", "author": "navinor", "created_at": "2026-10-15T11:32:04Z", "accepted_at": "2026-10-16T13:13:09Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001730427469823602", "kappa_fraction": "865213734911801/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/z4-typed-echo-supplier-instance/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/z4-typed-echo-supplier-instance/README.md, research/z4-typed-echo-supplier-instance/RESULT.json, research/z4-typed-echo-supplier-instance/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/z4-typed-echo-supplier-instance/README.md, research/z4-typed-echo-supplier-instance/RESULT.json, research/z4-typed-echo-supplier-instance/SOURCES.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/z4-typed-echo-supplier-instance/TASK.json#/selected_record after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2464-manifest.json", "sha256": "abe21a2ae04511239d52e2e2c8ea665ec157ca95ab04100b5925456e698925fa" }, { "file": "remaining-record-audit/artifacts/2464/priority-manifest.json", "sha256": "f401e0f960026915ccb5fc4e9844771e02d570d9299ed822fce6ec71de2ebeb9" } ], "source_head": "5c44715b6fa0806ad828e42fb53b84f6b5f7ddc6" } }, { "pr": 654, "title": "Conditional \u03ba = 0.001651390457077212: PR648 complex supplier with the merged #589 bit supplier (outdated, independent)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/654", "author": "GamingPuzzled", "created_at": "2026-10-13T02:00:47Z", "accepted_at": "2026-10-16T13:35:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001651390457077212", "kappa_fraction": "412847614269303/250000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr654-gaussian-only-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 103, "source_index": 152, "at": "2026-10-13T02:00:47Z", "until": "2026-10-13T03:30:54Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001651390457077212", "dashboard_float_text": "0.001651390457077212", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/654", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 120, "source_index": null, "at": "2026-10-13T02:00:47Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001651390457077212", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/654", "evidence_excerpt": "\u03ba = **412847614269303/250000000000000000 = 0.001651390457077212**, +0.01781% over #648 (0.001651096360425895). The complex side binds.", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr654-gaussian-only-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 7, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/654/priority-manifest.json", "sha256": "6f42205a984583d1f017781648107c570bff32cb4a7227df0b10cbf55c61c514" } ], "source_head": "a935a545760946489bd6f26fe5349a10820316c2" } }, { "pr": 669, "title": "Research: exact star-decoder hierarchies, target budgets, and COPY bounds", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/669", "author": "the-missionary-company", "created_at": "2026-10-13T03:27:58Z", "accepted_at": "2026-10-16T13:35:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661957774647029", "kappa_fraction": "1661957774647029/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/asymmetric-hypercube-decoder/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/asymmetric-hypercube-decoder/BOUNDARY-RESULTS.json, research/asymmetric-hypercube-decoder/CLAIM.json, research/asymmetric-hypercube-decoder/README.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/asymmetric-hypercube-decoder/BOUNDARY-RESULTS.json, research/asymmetric-hypercube-decoder/CLAIM.json, research/asymmetric-hypercube-decoder/README.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/asymmetric-hypercube-decoder/SOURCES.json#/selected_context after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/669-manifest.json", "sha256": "1b6932a234cfc186991ea399375f0c745ffaddd6197115c9738396612967359f" }, { "file": "remaining-record-audit/artifacts/669/priority-manifest.json", "sha256": "9c574989ea8cb069f7521c211e5e6419fb8a02f1c9b168e797c8354dc595d6f7" } ], "source_head": "8f4600b41bf1f0f5d07f209e5d3950eb22ef5cad" } }, { "pr": 1175, "title": "Conditional kappa 0.001675338871723469: whole-owner map at the packin\u2026", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1175", "author": "gvconly", "created_at": "2026-10-13T19:41:15Z", "accepted_at": "2026-10-16T13:35:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001675867534384272", "kappa_fraction": "104741720899017/62500000000000000", "kappa_status": "authenticated_actual_merged_source_selection", "kappa_scope": "The costed \u03ba comes from the explicitly selected source included at this merge. The original parser quote is retained and visibly distinguished. Actual final own CLAIM names the sixth-layer mixed-arcflow head package; own MANIFEST/RESULT/verifier/SPEC agree. Exact raw recipes and two complete native providers plus full PLAN/OWNERS/invoice are independently reconstructed. Earlier historical title/body arcflow fixture is preserved separately, not selected.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1175-final-mixed-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "frozen_kappa_metadata": { "kappa_fraction": "1675338871723469/1000000000000000000", "kappa_decimal": "0.001675338871723469", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews." }, "source_selected_kappa_correction": true, "source_selected_kappa_correction_basis": "Actual final own CLAIM names the sixth-layer mixed-arcflow head package; own MANIFEST/RESULT/verifier/SPEC agree. Exact raw recipes and two complete native providers plus full PLAN/OWNERS/invoice are independently reconstructed. Earlier historical title/body arcflow fixture is preserved separately, not selected.", "source_kappa_correction_primary_receipt": "data/operation-audit/pr1175-final-mixed-source/plot-chronology-primary-receipt.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1175-final-mixed-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 7, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1175/priority-manifest.json", "sha256": "39833394445643e508e65cc6d6390e0a14722d936f1e2d797216233fba733d3b" } ], "source_head": "007a7c64280053e2ddabdb92e60b51bfd9105119" } }, { "pr": 1337, "title": "Scoped negative result: no further helper-donor kernels or exact read re-timings on the #1297/#1305/#1324 words (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1337", "author": "mdumitrean", "created_at": "2026-10-13T23:03:04Z", "accepted_at": "2026-10-16T13:35:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001677380107853623", "kappa_fraction": "1677380107853623/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep the actual named multiplier/changedprogram as a distinct costing target. This contribution is validation, a restricted theorem or an unimplementedtarget; it defines no new fullruntime point. Its target-specific scope/negative controls/constant qualifications must be checked when a complete supplier is priced." ], "source_manifest": [ { "file": "individual-primary-interface-source/1337-manifest.json", "sha256": "38b3d1e7e37706b9ca03d8a88843dd88e9800d09beedb2e22d11184aef8403c5" }, { "file": "remaining-record-audit/artifacts/1337/priority-manifest.json", "sha256": "d2d80bc892432b5e51034be79cee751944d60d44e143fe94c1e4e31c17556c12" } ], "source_head": "c9da5f270d6a10f571a65cb3449230bdcc76df32" } }, { "pr": 2363, "title": "Improve conditional \u03ba to 0.001697147064845350 with whole-role augmenting paths", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2363", "author": "mason-hale", "created_at": "2026-10-15T06:38:53Z", "accepted_at": "2026-10-16T13:35:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00169714706484535", "kappa_fraction": "33942941296907/20000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 177, "source_index": 287, "at": "2026-10-15T06:38:53Z", "until": "2026-10-15T06:53:55Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001697147064845350", "dashboard_float_text": "0.00169714706484535", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2363", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 210, "source_index": null, "at": "2026-10-15T06:38:53Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001697147064845350", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2363", "evidence_excerpt": "Improve conditional \u03ba to 0.001697147064845350 with whole-role augmenting paths", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 488, "source_index": null, "at": "2026-10-15T06:38:53Z", "until": null, "date_basis": "body-version", "fraction": "33942941296907/20000000000000000", "value_decimal": "0.001697147064845350", "dashboard_float_text": null, "expression": "0.001697147064845350", "historical_title": "Improve conditional \u03ba to 0.001697147064845350 with whole-role augmenting paths", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2363", "evidence_excerpt": "mit a better complete owner assignment. This construction raises the conditional published point to \u03ba = 0.001697147064845350, above concurrent PR2349's full rational 0.0016970659941088806668214121951845796408\u2026. The gain over PR2349 is approximately 8.10707365e-8, or 0.004777% of \u03ba. This is an incrementa", "automated_comparable": true, "body_sha256": "d47594068602812973a12c593d0e39b25ad5e003be26088f2c8a17f89324d9e5" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t74-owner-augmenting-paths/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Recompute the complete own productive/paid histogram from research/t74-owner-augmenting-paths/evidence/PHYSICAL-INVOICE.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/t74-owner-augmenting-paths/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2363-manifest.json", "sha256": "47fe0e844c1764f450423b1d1ce8613c57607829103a6a4a047975181221c5cf" }, { "file": "remaining-record-audit/artifacts/2363/priority-manifest.json", "sha256": "aa7421b8b74e415698863dba4d759e433833b73011729902191528b316551eaf" } ], "source_head": "d815dbe374096f1b96a224a2dcb6a9167c5cfa91" } }, { "pr": 2839, "title": "Tensor block norm accounting: T114 raises conditional kappa by 5.160482894338e-11", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2839", "author": "Dugongue", "created_at": "2026-10-16T01:34:08Z", "accepted_at": "2026-10-16T13:35:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001717795274221416686577999999999999999999999900000000000", "kappa_fraction": "17177952742214166865779999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 12, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/tensor-block-kappa/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/tensor-block-kappa/CLAIM.json, research/tensor-block-kappa/validation/NATIVE.json, research/tensor-block-kappa/PROOF.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/tensor-block-kappa/CLAIM.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/tensor-block-kappa/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2839-manifest.json", "sha256": "945de15e1a60a0d4610fcd2d9634c82deacab1fc97e430f84fd341327846d741" }, { "file": "remaining-record-audit/artifacts/2839/priority-manifest.json", "sha256": "57d428e05fe6bb82632542cb8822d5021b07787d936b3b553a6b06311ed4bb9c" } ], "source_head": "2fdd289fcd0896f4691f9dd78a8bf1511573e434" } }, { "pr": 2848, "title": "T248 residue exchange: conditional \u03ba \u2248 0.00171865850830493", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2848", "author": "Lyy-iiis", "created_at": "2026-10-16T02:23:34Z", "accepted_at": "2026-10-16T13:35:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001718658508304930004818999999999999999999999900000000000", "kappa_fraction": "17186585083049300048189999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 202, "source_index": 318, "at": "2026-10-16T02:23:35Z", "until": "2026-10-16T02:49:56Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001718658508304930004819", "dashboard_float_text": "0.00171865850830493", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2848", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 236, "source_index": null, "at": "2026-10-16T02:23:35Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001718658508304930004819", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2848", "evidence_excerpt": "The conditional modern outer target is **\u03ba = 0.001718658508304930004819 \u2212 10\u207b\u2074\u2076 \u2212 10\u207b\u2077\u2070**, exactly **2.30463210106193e\u221210** above PR2843's full pinned headline. This is an actual allocation improvement, not a decimal refinement. Only `research/t248-dirtentry-residue/` is added; the selected frontier is unchanged.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 516, "source_index": null, "at": "2026-10-16T02:23:34Z", "until": null, "date_basis": "body-version", "fraction": "17186585083049300048189999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "value_decimal": "0.001718658508304930004819", "dashboard_float_text": null, "expression": "0.001718658508304930004819 - 10^-46 - 10^-70", "historical_title": "T248 residue exchange: conditional \u03ba \u2248 0.00171865850830493", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2848", "evidence_excerpt": "ds and all other calls, bridges, owners and costs retained.\n\nThe conditional modern outer target is \u03ba = 0.001718658508304930004819 - 10^-46 - 10^-70, exactly 2.30463210106193e-10 above PR2843's full pinned headline. This is an actual allocation improvement, not a decimal refinement. Only research/t248-dirtentry-residue/ is add", "automated_comparable": true, "body_sha256": "d79f5a9caceac68ed4f416910756605af2bbbca517a03acbac7de5792e8c2d74" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t248-dirtentry-residue/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/t248-dirtentry-residue/CLAIM.json, research/t248-dirtentry-residue/evidence/full/candidate/RESULT.json, research/t248-dirtentry-residue/evidence/full/candidate/owners/RESULT.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/t248-dirtentry-residue/CLAIM.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/t248-dirtentry-residue/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2848-manifest.json", "sha256": "eeb25ef6f812b821e3532e80bd5f874891b8773ed2555bef30457d8bc840adc0" }, { "file": "remaining-record-audit/artifacts/2848/priority-manifest.json", "sha256": "69df5e86d4ccd3964b93adb8b79b16baaddee5147306280bb5d9047d1a4fd73c" } ], "source_head": "c50d12e4720cd1fef2b5a65e337e37de9731879a" } }, { "pr": 2855, "title": "Apply the atlas: T372 concentration, mixed-fibre bounds and exact recovery", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2855", "author": "Dugongue", "created_at": "2026-10-16T03:35:14Z", "accepted_at": "2026-10-16T13:35:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001718659357407250209978999999999999999999999900000000000", "kappa_fraction": "17186593574072502099789999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/atlas-frontier-applications/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Recompute the complete own productive/paid histogram from research/atlas-frontier-applications/evidence/PREFIX-AND-INVOICE.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/atlas-frontier-applications/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2855-manifest.json", "sha256": "185431dcfe1b4ad22a7cb7c3f17bcb51657fae248c821c0bbe0d37d0868c7bac" }, { "file": "remaining-record-audit/artifacts/2855/priority-manifest.json", "sha256": "25947dc05fa5d349395b6e588cf0512c91877fca305dbbb20241ea0473e3b4d1" } ], "source_head": "90c52db35dd2f8cdf0dd81976e698a6192a09126" } }, { "pr": 2857, "title": "Improve conditional \u03ba to 0.00172009662868483 with shared kernels", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2857", "author": "Lyy-iiis", "created_at": "2026-10-16T03:50:52Z", "accepted_at": "2026-10-16T13:35:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001720096628684832600971999999999999999999999900000000000", "kappa_fraction": "17200966286848326009719999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 205, "source_index": 324, "at": "2026-10-16T03:50:54Z", "until": "2026-10-16T04:47:29Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001720096628684832600972", "dashboard_float_text": "0.0017200966286848327", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2857", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 239, "source_index": null, "at": "2026-10-16T03:50:54Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001720096628684832600972", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2857", "evidence_excerpt": "`\u03ba = 0.001720096628684832600972 \u2212 10^-46 \u2212 10^-70`.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 519, "source_index": null, "at": "2026-10-16T03:50:52Z", "until": null, "date_basis": "body-version", "fraction": "17200966286848326009719999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "value_decimal": "0.001720096628684832600972", "dashboard_float_text": null, "expression": "0.001720096628684832600972 - 10^-46 - 10^-70", "historical_title": "Improve conditional \u03ba to 0.00172009662868483 with shared kernels", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2857", "evidence_excerpt": "w chronological allocation, completing the conditional finite supplier and modern outer release at\n\n\u03ba = 0.001720096628684832600972 - 10^-46 - 10^-70.\n\nThe exact gain over #2848 (c50d12e4720cd1fef2b5a65e337e37de9731879a) is 1438120379902596153 / 10^24 \u2248 1.43812e-6. The exact comparator also exceeds concurrent #2853 (d01045dfb67", "automated_comparable": true, "body_sha256": "6b0378cc75900a845faaa80eb14133f1f4d44227a0e5707839242b90e4c1f3bd" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/shared-kernel-repacking/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/shared-kernel-repacking/CLAIM.json, research/shared-kernel-repacking/evidence/full/candidate/RESULT.json, research/shared-kernel-repacking/evidence/full/candidate/owners/RESULT.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/shared-kernel-repacking/CLAIM.json, research/shared-kernel-repacking/evidence/full/candidate/RESULT.json, research/shared-kernel-repacking/evidence/full/candidate/owners/RESULT.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/shared-kernel-repacking/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2857-manifest.json", "sha256": "4ef741d5480754a39e2c78d81dddab9c5a17c4efcb372eaf7cbe68c70ab0f128" }, { "file": "remaining-record-audit/artifacts/2857/priority-manifest.json", "sha256": "5d11817cbe4385190e67aa53d569c109bc843082c38346195acb52831179733f" } ], "source_head": "0b2e2537b368a0cade07ce3f71452ea018ebe394" } }, { "pr": 2875, "title": "Research: reproduce T185 and certify a precision-only kappa refinement", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2875", "author": "digitalis-p", "created_at": "2026-10-16T06:29:17Z", "accepted_at": "2026-10-16T13:35:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001720100805416885927944007075606335531200000000000000000", "kappa_fraction": "172010080541688592794400707560633553119999999999999999999998999999999999999999999999/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 241, "source_index": null, "at": "2026-10-16T06:29:17Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.0017201008054168859279440070756063355312", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2875", "evidence_excerpt": "- After: `0.0017201008054168859279440070756063355312 - 10^-62 - 10^-86`.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 521, "source_index": null, "at": "2026-10-16T06:29:17Z", "until": null, "date_basis": "manual-source-reconciliation", "fraction": "172010080541688592794400707560633553119999999999999999999998999999999999999999999999/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "value_decimal": "0.0017201008054168859279440070756063355312", "dashboard_float_text": null, "expression": "0.0017201008054168859279440070756063355312-10^-62-10^-86", "historical_title": "Research: reproduce T185 and certify a precision-only kappa refinement", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2875", "evidence_excerpt": "", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_own_source_selector_required; actual own source selector; expected 172010080541688592794400707560633553119999999999999999999998999999999999999999999999/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000; Read actual author-head CLAIM/verifier/SOURCES/MANIFEST and identify the selected complete kernel. A missing exact claim-kappa SPEC match is a discovery limitation, not mathematical rejection. Different quoted fixtures must not override a later actual final package. All listed SPEC candidates remain unselected until independently authenticated." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/2875/priority-manifest.json", "sha256": "fe247f00a5b4adb471be36599959ce4ca580873d958351c781c67ab2d94523d3" } ], "source_head": "4c60a82f183d1ba5e15007ab832c9eaca5d59a06" } }, { "pr": 2908, "title": "Conditional \u03ba \u2248 0.001720398337: two-sided helper extraction and charged T74 packing", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2908", "author": "jeremydiviney", "created_at": "2026-10-16T10:07:46Z", "accepted_at": "2026-10-16T13:35:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001720398337354237885930999999999999999999999900000000000", "kappa_fraction": "17203983373542378859309999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 207, "source_index": 328, "at": "2026-10-16T10:07:46Z", "until": "2026-10-16T10:52:06Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001720398337354237885931", "dashboard_float_text": "0.0017203983373542378", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2908", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 242, "source_index": null, "at": "2026-10-16T10:07:46Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001720398337354237885931", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2908", "evidence_excerpt": "The complete T74 owner repair and finite/outer release give **conditional \u03ba = 0.001720398337354237885931 \u2212 10\u207b\u2074\u2076 \u2212 10\u207b\u2077\u2070**, a gain of **2.13808976768352857\u00d710\u207b\u2077** over #2894 at `18d03c447886895ef9abf888398178e0428533ca` (about 0.0124%). Keeping the inherited allocation loses; 545 same-call width exchanges and 222 checked relocations realize the gain. No packing optimality or unconditional multiplication theorem is claimed.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 523, "source_index": null, "at": "2026-10-16T10:07:46Z", "until": null, "date_basis": "body-version", "fraction": "17203983373542378859309999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "value_decimal": "0.001720398337354237885931", "dashboard_float_text": null, "expression": "0.001720398337354237885931 - 10^-46 - 10^-70", "historical_title": "Conditional \u03ba \u2248 0.001720398337: two-sided helper extraction and charged T74 packing", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2908", "evidence_excerpt": " 66,795 physical families.\n\nThe complete T74 owner repair and finite/outer release give conditional \u03ba = 0.001720398337354237885931 - 10^-46 - 10^-70, a gain of 2.13808976768352857*10^-7 over #2894 at 18d03c447886895ef9abf888398178e0428533ca (about 0.0124%). Keeping the inherited allocation loses; 545 same-call width exchanges ", "automated_comparable": true, "body_sha256": "266129c8b64220825361cd4f31ebe1088d00a9a9d65718d3fa98385a1fcd6390" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/two-sided-helper-extraction/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/two-sided-helper-extraction/CLAIM.json, research/two-sided-helper-extraction/allocation/RESULT.json, research/two-sided-helper-extraction/allocation/baseline/CLAIM.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/two-sided-helper-extraction/allocation/RESULT.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/two-sided-helper-extraction/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2908-manifest.json", "sha256": "41af01cc334c34d14a3813bbc6867df0f35c571d9b23ac9959582bc20a47c9f2" }, { "file": "remaining-record-audit/artifacts/2908/priority-manifest.json", "sha256": "3b694f9fd7a081a13f47bbbd35a337e9ecdc3b0877f488ec6ed6e83e728fbb57" } ], "source_head": "51309592971e3b5be935599eed2a95404dc7781e" } }, { "pr": 2917, "title": "Conditional \u03ba \u2248 0.001721588647: nine additional paired helper extractions", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2917", "author": "mason-hale", "created_at": "2026-10-16T10:52:06Z", "accepted_at": "2026-10-16T13:35:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001721588647197801880604999999999999999999999900000000000", "kappa_fraction": "17215886471978018806049999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 208, "source_index": 329, "at": "2026-10-16T10:52:06Z", "until": "2026-10-16T12:18:36Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001721588647197801880605", "dashboard_float_text": "0.0017215886471978019", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2917", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 243, "source_index": null, "at": "2026-10-16T10:52:06Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001721588647197801880605", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2917", "evidence_excerpt": "**\u03ba = 0.001721588647197801880605 \u2212 10\u207b\u2074\u2076 \u2212 10\u207b\u2077\u2070**,", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 524, "source_index": null, "at": "2026-10-16T10:52:06Z", "until": null, "date_basis": "body-version", "fraction": "17215886471978018806049999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "value_decimal": "0.001721588647197801880605", "dashboard_float_text": null, "expression": "0.001721588647197801880605 - 10^-46 - 10^-70", "historical_title": "Conditional \u03ba \u2248 0.001721588647: nine additional paired helper extractions", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2917", "evidence_excerpt": " additional private buffers charged.\n\nThe final literal T74 allocation gives the conditional bound\n\n\u03ba = 0.001721588647197801880605 - 10^-46 - 10^-70,\n\nan increase of 0.000001190309843563994674 (about 0.06919%) over PR2908 at 51309592971e3b5be935599eed2a95404dc7781e. The complete stock is 66304 + 408 + 8 + 82 + 2 = 66804. All 2", "automated_comparable": true, "body_sha256": "749aa7aaccce017282f1244d4d921b094d42068be5ae60d75f97e588b756a95b" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/paired-helper-extension/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Recompute the complete own productive/paid histogram from research/paired-helper-extension/evidence/PHYSICAL-INVOICE.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/paired-helper-extension/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2917-manifest.json", "sha256": "1fa785bf27b0a920d642e16f8467c97b13502c0700b236905a273e4f3e827e08" }, { "file": "remaining-record-audit/artifacts/2917/priority-manifest.json", "sha256": "9d164a8423283de4d87a53337cfe38ef7555987419aac72b92059fbc360074c8" } ], "source_head": "224bd5e56041c40078ff6b5fa7393733a215de5c" } }, { "pr": 2309, "title": "Improve conditional \u03ba to 0.0016965151242727336 with a pure 44th dirty alias", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2309", "author": "Dugongue", "created_at": "2026-10-15T04:34:00Z", "accepted_at": "2026-10-16T13:35:39Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0016965151242727336", "kappa_fraction": "2120643905340917/1250000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 173, "source_index": 283, "at": "2026-10-15T04:34:00Z", "until": "2026-10-15T04:50:12Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.0016965151242727336", "dashboard_float_text": "0.0016965151242727336", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2309", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 206, "source_index": null, "at": "2026-10-15T04:34:00Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.0016965151242727336", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2309", "evidence_excerpt": "Improve conditional \u03ba to 0.0016965151242727336 with a pure 44th dirty alias", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 484, "source_index": null, "at": "2026-10-15T04:34:00Z", "until": null, "date_basis": "body-version", "fraction": "2120643905340917/1250000000000000000", "value_decimal": "0.0016965151242727336", "dashboard_float_text": null, "expression": "0.0016965151242727336", "historical_title": "Improve conditional \u03ba to 0.0016965151242727336 with a pure 44th dirty alias", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2309", "evidence_excerpt": "The new pure dirty alias 619 -> 530 and actual owner repacking give conditional \u03ba = 0.0016965151242727336. The full exact modern ledger point is 0.00169651512427273361603599999999979966069697504545327679280000000004, below the independently admitted native complex endpoint 0.001696515", "automated_comparable": true, "body_sha256": "f561c4f86bb50efb40f1afc5d80e463358f82b67986f99eb7a451dccaaf721f3" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_own_source_selector_required; actual own source selector; expected 2120643905340917/1250000000000000000; Read actual author-head CLAIM/verifier/SOURCES/MANIFEST and identify the selected complete kernel. A missing exact claim-kappa SPEC match is a discovery limitation, not mathematical rejection. Different quoted fixtures must not override a later actual final package. All listed SPEC candidates remain unselected until independently authenticated." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/2309/priority-manifest.json", "sha256": "7616697890d115d0841cde3e3f4b0cd581383ebe05f97157e136cd0625019ffe" } ], "source_head": "95aea1e24dede937f00545a4d8250caa02f60339" } }, { "pr": 2322, "title": "Improve conditional \u03ba to 0.001697060296258836 with coherent handoffs and retimed hosting", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2322", "author": "Vlado-V", "created_at": "2026-10-15T05:15:03Z", "accepted_at": "2026-10-16T13:35:39Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001697060296258836", "kappa_fraction": "424265074064709/250000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 175, "source_index": 285, "at": "2026-10-15T05:15:03Z", "until": "2026-10-15T06:07:34Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001697060296258836", "dashboard_float_text": "0.001697060296258836", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2322", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 208, "source_index": null, "at": "2026-10-15T05:15:03Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001697060296258836", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2322", "evidence_excerpt": "Improve conditional \u03ba to 0.001697060296258836 with coherent handoffs and retimed hosting", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 486, "source_index": null, "at": "2026-10-15T05:15:03Z", "until": null, "date_basis": "body-version", "fraction": "424265074064709/250000000000000000", "value_decimal": "0.001697060296258836", "dashboard_float_text": null, "expression": "1697060296258836/10^18", "historical_title": "Improve conditional \u03ba to 0.001697060296258836 with coherent handoffs and retimed hosting", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2322", "evidence_excerpt": "## Change and mathematical scope\n\nThis finite construction certifies conditional \u03ba = 1697060296258836/10^18 = 0.001697060296258836, exceeding the pinned PR2312 claim by approximately 1.69229e-7. It composes that supplier's width exchange and existing kernels with a new coherent four-hel", "automated_comparable": true, "body_sha256": "c547003274f496323da0fb0d173fc5f99dc41fad35b6e4e1ed522fc8659e5561" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_own_source_selector_required; actual own source selector; expected 424265074064709/250000000000000000; Read actual author-head CLAIM/verifier/SOURCES/MANIFEST and identify the selected complete kernel. A missing exact claim-kappa SPEC match is a discovery limitation, not mathematical rejection. Different quoted fixtures must not override a later actual final package. All listed SPEC candidates remain unselected until independently authenticated." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/2322/priority-manifest.json", "sha256": "8891fa1d8bf38e6df9479d80092730bbd8e0f608665fdd844de5b21fe5f66cd4" } ], "source_head": "002304ef01c4416a127916169ae6d94c1bee052b" } }, { "pr": 283, "title": "Conditional \u03ba = 7.26111344123732762670617e-4: gen4 response kernels and endpoint-aware composition of #279/#280", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/283", "author": "Dugongue", "created_at": "2026-10-10T05:31:12Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.000726111344123732762670617", "kappa_fraction": "726111344123732762670617/1000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "recovered_literal_highwater", "stream_row": 196, "source_index": null, "at": "2026-10-10T05:31:12Z", "until": null, "date_basis": "body-version", "fraction": "726111344123732762670617/1000000000000000000000000000", "value_decimal": "0.000726111344123732762670617", "dashboard_float_text": null, "expression": "726111344123732762670617 / 1000000000000000000000000000", "historical_title": "Conditional \u03ba = 7.26111344123732762670617e-4: gen4 response kernels and endpoint-aware composition of #279/#280", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/283", "evidence_excerpt": "\u03ba = 726111344123732762670617 / 1000000000000000000000000000 = 0.000726111344123732762670617, conditional.\n\nThis combines #276's gen4 bit word, sixteen terminal sinks, 741 fresh response-kernel pivots, all 880 source-pair retimings from #27", "automated_comparable": true, "body_sha256": "5aeb1bb38ac8747a3233027a85b1feca312ca3d9e306c04e807645f15d995c89" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/gen4-composed-endpoints120/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/cohort-kernel-entrances132/RESULT.json, research/filtered-kernel-target120/RESULT.json, research/gen4-composed-endpoints120/MANIFEST.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/cohort-kernel-entrances132/RESULT.json, research/filtered-kernel-target120/RESULT.json, research/gen4-composed-endpoints120/MANIFEST.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/cohort-kernel-entrances132/RESULT.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/283-manifest.json", "sha256": "2d69a43b163725f757540e93bcd9172049bfb4bcf3ce5c393eef4f4c0fa7353c" }, { "file": "remaining-record-audit/artifacts/283/priority-manifest.json", "sha256": "3df008580dead814a0b233ebc3b56ba8eb07ee35ebd0ffa430c5fae3eeb071f1" } ], "source_head": "19d148bd7aa199378816cf1fb9ff746eb4d815da" } }, { "pr": 455, "title": "research: whole-residual replica pooling and program portfolios, conditional kappa = 0.001266541949425315", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/455", "author": "Dugongue", "created_at": "2026-10-11T16:11:45Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001266541949425315", "kappa_fraction": "253308389885063/200000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "scope-flagged", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 40, "source_index": 58, "at": "2026-10-11T16:11:46Z", "until": "2026-10-11T16:14:12Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001266541949425315", "dashboard_float_text": "0.001266541949425315", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/455", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 57, "source_index": null, "at": "2026-10-11T16:11:46Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001266541949425315", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/455", "evidence_excerpt": "research: whole-residual replica pooling and program portfolios, conditional kappa = 0.001266541949425315", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 325, "source_index": null, "at": "2026-10-11T16:11:45Z", "until": null, "date_basis": "body-version", "fraction": "253308389885063/200000000000000000", "value_decimal": "0.001266541949425315", "dashboard_float_text": null, "expression": "(253308389885063)/(200000000000000000)", "historical_title": "research: whole-residual replica pooling and program portfolios, conditional kappa = 0.001266541949425315", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/455", "evidence_excerpt": "-whole-pool-portfolio, a reproducible conditional construction with\n\nT(n)=O(n(\\log n)^(1-\u03ba)),\\qquad\n\u03ba=(253308389885063)/(200000000000000000)=0.001266541949425315.\n\nThat is +0.04820338% over #451 (0.001265931727546219). The complex supplier binds.\nThis is a conditional finite artifact, not an unconditional multiplicatio", "automated_comparable": true, "body_sha256": "c0697b0e7f16bec53c7c7f1e094a1e43b996851a9cd1b41256c5c83c9f6fdf5a" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Read the exact event-specific objection/model flags [{'pr': 455, 'category': 'replay_integrity_hold', 'recommended_treatment': 'Report the unresolved complex-template hash mismatch; do not infer a mathematical counterexample.', 'quarantine_from_screened_TM_record_series': False, 'event_rule': 'The documented claim/mechanism at the pinned head; later repaired constructions require their own source-bound evidence.', 'reason': 'Scientific stages passed but complete source-bound template replay still has an unexplained digest mismatch. Abandoned exploratory split prices were withdrawn separately.', 'primary_url': 'https://github.com/CrocSwap/integer-mult-bounds/pull/455', 'ledger_url': 'https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/docs/research/pr-ledger.json', 'ledger_evidence_pr': 455, 'documented_question': 'The fresh scientific stages pass. A JSON LF-to-CRLF adapter resolves the bit-template pin and downstream bit audit, but the subsequent complex_template_sha256 remains unmatched: expected 02d4d0031a173664f8adc5bccf0244f8ce349307eac09c0d48a3c8948a7f5b17; regenerated 62d1e17fe80b82691e7cef2b03974a826b513da6af5689eb4c0aac1b38355971. The tested newline and gzip-header/level variants do not explain it. Supply a portable source-bound correction; no expected digest is bypassed.', 'documented_scopes': [{'head': 'f76fc4e36030d4e00b4cbb83b1dbc661a0974c4e', 'evidence': 'research/community-reconciliation-fourth100-audit/DISPOSITIONS.json', 'scope': 'Whole-residual replica pooling and heterogeneous program dispatch. Every occurrence has an intact physical owner and a fully checked provider. Abandoned split-based exploratory prices are retained as withdrawn, not achieved bounds. The bit-template pin is explained by JSON line endings; a later complex-template mismatch remains unresolved.', 'kind': 'integration_or_partial_review'}, {'head': 'f76fc4e36030d4e00b4cbb83b1dbc661a0974c4e', 'evidence': 'research/community-efficient2000-audit/DISPOSITIONS.json', 'scope': 'ARCHIVE ONLY: original author sources retained; source identity, new research paths, syntax and available flat manifest pins checked. No author code execution, mathematical validation, full reproduction or new selected kappa. Stored author receipts retain their original status.', 'kind': 'integration_or_partial_review'}]}] against this own head; neither positive title nor an unrelated repaired revision settles record validity.", "Adjudicate the actual own contribution/selected candidate from research/e8-whole-pool-portfolio/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/e8-response-subspaces/RESULT.json, research/e8-shared-donor-chains/RESULT.json, research/e8-whole-pool-portfolio/EXPECTED.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/e8-response-subspaces/RESULT.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/455-manifest.json", "sha256": "7d596d0863415a62220c744b2568b71033361a21acb62887b7afbed6b3c79ecb" }, { "file": "remaining-record-audit/artifacts/455/priority-manifest.json", "sha256": "f67fd98552bc94df4d1e9352a966e0b19e56dcfa74c6811f1196709fe0462f94" } ], "source_head": "f76fc4e36030d4e00b4cbb83b1dbc661a0974c4e" } }, { "pr": 498, "title": "Conditional kappa = 0.001301970637653655: geometric intersections and rational paired whole-owner hosting", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/498", "author": "Dugongue", "created_at": "2026-10-11T21:26:02Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001301970637653655", "kappa_fraction": "260394127530731/200000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/tensor-nonroot-pairs/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/tensor-nonroot-pairs/EXPECTED.json, research/tensor-nonroot-pairs/RESULT.json, research/tensor-nonroot-pairs/inherited/EXPECTED.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/tensor-nonroot-pairs/EXPECTED.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/498-manifest.json", "sha256": "a253204d4f9f8f8fc58fb0a2c2bd8c999aaa7d036b2dd2b2ded9b0e14a37dda7" }, { "file": "remaining-record-audit/artifacts/498/priority-manifest.json", "sha256": "322a8193df03c14d10016e3f384bbf9eadfb2347955aeb0053a31b4bbd8a0a40" } ], "source_head": "44a703782a69a897350572b5b078d5292fdbf92d" } }, { "pr": 636, "title": "Conditional \u03ba = 0.001636269762440408: combined cold ends and PR635 owner repair", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/636", "author": "vectorsss", "created_at": "2026-10-12T23:51:39Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001636269762440408", "kappa_fraction": "204533720305051/125000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr636-k492-mixed-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 97, "source_index": 145, "at": "2026-10-12T23:51:39Z", "until": "2026-10-13T00:13:32Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001636269762440408", "dashboard_float_text": "0.001636269762440408", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/636", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 114, "source_index": null, "at": "2026-10-12T23:51:39Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001636269762440408", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/636", "evidence_excerpt": "Conditional \u03ba = 0.001636269762440408: combined cold ends and PR635 owner repair", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 388, "source_index": null, "at": "2026-10-12T23:51:39Z", "until": null, "date_basis": "body-version", "fraction": "204533720305051/125000000000000000", "value_decimal": "0.001636269762440408", "dashboard_float_text": null, "expression": "0.001636269762440408", "historical_title": "Conditional \u03ba = 0.001636269762440408: combined cold ends and PR635 owner repair", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/636", "evidence_excerpt": "Raises conditional \u03ba to 0.001636269762440408, exactly 204533720305051/125000000000000000. This improves pinned [PR635](https://github.com/CrocSwap/integer-mult-bounds/pull/635) (a6895a69f8ad98ab45777b03e9e6f48888c39f6f) by 0", "automated_comparable": true, "body_sha256": "3e0e807b55679f30af06b126b0af39314f901ddac5e9b55fda9f229b640a3d9c" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr636-k492-mixed-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/636/priority-manifest.json", "sha256": "5bc97f96ec571c23e4ceb0381352468c12f2722c755f60edbd673a9925754351" } ], "source_head": "679621828a85bac68af869fb0e55b54508e6b14b" } }, { "pr": 638, "title": "Conditional \u03ba = 0.001636456810414854: twenty-row owner improvement over PR637", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/638", "author": "vectorsss", "created_at": "2026-10-13T00:13:32Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001636456810414854", "kappa_fraction": "818228405207427/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr638-k492-mixed-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 98, "source_index": 146, "at": "2026-10-13T00:13:32Z", "until": "2026-10-13T00:26:01Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001636456810414854", "dashboard_float_text": "0.001636456810414854", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/638", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 115, "source_index": null, "at": "2026-10-13T00:13:32Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001636456810414854", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/638", "evidence_excerpt": "Improves conditional **\u03ba from 0.001636448463297071 (PR637) to 0.001636456810414854**, a gain of **0.000000008347117783**. Pinned comparison: PR637 head `4edb0dda99c495141cc56ae6e8a74e632a74db8a`.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 390, "source_index": null, "at": "2026-10-13T00:13:32Z", "until": null, "date_basis": "opening-title", "fraction": "818228405207427/500000000000000000", "value_decimal": "0.001636456810414854", "dashboard_float_text": null, "expression": "0.001636456810414854", "historical_title": "Conditional \u03ba = 0.001636456810414854: twenty-row owner improvement over PR637", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/638", "evidence_excerpt": "Conditional \u03ba = 0.001636456810414854: twenty-row owner improvement over PR637", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr638-k492-mixed-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/638/priority-manifest.json", "sha256": "e1b22f95d1a0259c97d2d34fdaae8ebc08b5c7c27c6ac7fe32d746cbf148f4ba" } ], "source_head": "a77f4a358b5129cda3e510a11a7f9a818aba5274" } }, { "pr": 640, "title": "Conditional \u03ba = 0.001636464689763295: four CK cold ends and concentrated packing", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/640", "author": "vectorsss", "created_at": "2026-10-13T00:35:48Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001636464689763295", "kappa_fraction": "327292937952659/200000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr640-k492-mixed-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 100, "source_index": 148, "at": "2026-10-13T00:35:48Z", "until": "2026-10-13T00:40:40Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001636464689763295", "dashboard_float_text": "0.001636464689763295", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/640", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 117, "source_index": null, "at": "2026-10-13T00:35:48Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001636464689763295", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/640", "evidence_excerpt": "Improves conditional **\u03ba to 0.001636464689763295**, exceeding PR639's packing-only result by **0.000000003096986179**.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 392, "source_index": null, "at": "2026-10-13T00:35:48Z", "until": null, "date_basis": "body-version", "fraction": "327292937952659/200000000000000000", "value_decimal": "0.001636464689763295", "dashboard_float_text": null, "expression": "0.001636464689763295", "historical_title": "Conditional \u03ba = 0.001636464689763295: four CK cold ends and concentrated packing", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/640", "evidence_excerpt": "Improves conditional \u03ba to 0.001636464689763295, exceeding PR639's packing-only result by 0.000000003096986179.\n\nTransfers PR637's four dim-8 cold ends to CK (raw helpers233,265,425,441). Each width drops9\u21928; CK's paid-profile ", "automated_comparable": true, "body_sha256": "48fabc2706e271d171c02274c2f9334880eda16cdff106348f9e9d11734fe39b" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr640-k492-mixed-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/640/priority-manifest.json", "sha256": "2db8aeba24f1694e0cbd466a2d7730be678150e23cbbeada030e5876dc1cf6eb" } ], "source_head": "8ef4414fc65c8189f37fc43dc51915cb565d041e" } }, { "pr": 642, "title": "Conditional \u03ba = 0.001636472098484378: selective helper-249 dispatch", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/642", "author": "vectorsss", "created_at": "2026-10-13T00:40:40Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001636472098484378", "kappa_fraction": "818236049242189/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr642-k492-mixed-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 101, "source_index": 149, "at": "2026-10-13T00:40:40Z", "until": "2026-10-13T01:11:17Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001636472098484378", "dashboard_float_text": "0.001636472098484378", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/642", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 118, "source_index": null, "at": "2026-10-13T00:40:40Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001636472098484378", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/642", "evidence_excerpt": "Improves conditional **\u03ba to 0.001636472098484378**, exceeding PR639 by **0.000000010505707262** and PR640 by **0.000000007408721083**.", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr642-k492-mixed-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/642/priority-manifest.json", "sha256": "d54312b2d56dbffdfdd866a5f4b5ae0ad4e745c685504f6b81a1e0ed8da8159a" } ], "source_head": "d1154e23e13d85fdbf64d4b41fa20bb0f56a428f" } }, { "pr": 644, "title": "Conditional \u03ba = 0.001636569158555067: attain PR643 fixed-dispatch packing ceiling", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/644", "author": "vectorsss", "created_at": "2026-10-13T01:11:17Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001636569158555067", "kappa_fraction": "1636569158555067/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr644-k492-mixed-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 102, "source_index": 150, "at": "2026-10-13T01:11:17Z", "until": "2026-10-13T01:15:30Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001636569158555067", "dashboard_float_text": "0.001636569158555067", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/644", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 119, "source_index": null, "at": "2026-10-13T01:11:17Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001636569158555067", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/644", "evidence_excerpt": "Conditional **\u03ba = 0.001636569158555067**, improving [PR643](https://github.com/CrocSwap/integer-mult-bounds/pull/643)'s 0.001636542223442109 by **0.000000026935112958**. The conservative model gives **0.001636569155685695**.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 395, "source_index": null, "at": "2026-10-13T01:11:17Z", "until": null, "date_basis": "body-version", "fraction": "1636569158555067/1000000000000000000", "value_decimal": "0.001636569158555067", "dashboard_float_text": null, "expression": "0.001636569158555067", "historical_title": "Conditional \u03ba = 0.001636569158555067: attain PR643 fixed-dispatch packing ceiling", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/644", "evidence_excerpt": "## Result\n\nConditional \u03ba = 0.001636569158555067, improving [PR643](https://github.com/CrocSwap/integer-mult-bounds/pull/643)'s 0.001636542223442109 by 0.000000026935112958. The conservative model gives 0.001636569155685695.\n\nTh", "automated_comparable": true, "body_sha256": "bd6cfd4eadda3df6dcb384f20698469cc95788ebdae0cd08885aded75baa4e52" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr644-k492-mixed-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/644/priority-manifest.json", "sha256": "6367326a1ce13b28f9466293dfd10f194e63f6fc5c62c984e5b05b99469fa2ab" } ], "source_head": "5d9427d492b0d3f22a895e2c519624f293eac44e" } }, { "pr": 646, "title": "Research: eight signed-root K triangles with 480 helpers (no record claim)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/646", "author": "jeremydiviney", "created_at": "2026-10-13T01:15:30Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001627103256702062", "kappa_fraction": "813551628351031/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr646-signed-root-K480-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr646-signed-root-K480-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/646/priority-manifest.json", "sha256": "aca1eb6305cfc414721ad1bde498cc5745a91a50b062b40058805a7e02f29b84" } ], "source_head": "cdfe8273bb5054e0a837a3594309c6262e995b1f" } }, { "pr": 671, "title": "Conditional \u03ba = 0.001658714981837397: pattern-flow owner map on the PR664 promoted word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/671", "author": "jeremykothe2", "created_at": "2026-10-13T03:30:54Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001658714981837397", "kappa_fraction": "1658714981837397/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 104, "source_index": 153, "at": "2026-10-13T03:30:54Z", "until": "2026-10-13T03:43:54Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001658714981837397", "dashboard_float_text": "0.001658714981837397", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/671", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 121, "source_index": null, "at": "2026-10-13T03:30:54Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001658714981837397", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/671", "evidence_excerpt": "Conditional \u03ba = **0.001658714981837397** (conservative 0.001658714978954851). This is +1.01\u00d710\u207b\u2077 over PR664 (0.00165861362787227).", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 405, "source_index": null, "at": "2026-10-13T03:30:54Z", "until": null, "date_basis": "body-version", "fraction": "1658714981837397/1000000000000000000", "value_decimal": "0.001658714981837397", "dashboard_float_text": null, "expression": "0.001658714981837397", "historical_title": "Conditional \u03ba = 0.001658714981837397: pattern-flow owner map on the PR664 promoted word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/671", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001658714981837397 (conservative 0.001658714978954851). This is +1.01*10^-7 over PR664 (0.00165861362787227).\n\nChange: owner map only. The word, construction, all code and the PR589 bit supplier are", "automated_comparable": true, "body_sha256": "9f88ae9cd2c47188c9c8217bb46b01ee02d049ef84314a57753e9c8f8aca9974" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_selected_full_program_bytes_missing; gauge44; required full program 1ef1554e9d39fab4387d69bc646bfa2cdeff56f3a617aaa4cf8e11f2273d84df; both orientations {\"backward\": \"1ee9d56b5342eafc130bbea596455d4b273d121e056422376f348ac5b464ad69\", \"forward\": \"1939ef2a979bb1b69d7b12a43af71413b2c7c0ba4a7e285e8fe0c859898ad30e\"}; Recover exact actual complete selected program bytes, by own immutable primary source or deterministic pinned constructor/recipe with mandatory complete semantic and orientation commitments. A matching profile, scalar saving or another provider does not fill this gap. Missing canonical catalogue may remain a separately stated endpoint premise only after the actual selected program and complete own physical/invoice are bound." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/671/priority-manifest.json", "sha256": "588bf9e919b08615964ae301da74100d53f225f635640dbf13a15a8accd675bd" } ], "source_head": "16a27439d4ba1db451b6179c9475793529a485b6" } }, { "pr": 673, "title": "Research: dirty echo, verifier repair, and priced bit-sharing boundaries", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/673", "author": "androolloyd", "created_at": "2026-10-13T03:40:30Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.01", "kappa_fraction": "1/100", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "scope-flagged", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/dirty-echo-integration/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/bit-paired-boundary-gate/CLAIM.json, research/bit-role-sharing-budget/CLAIM.json, research/bit-role-sharing-budget/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/bit-paired-boundary-gate/CLAIM.json, research/bit-role-sharing-budget/CLAIM.json, research/bit-role-sharing-budget/SOURCES.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/gauge44-notri-fine-grid/evidence/CERTIFICATE.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/673-manifest.json", "sha256": "b2ee027f37a36322015dcd097372ebcffc865d14999a03fdd445639d5c3a20a9" }, { "file": "remaining-record-audit/artifacts/673/priority-manifest.json", "sha256": "e65d663db4c014f6f37a477d91e16987f555724d60a0a1840d89d0325e977f48" } ], "source_head": "0b4f514c60d9bc7786415d7cbc24754f24d6dc3b" } }, { "pr": 676, "title": "Conditional \u03ba = 0.001659319032684569: six dim-8 cold ends and three entrance promotions on the PR659 no-triangle word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/676", "author": "jeremykothe2", "created_at": "2026-10-13T03:43:54Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001659319032684569", "kappa_fraction": "1659319032684569/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 105, "source_index": 154, "at": "2026-10-13T03:43:54Z", "until": "2026-10-13T04:02:54Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001659319032684569", "dashboard_float_text": "0.001659319032684569", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/676", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 122, "source_index": null, "at": "2026-10-13T03:43:54Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001659319032684569", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/676", "evidence_excerpt": "Conditional \u03ba = **0.001659319032684569** (conservative 0.001659319029797309). This is +6.04\u00d710\u207b\u2077 over PR671 (0.001658714981837397). The complex side binds; PR589's bit supplier gives 0.0017334.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 406, "source_index": null, "at": "2026-10-13T03:43:54Z", "until": null, "date_basis": "body-version", "fraction": "1659319032684569/1000000000000000000", "value_decimal": "0.001659319032684569", "dashboard_float_text": null, "expression": "0.001659319032684569", "historical_title": "Conditional \u03ba = 0.001659319032684569: six dim-8 cold ends and three entrance promotions on the PR659 no-triangle word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/676", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001659319032684569 (conservative 0.001659319029797309). This is +6.04*10^-7 over PR671 (0.001658714981837397). The complex side binds; PR589's bit supplier gives 0.0017334.\n\nConstruction, on PR659's", "automated_comparable": true, "body_sha256": "29a8d1a3bc0c56b6e991a670e2aa8fba71e687f7ba6fa391d22739a8d9fecc23" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1094.json", "path": "certificates/checkpoints/frontier1094.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier741.json", "path": "certificates/checkpoints/frontier741.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier799.json", "path": "certificates/checkpoints/frontier799.json", "commit": null, "at": null, "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. Not a full Lean multiplication theorem. Integration Linux CI status is separate." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier890.json", "path": "certificates/checkpoints/frontier890.json", "commit": null, "at": null, "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier942.json", "path": "certificates/checkpoints/frontier942.json", "commit": null, "at": null, "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/87db776d70ad1d28a27e9f7906237e5a279414f3/certificates/selected-result.json", "path": null, "commit": "87db776d70ad1d28a27e9f7906237e5a279414f3", "at": "2026-10-13T18:05:11Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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Not a full Lean multiplication theorem. Integration Linux CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/c290b7b919790300e14004a75d8d24b55ca3c5b5/certificates/selected-result.json", "path": null, "commit": "c290b7b919790300e14004a75d8d24b55ca3c5b5", "at": "2026-10-13T06:10:31Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/2cdd93d0250554e5160edbb8535c4500c4227349/certificates/selected-result.json", "path": null, "commit": "2cdd93d0250554e5160edbb8535c4500c4227349", "at": "2026-10-13T05:57:09Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_selected_full_program_bytes_missing; gauge44; required full program ebecf9a469de65d35bccc84a4ec45fac23d4f5d10232a3ecedadb6f5b17b6a3e; both orientations {\"backward\": \"7bbb5b3651e1b4e418be9a9112684fed899c8fa77babfa8f94bfcf197212d1f0\", \"forward\": \"9dfad5e6413873b639d7c6e0cd3002aa3ac601da397784878dd312a6193db067\"}; Recover exact actual complete selected program bytes, by own immutable primary source or deterministic pinned constructor/recipe with mandatory complete semantic and orientation commitments. A matching profile, scalar saving or another provider does not fill this gap. Missing canonical catalogue may remain a separately stated endpoint premise only after the actual selected program and complete own physical/invoice are bound." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/676/priority-manifest.json", "sha256": "bb06273a422f166bfb394e9a4464c2866399d85d423f756a544fc3b62534f22c" } ], "source_head": "18649d6b37a6865894e0c0775ba4b558e3168877" } }, { "pr": 699, "title": "Conditional \u03ba = 0.001660666354374641: four entrance promotions, six dim-8 ends and a width-neutral B read exchange on the PR659 word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/699", "author": "jeremykothe2", "created_at": "2026-10-13T04:23:47Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001660666354374641", "kappa_fraction": "1660666354374641/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 107, "source_index": 156, "at": "2026-10-13T04:23:47Z", "until": "2026-10-13T05:01:16Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001660666354374641", "dashboard_float_text": "0.001660666354374641", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/699", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 124, "source_index": null, "at": "2026-10-13T04:23:47Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001660666354374641", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/699", "evidence_excerpt": "Conditional \u03ba = 0.001660666354374641: four entrance promotions, six dim-8 ends and a width-neutral B read exchange on the PR659 word", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 408, "source_index": null, "at": "2026-10-13T04:23:47Z", "until": null, "date_basis": "body-version", "fraction": "1660666354374641/1000000000000000000", "value_decimal": "0.001660666354374641", "dashboard_float_text": null, "expression": "0.001660666354374641", "historical_title": "Conditional \u03ba = 0.001660666354374641: four entrance promotions, six dim-8 ends and a width-neutral B read exchange on the PR659 word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/699", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001660666354374641 (conservative 0.001660666351491326). This is +3.27*10^-7 over PR685 (0.001660339298410333) and +1.35*10^-6 over PR676. The complex side binds; PR589's bit supplier gives 0.0017334", "automated_comparable": true, "body_sha256": "c961a36a04acfbb273d2ca9aa5a2888c21c00c41b7693e0a72cc67e58df29ff9" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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Not a full Lean multiplication theorem." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier741.json", "path": "certificates/checkpoints/frontier741.json", "commit": null, "at": null, "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier799.json", "path": "certificates/checkpoints/frontier799.json", "commit": null, "at": null, "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. Not a full Lean multiplication theorem. Integration Linux CI status is separate." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier890.json", "path": "certificates/checkpoints/frontier890.json", "commit": null, "at": null, "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier942.json", "path": "certificates/checkpoints/frontier942.json", "commit": null, "at": null, "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d359705715f45a25d46c593a542e8d071c47160a/certificates/selected-result.json", "path": null, "commit": "d359705715f45a25d46c593a542e8d071c47160a", "at": "2026-10-16T01:56:08Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "836330098538459/500000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/0a31ad88419a4eebf515d3df4f6732c4e38c0029/certificates/selected-result.json", "path": null, "commit": "0a31ad88419a4eebf515d3df4f6732c4e38c0029", "at": "2026-10-13T18:45:23Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/87db776d70ad1d28a27e9f7906237e5a279414f3/certificates/selected-result.json", "path": null, "commit": "87db776d70ad1d28a27e9f7906237e5a279414f3", "at": "2026-10-13T18:05:11Z", "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. Not a full Lean multiplication theorem." }, { "stream": "all_selected_result_history", "record_kappa": "1661960547713947/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3825dc0ea1317629864ebeb6929719cc4bbf525f/certificates/selected-result.json", "path": null, "commit": "3825dc0ea1317629864ebeb6929719cc4bbf525f", "at": "2026-10-13T15:06:01Z", "scope": "U8/T37 finite composition with 1024-bit complex prefix allowance and complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661957774647029/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/3b83e4f14825ce1ae038a8c8159f130646991086/certificates/selected-result.json", "path": null, "commit": "3b83e4f14825ce1ae038a8c8159f130646991086", "at": "2026-10-13T13:30:30Z", "scope": "U8/T21 finite composition with complete source-bound baseline coverage; explicit reused ancestry recorded. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 obligations remain. Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d6dfd8f21b1e0b7e3f93b7e30e64639390e48504/certificates/selected-result.json", "path": null, "commit": "d6dfd8f21b1e0b7e3f93b7e30e64639390e48504", "at": "2026-10-13T06:44:14Z", "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. Not a full Lean multiplication theorem. Integration Linux CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/c290b7b919790300e14004a75d8d24b55ca3c5b5/certificates/selected-result.json", "path": null, "commit": "c290b7b919790300e14004a75d8d24b55ca3c5b5", "at": "2026-10-13T06:10:31Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/2cdd93d0250554e5160edbb8535c4500c4227349/certificates/selected-result.json", "path": null, "commit": "2cdd93d0250554e5160edbb8535c4500c4227349", "at": "2026-10-13T05:57:09Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_selected_full_program_bytes_missing; gauge44; required full program 59d4e0de420bfc81f36f193c9cd898dbf0bf73c0ddbf4f169e6214f61d75e350; both orientations {\"backward\": \"3176ccde98d90e754105e60096598fee348e2455e046290d3674b79dd6b402df\", \"forward\": \"36e75fc972766fa42f1b371a055e74976a165c894b816911c3510a88b431ea09\"}; Recover exact actual complete selected program bytes, by own immutable primary source or deterministic pinned constructor/recipe with mandatory complete semantic and orientation commitments. A matching profile, scalar saving or another provider does not fill this gap. Missing canonical catalogue may remain a separately stated endpoint premise only after the actual selected program and complete own physical/invoice are bound." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/699/priority-manifest.json", "sha256": "5f7319e9a5cd05029135d333a79a62cb99d44d3f51b7623173d8cf88471ec078" } ], "source_head": "f042731cb332359166e8215839f9a3da28c46c5b" } }, { "pr": 1147, "title": "Research: a fifth joint exchange on X4 does not improve \u03ba (complete census)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1147", "author": "RaphaelFakhri", "created_at": "2026-10-13T19:07:52Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661634653669567", "kappa_fraction": "1661634653669567/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "A numerical whole-multiplier comparison must separately identify an actual complete selected native/caller/owner/recursive work-height-stock interface and precision/analytic/outer realization. This source-scope disposition neither supplies nor transfers that bound, and does not extend a restricted negative result beyond its stated family." ], "source_manifest": [ { "file": "individual-primary-interface-source/1147-manifest.json", "sha256": "51224b0539e9983610c30cc05dcc6020f8973c01b0ecfcf2e1dfa68e1d36d771" }, { "file": "remaining-record-audit/artifacts/1147/priority-manifest.json", "sha256": "f46a903c5b8a6630e6d4c5432c05980f7badd8eaa87f84a23ad93aa808738a73" } ], "source_head": "0ffb3c804c44150153edd4a377d57685448d944d" } }, { "pr": 1148, "title": "Conditional \u03ba = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1148", "author": "tomdif", "created_at": "2026-10-13T19:08:12Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001675560947524449", "kappa_fraction": "1675560947524449/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1148-joint-entrance-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 141, "source_index": 201, "at": "2026-10-13T19:30:57.285304Z", "until": "2026-10-13T19:34:47.562407Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001675560947524449", "dashboard_float_text": "0.001675560947524449", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1148", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 158, "source_index": null, "at": "2026-10-13T19:30:57.285304+00:00", "until": null, "date_basis": "observed_revision", "fraction": null, "value_decimal": "0.001675560947524449", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1148", "evidence_excerpt": "This proposes the conditional finite witness **\u03ba = 0.001675560947524449**. Joint entrance choices replace eight local rank-one recursive children with four rank-two children while preserving the helper-width inventory. An exact within-call permutation therefore transfers the preceding T16 packing without another owner search.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 446, "source_index": null, "at": "2026-10-13T19:08:12Z", "until": null, "date_basis": "body-version", "fraction": "1675121647789207/1000000000000000000", "value_decimal": "0.001675560947524449", "dashboard_float_text": null, "expression": "0.001675121647789207", "historical_title": "Conditional \u03ba = 0.001675121647789207: changed k8 entrances, rank-seven ends, and T16 hosting", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1148", "evidence_excerpt": "## Change and mathematical scope\n\nThis proposes the conditional finite witness \u03ba = 0.001675121647789207. Twelve helper entrances change from dimension five to four, and local recursive frames are refitted. The resulting local paid profile is {1:2372,2:494,3:412,4:130,5:82,8:8}; each", "automated_comparable": true, "body_sha256": "671fcc886fbf0115caf8a809683d83d72a1c7f81b57a1fbda8eb9ab48a6277db" }, { "stream": "recovered_literal_highwater", "stream_row": 448, "source_index": null, "at": "2026-10-13T19:30:17Z", "until": null, "date_basis": "body-version", "fraction": "1675560947524449/1000000000000000000", "value_decimal": "0.001675560947524449", "dashboard_float_text": null, "expression": "0.001675560947524449", "historical_title": "Conditional \u03ba = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1148", "evidence_excerpt": "## Change and mathematical scope\n\nThis proposes the conditional finite witness \u03ba = 0.001675560947524449. Joint entrance choices replace eight local rank-one recursive children with four rank-two children while preserving the helper-width inventory. An exact within-call permutation t", "automated_comparable": true, "body_sha256": "aa6704117027f832ecf659e1c51cff1841166929d392eb91a84987008f79e3ac" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1148-joint-entrance-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1148/priority-manifest.json", "sha256": "9b5234ab782f5704ab5a7299050c3ff7ec279b95be367bccbbd0476dec200563" } ], "source_head": "506ea08dd77388105682044ebb0848ce9b274964" } }, { "pr": 1150, "title": "Conditional kappa 0.001672716806120974: rank-seven T16 owner exchanges", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1150", "author": "rohanarun", "created_at": "2026-10-13T19:10:25Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672716806120974", "kappa_fraction": "836358403060487/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1150-ends7-exchange-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1150-ends7-exchange-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 4, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1150/priority-manifest.json", "sha256": "002404169c4b4b80b810f21cbfd17cf4744b420f152ebbd5d6af28158ed01ab4" } ], "source_head": "bebf64ffda3fd5128342d19ee6d419b1150b49f7" } }, { "pr": 1154, "title": "Conditional kappa = 0.001673260706543984: adaptive joint kernel demotion on PR1117", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1154", "author": "Dugongue", "created_at": "2026-10-13T19:14:51Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001673260706543984", "kappa_fraction": "104578794158999/62500000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1154-dynamic-kernel-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "Own required physical partial initial/output Gaussian operators, identity on spectators, absolute phases, bounded73-axis affine/even-Z4 monomial grammar and normalized completed-child identities remain explicit; scalar/rank checks alone do not prove them.", "Own arbitrary dirty restoration, common-label, whole-call/all-column/all-size hosting and fixed group/compiler interfaces.", "A new complete numeric parent and full operation invoice are priced; no historical full PLAN byte identity or old billed amount is claimed.", "The original optional BIT supplier is not consumed by this direct Gaussian realization." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "Own required physical partial initial/output Gaussian operators, identity on spectators, absolute phases, bounded73-axis affine/even-Z4 monomial grammar and normalized completed-child identities remain explicit; scalar/rank checks alone do not prove them.", "Own arbitrary dirty restoration, common-label, whole-call/all-column/all-size hosting and fixed group/compiler interfaces.", "A new complete numeric parent and full operation invoice are priced; no historical full PLAN byte identity or old billed amount is claimed.", "The original optional BIT supplier is not consumed by this direct Gaussian realization." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1154-dynamic-kernel-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 5, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1154/priority-manifest.json", "sha256": "9476f2d31920e86db9ae7475bd30bdac7886a86f2e62fc8af935dad95ae0de99" } ], "source_head": "390de2866a03758e7f4ddbb2846e5b2ee4e72154" } }, { "pr": 1176, "title": "Add files via uplConditional kappa = 0.001675224519162937: cross-call gap augmentation for three extra kernel islandsoad", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1176", "author": "Dugongue", "created_at": "2026-10-13T19:41:25Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001675224519162937", "kappa_fraction": "1675224519162937/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1176-dynamic-kernel-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "Own required physical partial initial/output Gaussian operators, identity on spectators, absolute phases, bounded73-axis affine/even-Z4 monomial grammar and normalized completed-child identities remain explicit; scalar/rank checks alone do not prove them.", "Own arbitrary dirty restoration, common-label, whole-call/all-column/all-size hosting and fixed group/compiler interfaces.", "A new complete numeric parent and full operation invoice are priced; no historical full PLAN byte identity or old billed amount is claimed.", "The original optional BIT supplier is not consumed by this direct Gaussian realization." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "Own required physical partial initial/output Gaussian operators, identity on spectators, absolute phases, bounded73-axis affine/even-Z4 monomial grammar and normalized completed-child identities remain explicit; scalar/rank checks alone do not prove them.", "Own arbitrary dirty restoration, common-label, whole-call/all-column/all-size hosting and fixed group/compiler interfaces.", "A new complete numeric parent and full operation invoice are priced; no historical full PLAN byte identity or old billed amount is claimed.", "The original optional BIT supplier is not consumed by this direct Gaussian realization." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1176-dynamic-kernel-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 6, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1176/priority-manifest.json", "sha256": "aed7efd9fdacd960c67691f230636d1c09741bf320b19d69400ee4da6751b6ed" } ], "source_head": "3a0d419341879a395d921693112c3b826de93677" } }, { "pr": 1183, "title": "Conditional kappa 0.001675603180601302: mixed entrance providers on T37 owners", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1183", "author": "rohanarun", "created_at": "2026-10-13T19:48:07Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001675603180601302", "kappa_fraction": "837801590300651/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1183-joint-entrance-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 143, "source_index": 206, "at": "2026-10-13T19:48:07Z", "until": "2026-10-13T19:55:18Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001675603180601302", "dashboard_float_text": "0.001675603180601302", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1183", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 160, "source_index": null, "at": "2026-10-13T19:48:07Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001675603180601302", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1183", "evidence_excerpt": "This composes PR1169's joint-entrance T37 construction with mixed local providers matched to actual idle axes. The locally verified conditional bound is **kappa = 0.001675603180601302**, **0.00205932471045090295277136174392800053609319132679508398683629385640127295304%** above PR1169's 0.001675568675201533.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 450, "source_index": null, "at": "2026-10-13T19:48:07Z", "until": null, "date_basis": "body-version", "fraction": "837801590300651/500000000000000000", "value_decimal": "0.001675603180601302", "dashboard_float_text": null, "expression": "0.001675603180601302", "historical_title": "Conditional kappa 0.001675603180601302: mixed entrance providers on T37 owners", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1183", "evidence_excerpt": "truction with the mixed-provider, actual-gap mechanism explored in PR1176. It nominates conditional kappa 0.001675603180601302, a 0.00205932471045090295277136174392800053609319132679508398683629385640127295304% increase over PR1169's 0.001675568675201533.\n\nIn 23 of 333 calls, demote three additional four-", "automated_comparable": true, "body_sha256": "97b75ec564346b19f2d763f86dde9ff4a17ce597d04c304ec1ecb05d1cc6dd45" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1183-joint-entrance-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 6, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1183/priority-manifest.json", "sha256": "9763405a501a15dee42e1205c50707154986fa1ac59f2a71ba979c535beacfe8" } ], "source_head": "9e7ccda21f28f5dd0397aa04a596e4f0e1d75d1d" } }, { "pr": 1186, "title": "Tooling: exact frame solver and delivery-rewrite search for gauge44/k8 local words (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1186", "author": "mdumitrean", "created_at": "2026-10-13T19:50:35Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672756914849856", "kappa_fraction": "26136826794529/15625000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "A numerical whole-multiplier comparison must separately identify an actual complete selected native/caller/owner/recursive work-height-stock interface and precision/analytic/outer realization. This source-scope disposition neither supplies nor transfers that bound, and does not extend a restricted negative result beyond its stated family." ], "source_manifest": [ { "file": "individual-primary-interface-source/1186-manifest.json", "sha256": "022ca4b926f73059b53e54b0bbb02ddd9da7c893bd3dec1c71baa09fcc311a1e" }, { "file": "remaining-record-audit/artifacts/1186/priority-manifest.json", "sha256": "187b70d93a21f66cc0ccdec05e0954202f744e4440093a24f535fbe650638f76" } ], "source_head": "c37dfb077ad77ef391cefa56c98db87a40b7e28c" } }, { "pr": 1192, "title": "Conditional kappa 0.001675670695307702: cross-call T37 entrance augmentation", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1192", "author": "rohanarun", "created_at": "2026-10-13T19:55:18Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001675670695307702", "kappa_fraction": "837835347653851/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1192-joint-entrance-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 144, "source_index": 207, "at": "2026-10-13T19:55:18Z", "until": "2026-10-13T19:56:07Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001675670695307702", "dashboard_float_text": "0.001675670695307702", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1192", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 161, "source_index": null, "at": "2026-10-13T19:55:18Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001675670695307702", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1192", "evidence_excerpt": "Cross-call whole-owner augmentation of PR1183 has locally verified conditional **kappa = 0.001675670695307702**, **0.00402927776585932906908976725151487524160082012226483340694179820232800158409%** above PR1183's 0.001675603180601302. A concurrent draft PR1193 now reports 0.001675672695827067, slightly higher; this package is an independently admitted improvement on our previous bound, not the highest current claim.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 451, "source_index": null, "at": "2026-10-13T19:55:18Z", "until": null, "date_basis": "body-version", "fraction": "837835347653851/500000000000000000", "value_decimal": "0.001675670695307702", "dashboard_float_text": null, "expression": "0.001675670695307702", "historical_title": "Conditional kappa 0.001675670695307702: cross-call T37 entrance augmentation", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1192", "evidence_excerpt": "Draft continuation of PR1183: cross-call whole-owner exchanges nominate conditional kappa 0.001675670695307702, 0.00402927776585932906908976725151487524160082012226483340694179820232800158409% above the locally admitted PR1183 bound 0.001675603180601302.\n\nThe same two native providers are ", "automated_comparable": true, "body_sha256": "ea80894280f0297889bd36c81393bcd7656bc3812d10373565d671d1d2741307" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1192-joint-entrance-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 6, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1192/priority-manifest.json", "sha256": "86e1bf0bf2a5ff57eab811b2a76dcb9c3e8853ceb52ea5c5e14dce1e8094a334" } ], "source_head": "970793428d346b4aa8d8fa2af03aa6dd5ad6f994" } }, { "pr": 1201, "title": "Conditional kappa 0.00167576776285696: mixed T37 source-holder fusions", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1201", "author": "rohanarun", "created_at": "2026-10-13T20:00:49Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00167576776285696", "kappa_fraction": "327298391183/195312500000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 145, "source_index": 210, "at": "2026-10-13T20:00:49Z", "until": "2026-10-13T20:02:58Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.00167576776285696", "dashboard_float_text": "0.00167576776285696", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1201", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 162, "source_index": null, "at": "2026-10-13T20:00:49Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00167576776285696", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1201", "evidence_excerpt": "Composing PR1195's two source-holder fusions with PR1192's mixed-entrance T37 owner map gives locally verified conditional **kappa = 0.00167576776285696**, **0.00567336509867026683748527537922408274841005006262320525838514871578973255698%** above PR1193's reported 0.001675672695827067.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 453, "source_index": null, "at": "2026-10-13T20:00:49Z", "until": null, "date_basis": "body-version", "fraction": "327298391183/195312500000000", "value_decimal": "0.00167576776285696", "dashboard_float_text": null, "expression": "0.00167576776285696", "historical_title": "Conditional kappa 0.00167576776285696: mixed T37 source-holder fusions", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1201", "evidence_excerpt": "ions with PR1192's 68-call mixed-entrance T37 owner map. The complete profile prices at conditional kappa = 0.00167576776285696, 0.00567336509867026683748527537922408274841005006262320525838514871578973255698% above PR1193's reported 0.001675672695827067.\n\nThe two fusions at X=439 and X=444 are applied to ", "automated_comparable": true, "body_sha256": "bf7f5531b40d5c2b4cfbe4f1f81595bc29682cc2d94c5e905aa56a6247ebd257" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_selected_full_program_bytes_missing; extra; required full program 4f5b98fb181c2e2a4fcfd477779b66f9ee3a1d9e163c79e40912a14a0e01cb75; both orientations {\"backward\": \"3b41ef4a62f2e3d2641971db84d3bec58fd5c6dac60cf8dfec529764b059208b\", \"forward\": \"65dd969bd2dc28f4e43cb0589320ad7e151ddd082e41d83b8486c78a6a6f43ea\"}; Recover exact actual complete selected program bytes, by own immutable primary source or deterministic pinned constructor/recipe with mandatory complete semantic and orientation commitments. A matching profile, scalar saving or another provider does not fill this gap. Missing canonical catalogue may remain a separately stated endpoint premise only after the actual selected program and complete own physical/invoice are bound.", "Source-specific frozen V10 discovery snapshot: actual_selected_full_program_bytes_missing; gauge44; required full program 82285d3f6365c64259222c4a0c32e06ca24951e193fb8c19341d922c107a891c; both orientations {\"backward\": \"75901f425fb3e2906bef381e8c8bb26fe6414c8b5eacb33e254a726fdb590b5d\", \"forward\": \"6e3f6d92f3f2c0f2df7f59689af78b15209046e66634f4020d46c17d05d5eb8d\"}; Recover exact actual complete selected program bytes, by own immutable primary source or deterministic pinned constructor/recipe with mandatory complete semantic and orientation commitments. A matching profile, scalar saving or another provider does not fill this gap. Missing canonical catalogue may remain a separately stated endpoint premise only after the actual selected program and complete own physical/invoice are bound." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1201/priority-manifest.json", "sha256": "b3752c3d1abd37ebd7798b13e778daff1aaec9a1136d4872f3076a9edd873a4a" } ], "source_head": "86a7072626d9b3e49222378bb76601a11d2f58ea" } }, { "pr": 1207, "title": "Conditional kappa 0.001675807682652: X54 on mixed T37 fusion providers", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1207", "author": "rohanarun", "created_at": "2026-10-13T20:09:25Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001675807682652", "kappa_fraction": "418951920663/250000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 146, "source_index": 212, "at": "2026-10-13T20:20:17.793319Z", "until": "2026-10-13T20:20:34Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001675807682652", "dashboard_float_text": "0.001675807682652", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1207", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 163, "source_index": null, "at": "2026-10-13T20:20:17.793319+00:00", "until": null, "date_basis": "observed_revision", "fraction": null, "value_decimal": "0.001675807682652", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1207", "evidence_excerpt": "Composing X54 with both PR1201 source-holder fusion providers gives locally verified conditional **kappa = 0.001675807682652**, **0.00238217943588687291540245383143771992709520302329129948804939952695019477370%** above PR1201's 0.001675767762856960.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 454, "source_index": null, "at": "2026-10-13T20:09:25Z", "until": null, "date_basis": "body-version", "fraction": "418951920663/250000000000000", "value_decimal": "0.001675807682652", "dashboard_float_text": null, "expression": "0.001675807682652", "historical_title": "Conditional kappa 0.001675807682652: X54 on mixed T37 fusion providers", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1207", "evidence_excerpt": "on with BOTH source-holder fusion providers from PR1201. The complete profile prices at conditional kappa = 0.001675807682652, 0.00238217943588687291540245383143771992709520302329129948804939952695019477370% above the locally verified PR1201 value 0.001675767762856960.\n\nThe X54 scalar edits are relocated", "automated_comparable": true, "body_sha256": "3631bd780124d28afc07294391eb21e2b2d645830ce28dcbfaf3849736e4b5d2" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_selected_full_program_bytes_missing; extra; required full program 545df5f1ddde2c8c2e2f174e028fb8df51c36965c6c05e84b727755fce76d670; both orientations {\"backward\": \"0271f2533a88b36e86e99700a1837549e76408cdbe670cd2471afb42dec850aa\", \"forward\": \"a6da40f7bc421dd6faaa516ecd8a7dec5e3f5f975d6b44eae994d6804c082bfb\"}; Recover exact actual complete selected program bytes, by own immutable primary source or deterministic pinned constructor/recipe with mandatory complete semantic and orientation commitments. A matching profile, scalar saving or another provider does not fill this gap. Missing canonical catalogue may remain a separately stated endpoint premise only after the actual selected program and complete own physical/invoice are bound.", "Source-specific frozen V10 discovery snapshot: actual_selected_full_program_bytes_missing; gauge44; required full program 3cf9daa25562d324d3eaf4b854e78aff98bc254891e8aaafef4ac66e0c731517; both orientations {\"backward\": \"f15c1600543ada5b5e4e3c68bf2f171ea35ca520a571d91bf29f8f612361771a\", \"forward\": \"66632cb2270b40618c0f013d71ef600b3809b51de7e2f4833c266dfce4afe77c\"}; Recover exact actual complete selected program bytes, by own immutable primary source or deterministic pinned constructor/recipe with mandatory complete semantic and orientation commitments. A matching profile, scalar saving or another provider does not fill this gap. Missing canonical catalogue may remain a separately stated endpoint premise only after the actual selected program and complete own physical/invoice are bound." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1207/priority-manifest.json", "sha256": "cd328d821ffbfbd6414de84b26729bc08ff895e12a759165525276112e096eaf" } ], "source_head": "d53f23eafc378a6e680294081d09886597129733" } }, { "pr": 1218, "title": "Conditional kappa 0.001675809683500501: global mixed allocation with X54 and fusions", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1218", "author": "rohanarun", "created_at": "2026-10-13T20:20:34Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001675809683500501", "kappa_fraction": "1675809683500501/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 147, "source_index": 213, "at": "2026-10-13T20:20:34Z", "until": "2026-10-13T20:27:20Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001675809683500501", "dashboard_float_text": "0.001675809683500501", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1218", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 164, "source_index": null, "at": "2026-10-13T20:20:34Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001675809683500501", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1218", "evidence_excerpt": "Composing PR1193's globally allocated mixed T37 owner map with both source-holder fusions and X54 gives locally verified conditional **kappa = 0.001675809683500501**, **0.000119396069233530201026813474728132684665218935067679952511324429507309342887%** above PR1207's 0.001675807682652000.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 455, "source_index": null, "at": "2026-10-13T20:20:34Z", "until": null, "date_basis": "body-version", "fraction": "1675809683500501/1000000000000000000", "value_decimal": "0.001675809683500501", "dashboard_float_text": null, "expression": "0.001675809683500501", "historical_title": "Conditional kappa 0.001675809683500501: global mixed allocation with X54 and fusions", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1218", "evidence_excerpt": "ion with both source-holder fusions and X54 from PR1207. The complete profile prices at conditional kappa = 0.001675809683500501, 0.000119396069233530201026813474728132684665218935067679952511324429507309342887% above our locally admitted PR1207 bound 0.001675807682652.\n\nPR1193's frozen allocation uses 125 ", "automated_comparable": true, "body_sha256": "c04f78a98b1f23a1d1ba0d8dc0259e9d82a3025f7292613d8d56fb43090c27c0" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_selected_full_program_bytes_missing; extra; required full program 820aac386d3f651eb976baa991075b267ab7dd42997a966c18bbea2b277dfb46; both orientations {\"backward\": \"d0a8c0d082e5f079c8b9bbae2000971691d2586be0d985435a22cdcd488eb05b\", \"forward\": \"f7db7b1f9b0b048ee678abc49e3798831edd01aad7ea34fe058d53dda714ffdd\"}; Recover exact actual complete selected program bytes, by own immutable primary source or deterministic pinned constructor/recipe with mandatory complete semantic and orientation commitments. A matching profile, scalar saving or another provider does not fill this gap. Missing canonical catalogue may remain a separately stated endpoint premise only after the actual selected program and complete own physical/invoice are bound.", "Source-specific frozen V10 discovery snapshot: actual_selected_full_program_bytes_missing; gauge44; required full program 3cf9daa25562d324d3eaf4b854e78aff98bc254891e8aaafef4ac66e0c731517; both orientations {\"backward\": \"f15c1600543ada5b5e4e3c68bf2f171ea35ca520a571d91bf29f8f612361771a\", \"forward\": \"66632cb2270b40618c0f013d71ef600b3809b51de7e2f4833c266dfce4afe77c\"}; Recover exact actual complete selected program bytes, by own immutable primary source or deterministic pinned constructor/recipe with mandatory complete semantic and orientation commitments. A matching profile, scalar saving or another provider does not fill this gap. Missing canonical catalogue may remain a separately stated endpoint premise only after the actual selected program and complete own physical/invoice are bound." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1218/priority-manifest.json", "sha256": "5a06016e890d9e2e2fff3c3b87eb597e9e43bbb97339f920e63f1f2c9227c6e1" } ], "source_head": "0aa147977ad226f9d777d6a21a610ab037985b1e" } }, { "pr": 1225, "title": "Conditional \u03ba = 0.001675608585476885: X54 slot on #1148's joint-entrance k8 word with #1169's exact T37 owners", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1225", "author": "rohanarun", "created_at": "2026-10-13T20:27:20Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001675608585476885", "kappa_fraction": "335121717095377/200000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_selected_full_program_bytes_missing; gauge44; required full program b6e6d496eefc02532f91e833561b8cb676062c57d3943afc2ae0932810a5a36b; both orientations {\"backward\": \"1e1f4ada65568b65479452e89569a7c9ec1c1900a10684ebfe3ec835800dfddb\", \"forward\": \"12960a48d39ca4e4187dbcafa0cd8ecfc43fd7a9479c1a2fb3ba8438c3ddfb5e\"}; Recover exact actual complete selected program bytes, by own immutable primary source or deterministic pinned constructor/recipe with mandatory complete semantic and orientation commitments. A matching profile, scalar saving or another provider does not fill this gap. Missing canonical catalogue may remain a separately stated endpoint premise only after the actual selected program and complete own physical/invoice are bound.", "Source-specific frozen V10 discovery snapshot: actual_selected_physical_input_unresolved; OWNERS; expected 7fd6f69e806aaa5a6094d52b1400d8bde25aaa8ea26216eb4ffc989151ad0ab6; Bind the actual complete own PLAN/OWNERS bytes or reconstruct a source-equivalent complete physical realization with explicit changed-parent provenance, actual role/program/windows/stock checks and fresh full invoice. A404 under conventional local paths is not proof that an explicitly pinned parent archive is absent." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1225/priority-manifest.json", "sha256": "268549bbd0cd1ff3572a728b955feb8a2ebdea3d7733c375472754d396fc43c8" } ], "source_head": "aac9ce7d83e02989eed76e08815cfd2399214e90" } }, { "pr": 1238, "title": "The end-cap wall: why copies are forced in the E8 skeleton's verifier model (no \u03ba claim)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1238", "author": "DreamingOfClouds", "created_at": "2026-10-13T20:48:02Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00167166528321877", "kappa_fraction": "167166528321877/100000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep the actual named multiplier/changedprogram as a distinct costing target. This contribution is validation, a restricted theorem or an unimplementedtarget; it defines no new fullruntime point. Its target-specific scope/negative controls/constant qualifications must be checked when a complete supplier is priced." ], "source_manifest": [ { "file": "individual-primary-interface-source/1238-manifest.json", "sha256": "e7072abba535a9fcee90870b0d5a6570daa2548350859289d2d838e532057947" }, { "file": "remaining-record-audit/artifacts/1238/priority-manifest.json", "sha256": "e1fd85fc37f7e6e45b207177da0029bb07bc518378321cb4410434078756336a" } ], "source_head": "50a1c992ce28c95d83d11bc691353aaa289d9d65" } }, { "pr": 1286, "title": "Conditional kappa 0.001676332167598458: composed pivot 531 and 543 helper-donor kernels", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1286", "author": "rohanarun", "created_at": "2026-10-13T21:45:05Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676332167598458", "kappa_fraction": "838166083799229/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 150, "source_index": 220, "at": "2026-10-13T21:45:05Z", "until": "2026-10-13T21:57:16Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001676332167598458", "dashboard_float_text": "0.001676332167598458", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1286", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 167, "source_index": null, "at": "2026-10-13T21:45:05Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001676332167598458", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1286", "evidence_excerpt": "Conditional kappa 0.001676332167598458: composed pivot 531 and 543 helper-donor kernels", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_selected_full_program_bytes_missing; extra; required full program 2eb0b24b5c66bbeb0ae271eb7c67ef2bfd628c28c693ca63c08907286ba56201; both orientations {\"backward\": \"33aee767519786555dfab56a75f7a0451a2adb5629f88814006d97075040076b\", \"forward\": \"3df042947978f7fbdb4aab2bc3d3c1bc897b6255bff39a1b374e9d3f8f10463f\"}; Recover exact actual complete selected program bytes, by own immutable primary source or deterministic pinned constructor/recipe with mandatory complete semantic and orientation commitments. A matching profile, scalar saving or another provider does not fill this gap. Missing canonical catalogue may remain a separately stated endpoint premise only after the actual selected program and complete own physical/invoice are bound.", "Source-specific frozen V10 discovery snapshot: actual_selected_full_program_bytes_missing; gauge44; required full program 2b86c69ded1ab945d9664c7a4519115ff43c1db1760d15fb595fde374c978a52; both orientations {\"backward\": \"d4b533c0ef1500494a092ccce59f964a98bc785eebb9276958dbb5841c30c74b\", \"forward\": \"006abd4495821dad841eef2c85bcc18a1b76f8d0ce3dfafd05b886e38b3ba390\"}; Recover exact actual complete selected program bytes, by own immutable primary source or deterministic pinned constructor/recipe with mandatory complete semantic and orientation commitments. A matching profile, scalar saving or another provider does not fill this gap. Missing canonical catalogue may remain a separately stated endpoint premise only after the actual selected program and complete own physical/invoice are bound." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1286/priority-manifest.json", "sha256": "f13cf745970783ddd06cd5e7e99ebfdb78741dfac221ba973d0049a5ff2cec60" } ], "source_head": "57502a3f396f7db2237c8f5747bab4b8f2864d19" } }, { "pr": 1297, "title": "Conditional kappa 0.001676854978651125: four composed helper-donor cold kernels", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1297", "author": "rohanarun", "created_at": "2026-10-13T21:57:16Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676854978651125", "kappa_fraction": "13414839829209/8000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1297-dispatched-finite-controller-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 151, "source_index": 221, "at": "2026-10-13T21:57:16Z", "until": "2026-10-13T22:36:14Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001676854978651125", "dashboard_float_text": "0.001676854978651125", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1297", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 168, "source_index": null, "at": "2026-10-13T21:57:16Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001676854978651125", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1297", "evidence_excerpt": "Conditional kappa 0.001676854978651125: four composed helper-donor cold kernels", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 460, "source_index": null, "at": "2026-10-13T21:57:16Z", "until": null, "date_basis": "body-version", "fraction": "13414839829209/8000000000000000", "value_decimal": "0.001676854978651125", "dashboard_float_text": null, "expression": "0.001676854978651125", "historical_title": "Draft conditional kappa 0.001676854978651125: compose four helper-donor cold kernels", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1297", "evidence_excerpt": "Conditional candidate \u03ba = 0.001676854978651125, 0.031187795% above our locally verified PR1286 (0.001676332167598458). Compose two further exact helper-donor cold kernels, pivots 555 and 567, with PR1286's pivots 531 and 543. ", "automated_comparable": true, "body_sha256": "b9ef38836325d1f841959a4ac787f46e25e785711bdbca744948c78ace675f5e" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. 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Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1424-gaussian-only-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1424/priority-manifest.json", "sha256": "7f1bf8b341edd6f6eb81644660bf2f45cec7d763359babb56e6edb9efd6694d2" } ], "source_head": "bfe423c24555baf35dab991a8d6fe723a038945c" } }, { "pr": 1464, "title": "Conditional \u03ba 0.0016768552290713218862064567722745926195124487395104752628033651837667029477836: verified fine64 endpoint refinement, unchanged construction", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1464", "author": "rohanarun", "created_at": "2026-10-14T01:05:25Z", "accepted_at": "2026-10-16T13:45:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676855229071321886206456772274592619512448739510475263", "kappa_fraction": "4192138072678304715516141930686481548781121848776188157008412959416757369459/2500000000000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1464-gaussian-only-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. 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Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 176, "source_index": null, "at": "2026-10-14T01:30:57Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00167685522907132188620645677227459261951244873951047526280336519105115665521200964951578469164138454299292754381039421745513966674764384056", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1485", "evidence_excerpt": "Conditional candidate \u03ba = **0.00167685522907132188620645677227459261951244873951047526280336519105115665521200964951578469164138454299292754381039421745513966674764384056**. This exceeds PR1479 (`0a211a4608d2c3d295f8bb94b12ca446714186ab`) by **5.115665521200964951578469164138454299292754381039421745513966674764384056E-68**.", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1485-gaussian-only-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1485/priority-manifest.json", "sha256": "67a7abcee16d0726298370ab150ad8b4928fbda6de6f03a43437ae4765544776" } ], "source_head": "cf2dce728594ad005c3794ae3f1fb3622590f8c1" } }, { "pr": 259, "title": "Multi-cut kernel condensation: 518 entrances, kappa = 7.11029386054035e-4", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/259", "author": "Dugongue", "created_at": "2026-10-10T01:55:24Z", "accepted_at": "2026-10-16T13:45:39Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.000711029386054035", "kappa_fraction": "142205877210807/200000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "recovered_literal_highwater", "stream_row": 181, "source_index": null, "at": "2026-10-10T01:55:24Z", "until": null, "date_basis": "body-version", "fraction": "142205877210807/200000000000000000", "value_decimal": "0.000711029386054035", "dashboard_float_text": null, "expression": "142205877210807 / 200000000000000000", "historical_title": "Multi-cut kernel condensation: 518 entrances, kappa = 7.11029386054035e-4", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/259", "evidence_excerpt": "Conditional kappa = 142205877210807 / 200000000000000000 = 0.000711029386054035.\n\nThis extends the pinned [PR249](https://github.com/CrocSwap/integer-mult-bounds/pull/249) construction at 96495746c786d6d0339dbb38c7f553d4af3f88ed. It imp", "automated_comparable": true, "body_sha256": "025218cfd061d599a49babb4a1d622cb3d600026560494ce53505c4c6b0e83de" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 24, "source_family": "finite_symbolic_bridge", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/multicut-kernel-condensation/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/balanced-nullity-banks-163/expected.json, research/cohort-kernel-entrances132/RESULT.json, research/multicut-kernel-condensation/MANIFEST.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/balanced-nullity-banks-163/expected.json, research/cohort-kernel-entrances132/RESULT.json, research/multicut-kernel-condensation/MANIFEST.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "Bind/recompute the source finite work, scalar coefficient grammar, denominator/precision/guard and all-size row-stock from research/balanced-nullity-banks-163/expected.json#/combo before using the stopped recurrence or compiled uniform supplier.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/balanced-nullity-banks-163/expected.json#/combo after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "finite-bridge-source-expansion/259-manifest.json", "sha256": "d86294d80d00e492863ff5cbdd408c885572b97aef2160c020c907a4ac409fcc" }, { "file": "remaining-record-audit/artifacts/259/priority-manifest.json", "sha256": "51436a6b0e4d7195582f8f613e6e3bc6abeeb302e7a7684992767d7e881dd31b" } ], "source_head": "a53ec0ca4d59634f16630dd16adf035c9f12595c" } }, { "pr": 309, "title": "Conditional \u03ba = 7.51499335697560e-4: local dirty-response transport, commuting schedules and37 additional gauges on weighted gen5b", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/309", "author": "Dugongue", "created_at": "2026-10-10T13:29:19Z", "accepted_at": "2026-10-16T13:45:39Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.000751499335697559705920828", "kappa_fraction": "187874833924389926480207/250000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 22, "source_index": 36, "at": "2026-10-10T17:58:12Z", "until": "2026-10-10T20:05:33Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.000751499335697559705920828", "dashboard_float_text": "0.0007514993356975597", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/309", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 39, "source_index": null, "at": "2026-10-10T17:58:12Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.000751499335697559705920828", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/309", "evidence_excerpt": " = 0.000751499335697559705920828.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 216, "source_index": null, "at": "2026-10-10T13:29:19Z", "until": null, "date_basis": "body-version", "fraction": "187874833924389926480207/250000000000000000000000000", "value_decimal": "0.000751499335697559705920828", "dashboard_float_text": null, "expression": "187874833924389926480207 / 250000000000000000000000000", "historical_title": "Conditional \u03ba = 7.51499335697560e-4: local dirty-response transport, commuting schedules and37 additional gauges on weighted gen5b", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/309", "evidence_excerpt": "This adds a source-bound construction at exact conditional\n\n \u03ba = 187874833924389926480207 / 250000000000000000000000000\n = 0.000751499335697559705920828.\n\nThe new mechanism transports complete signed dirty-helper responses to separate legal target-component cuts. It admits ten unchanged helper", "automated_comparable": true, "body_sha256": "0354c1a95f40e68a91542de593bdb044850591ae53f6873800cf112215b338c2" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/ti-local-response-schedules/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/cohort-kernel-entrances132/RESULT.json, research/filtered-kernel-target120/RESULT.json, research/gen4-composed-endpoints120/RESULT.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/cohort-kernel-entrances132/RESULT.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/309-manifest.json", "sha256": "4ec3dc888c31937ac713733964e064aa49d6cafb73a201fe461154c0a843605e" }, { "file": "remaining-record-audit/artifacts/309/priority-manifest.json", "sha256": "ce466f410a4a19b5bdf539887881ee4015088ae1ebb9f79cfe49f835133368da" } ], "source_head": "aeb4808af1392e565e7071cbeb2c29608201cf24" } }, { "pr": 379, "title": "E8 low-read bit with seven-stage complex supplier", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/379", "author": "eumemic", "created_at": "2026-10-11T06:03:10Z", "accepted_at": "2026-10-16T13:45:39Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00090456959714325", "kappa_fraction": "3618278388573/4000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/e8-low-read-seven-complex/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/e8-low-read-seven-complex/README.md, research/e8-low-read-seven-complex/proof/signed-source/RESULT.json, research/e8-low-read-seven-complex/proof/signed-source/independent-carrier/RESULT.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/e8-low-read-seven-complex/proof/signed-source/RESULT.json#/forward_and_reflected_ledgers/1 and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/e8-low-read-seven-complex/proof/assembly.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/379-manifest.json", "sha256": "eccacae1acc4cfd1764c625b8235f2fad49dc9041dddea19934f7eef7466b17d" }, { "file": "remaining-record-audit/artifacts/379/priority-manifest.json", "sha256": "f07e53c91dd7e6b1ea6a99bcc53ea5e301afe63acdda21b80dbb9bfaf7507801" } ], "source_head": "e01bcc51ca7ee93cec54350afae8f163aafc8f93" } }, { "pr": 639, "title": "Conditional \u03ba = 0.001636461592777116: attain the fixed-dispatch packing ceiling", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/639", "author": "vectorsss", "created_at": "2026-10-13T00:26:01Z", "accepted_at": "2026-10-16T13:45:39Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001636461592777116", "kappa_fraction": "409115398194279/250000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr639-k492-mixed-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 99, "source_index": 147, "at": "2026-10-13T00:26:01Z", "until": "2026-10-13T00:35:48Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001636461592777116", "dashboard_float_text": "0.001636461592777116", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/639", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 116, "source_index": null, "at": "2026-10-13T00:26:01Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001636461592777116", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/639", "evidence_excerpt": "Improves conditional **\u03ba from 0.001636456810414854 (PR638) to 0.001636461592777116**, a gain of **0.000000004782362262**. Comparison is pinned to PR638 head `a77f4a358b5129cda3e510a11a7f9a818aba5274`.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 391, "source_index": null, "at": "2026-10-13T00:26:01Z", "until": null, "date_basis": "opening-title", "fraction": "409115398194279/250000000000000000", "value_decimal": "0.001636461592777116", "dashboard_float_text": null, "expression": "0.001636461592777116", "historical_title": "Conditional \u03ba = 0.001636461592777116: attain the fixed-dispatch packing ceiling", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/639", "evidence_excerpt": "Conditional \u03ba = 0.001636461592777116: attain the fixed-dispatch packing ceiling", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr639-k492-mixed-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/639/priority-manifest.json", "sha256": "60e9f8181fc4a248fc613602174115faacc7ee21a14c55ae7e243c6721cdde5a" } ], "source_head": "a374528ad44924951514067c3e104b7afb0e54c3" } }, { "pr": 1169, "title": "Conditional \u03ba = 0.001675568675201533: joint entrances with T37 owner packing", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1169", "author": "rohanarun", "created_at": "2026-10-13T19:27:43Z", "accepted_at": "2026-10-16T13:45:39Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001675568675201533", "kappa_fraction": "1675568675201533/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1169-joint-entrance-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 142, "source_index": 202, "at": "2026-10-13T19:34:47.562407Z", "until": "2026-10-13T19:41:15Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001675568675201533", "dashboard_float_text": "0.001675568675201533", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1169", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 159, "source_index": null, "at": "2026-10-13T19:34:47.562407+00:00", "until": null, "date_basis": "observed_revision", "fraction": null, "value_decimal": "0.001675568675201533", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1169", "evidence_excerpt": "This composes PR1148's joint entrance choices (head `f1d8dc59288dcab77cae713c450d14069e7eec05`) with a new exact T37 owner flow on PR1131's wave order. The verified conditional value is **\u03ba = 0.001675568675201533**, **0.0004611994%** above PR1148's T16 value `0.001675560947524449`.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 447, "source_index": null, "at": "2026-10-13T19:27:43Z", "until": null, "date_basis": "body-version", "fraction": "52347792856627/31250000000000000", "value_decimal": "0.001675568675201533", "dashboard_float_text": null, "expression": "0.001675129371412064", "historical_title": "Draft conditional \u03ba = 0.001675129371412064: three-demotion provider with T37 packing", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1169", "evidence_excerpt": "eral owner construction pass; full global admission is pending.\n\nThe candidate conditional price is \u03ba = 0.001675129371412064, 0.0004610783% above PR1148 at 0.001675121647789207. It combines PR1148's unchanged local word with a new integer flow on PR1131's T37 wave order. It has 159,840 whole-helper role", "automated_comparable": true, "body_sha256": "5170769a8286c592a30a56ee5fce863428da1bc0ae07b61acd5370f2289a1afc" }, { "stream": "recovered_literal_highwater", "stream_row": 449, "source_index": null, "at": "2026-10-13T19:34:05Z", "until": null, "date_basis": "body-version", "fraction": "1675568675201533/1000000000000000000", "value_decimal": "0.001675568675201533", "dashboard_float_text": null, "expression": "0.001675568675201533", "historical_title": "Draft conditional \u03ba = 0.001675568675201533: joint entrances with T37 owner packing", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1169", "evidence_excerpt": "e7eec05) with a new exact T37 owner flow on PR1131's wave order. The candidate conditional price is \u03ba = 0.001675568675201533, 0.0004611994% above that PR1148 head at 0.001675560947524449.\n\nVerification pending: the 159,840 literal whole-helper roles in 333 calls, exact integer flow equations, bipartite ", "automated_comparable": true, "body_sha256": "6d0741ca5d8d2520a933700eb262bb1ba45aae55dadfec7d071791c3d0672905" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1169-joint-entrance-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 5, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1169/priority-manifest.json", "sha256": "3c94629db0e78a6891e46560f42893f96942489bd775c06ad7c96ee8d7e577d3" } ], "source_head": "13d02293a7af67d7e3bd2e4d7f1a2943ac20537e" } }, { "pr": 1195, "title": "Conditional \u03ba = 0.001675658002271934: two source-holder fusions on #1148's joint-entrance k8 word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1195", "author": "mdumitrean", "created_at": "2026-10-13T19:56:07Z", "accepted_at": "2026-10-16T13:45:39Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001675658002271934", "kappa_fraction": "837829001135967/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_selected_full_program_bytes_missing; gauge44; required full program 82285d3f6365c64259222c4a0c32e06ca24951e193fb8c19341d922c107a891c; both orientations {\"backward\": \"75901f425fb3e2906bef381e8c8bb26fe6414c8b5eacb33e254a726fdb590b5d\", \"forward\": \"6e3f6d92f3f2c0f2df7f59689af78b15209046e66634f4020d46c17d05d5eb8d\"}; Recover exact actual complete selected program bytes, by own immutable primary source or deterministic pinned constructor/recipe with mandatory complete semantic and orientation commitments. A matching profile, scalar saving or another provider does not fill this gap. Missing canonical catalogue may remain a separately stated endpoint premise only after the actual selected program and complete own physical/invoice are bound.", "Source-specific frozen V10 discovery snapshot: actual_selected_physical_input_unresolved; PLAN; expected 4a9e68c06883ba4dffc24074e189d27b40cd95e349559b941f55327c25ee7b1e; Bind the actual complete own PLAN/OWNERS bytes or reconstruct a source-equivalent complete physical realization with explicit changed-parent provenance, actual role/program/windows/stock checks and fresh full invoice. A404 under conventional local paths is not proof that an explicitly pinned parent archive is absent.", "Source-specific frozen V10 discovery snapshot: actual_selected_physical_input_unresolved; OWNERS; expected 7755af4108f066cf1eb13dbaac0a0fbb97a2852ffa7403588d2b5218c81101bf; Bind the actual complete own PLAN/OWNERS bytes or reconstruct a source-equivalent complete physical realization with explicit changed-parent provenance, actual role/program/windows/stock checks and fresh full invoice. A404 under conventional local paths is not proof that an explicitly pinned parent archive is absent." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1195/priority-manifest.json", "sha256": "b46bd025b33b3f3436fcb6feaf3ff85b28a25059b77ad7efa9f383b5879ea01d" } ], "source_head": "99a8a4246fc45ef4f12531fb8545e9e59f7c1652" } }, { "pr": 2260, "title": "Improve conditional \u03ba to 0.0016805 with selective dirty borrowing and physical owner repacking", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2260", "author": "Dugongue", "created_at": "2026-10-15T02:35:02Z", "accepted_at": "2026-10-16T13:49:46Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0016805", "kappa_fraction": "3361/2000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 169, "source_index": 275, "at": "2026-10-15T02:35:02Z", "until": "2026-10-15T02:48:56Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.0016805", "dashboard_float_text": "0.0016805", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2260", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 201, "source_index": null, "at": "2026-10-15T02:35:02Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.0016805", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2260", "evidence_excerpt": "This adds a new exact finite complex supplier and obtains **\u03ba=3361/2000000=0.0016805** under the project's retained all-size and analytic interfaces. It exceeds the highest competing open conditional claim in the recorded review (PR #2220, approximately 0.0016797549561255445) by approximately 7.45044e-7, or 0.0443543%. The gain changes the actual paid construction rather than refining digits of the same supplier. Selected-result pointers remain unchanged.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 479, "source_index": null, "at": "2026-10-15T02:35:02Z", "until": null, "date_basis": "body-version", "fraction": "3361/2000000", "value_decimal": "0.0016805", "dashboard_float_text": null, "expression": "0.0016805", "historical_title": "Improve conditional \u03ba to 0.0016805 with selective dirty borrowing and physical owner repacking", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2260", "evidence_excerpt": "Improve conditional \u03ba to 0.0016805 with selective dirty borrowing and physical owner repacking\n\nThis adds a new exact finite complex supplier and obtains \u03ba=3361/2000000=0.0016805 under the project's retained all-si", "automated_comparable": true, "body_sha256": "5b17654e85913d16c5a006802a9f406af2d75faaab85e50765257458d8b81086" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 9, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/selective-borrowing-kappa/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/selective-borrowing-kappa/arithmetic/EXPECTED.json, research/selective-borrowing-kappa/independent/EXPECTED.json, research/selective-borrowing-kappa/local/data/finite-invoice.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/selective-borrowing-kappa/arithmetic/EXPECTED.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/selective-borrowing-kappa/arithmetic/EXPECTED.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2260-manifest.json", "sha256": "921670d6b15ba53cd0babee4b34ba3c7d208c8ae18fba1e71dc6582fe6a29908" }, { "file": "remaining-record-audit/artifacts/2260/priority-manifest.json", "sha256": "df38eb40e7eef1e77c4348dbe990abe97bba9a43efeaec9469288a53805c16a2" } ], "source_head": "fde6b107e26a14da5bac5b66913c914708ea6901" } }, { "pr": 2284, "title": "Add 87 reusable Lean theorem APIs and conditional \u03ba = 0.00168357", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2284", "author": "Dugongue", "created_at": "2026-10-15T03:28:12Z", "accepted_at": "2026-10-16T13:49:46Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00168357", "kappa_fraction": "168357/100000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_own_source_selector_required; actual own source selector; expected 168357/100000000; Read actual author-head CLAIM/verifier/SOURCES/MANIFEST and identify the selected complete kernel. A missing exact claim-kappa SPEC match is a discovery limitation, not mathematical rejection. Different quoted fixtures must not override a later actual final package. All listed SPEC candidates remain unselected until independently authenticated." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/2284/priority-manifest.json", "sha256": "f6c9b172c8fe8c6b5711f78585ced6ebb32f61b8e7d5448e4de2bfd86178c72b" } ], "source_head": "e71574b92f6af546013c71293cd03ff58742a1e6" } }, { "pr": 2530, "title": "Conditional \u03ba \u2248 0.0017137379215475043 from source-partner lifetimes and physical rehosting", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2530", "author": "zxv", "created_at": "2026-10-15T13:42:07Z", "accepted_at": "2026-10-16T13:49:46Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0017137379215475043", "kappa_fraction": "17137379215475043/10000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 186, "source_index": 297, "at": "2026-10-15T13:42:07Z", "until": "2026-10-15T14:05:22.847556Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001713737921547504346752", "dashboard_float_text": "0.0017137379215475044", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2530", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 219, "source_index": null, "at": "2026-10-15T13:42:07Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001713737921547504346752", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2530", "evidence_excerpt": "The full global paid profile is `{1:1599730, 2:420912, 3:219782, 4:78588, 5:17756, 7:5328, 8:114, 16:172, 32:3, 48:26488}`. There are 74 replicas, 666 calls, dimension 73, live stock 66304, physical stock 66814, deficit 23680, and charged prefix reserve 2048 bits. The exact hosted rank mass is 4,816,512. The supplier endpoint is 0.001713737921547504346752; exact outer refinement establishes the final claim.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 496, "source_index": null, "at": "2026-10-15T13:42:07Z", "until": null, "date_basis": "body-version", "fraction": "17137379215475043/10000000000000000000", "value_decimal": "0.001713737921547504346752", "dashboard_float_text": null, "expression": "0.0017137379215475043", "historical_title": "Conditional \u03ba \u2248 0.0017137379215475043 from source-partner lifetimes and physical rehosting", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2530", "evidence_excerpt": "y aliases on the pinned PR2462 words, followed by a new whole-call owner schedule, give conditional \u03ba \u2248 0.0017137379215475043, about 0.59058% above the pinned PR2474 comparison claim. The exact rational is in research/source-partner-lifetimes/CLAIM.json.\n\nRestore jointly recoverable source partners befor", "automated_comparable": true, "body_sha256": "65b15930c8dde12a97705d799cadd58562e2ff6bc4edad66eb8086eb04dd2ea6" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_own_source_selector_required; actual own source selector; expected 17137379215475043/10000000000000000000; Read actual author-head CLAIM/verifier/SOURCES/MANIFEST and identify the selected complete kernel. A missing exact claim-kappa SPEC match is a discovery limitation, not mathematical rejection. Different quoted fixtures must not override a later actual final package. All listed SPEC candidates remain unselected until independently authenticated." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/2530/priority-manifest.json", "sha256": "1ac5f54bdca71a7f079769134745b4a28359522b8e0a15a7dae912ec8acfd044" } ], "source_head": "b4012098048e12500b2d33d2e84be281915a27ac" } }, { "pr": 1574, "title": "Conditional kappa 0.001676855229071321886...46232: verified outer320 certificate refinement", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1574", "author": "rohanarun", "created_at": "2026-10-14T03:13:14Z", "accepted_at": "2026-10-16T13:49:47Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676855229071321886206456772274592619512448739510475263", "kappa_fraction": "20960690363391523577580709653432407743905609243880940785042064888139458190150120618947308645517306787411594297629927725788771206610253564028669239839696483063641076603811835992041322819305851862929976904089416876423930634114733172337475459206681075867199107741186690035167468492845353630142698008003963184344710093279/12500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1574-gaussian-only-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 181, "source_index": null, "at": "2026-10-14T03:13:14Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00167685522907132188620645677227459261951244873951047526280336519105115665521200964951578469164138454299292754381039421806310169652882028512229353918717571864509128612830494687936330582554446814903439815232715335011391445072917865378699803673653448606937592861929493520281339747942762829041141584064031705474757680746232", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1574", "evidence_excerpt": "Conditional kappa = **0.00167685522907132188620645677227459261951244873951047526280336519105115665521200964951578469164138454299292754381039421806310169652882028512229353918717571864509128612830494687936330582554446814903439815232715335011391445072917865378699803673653448606937592861929493520281339747942762829041141584064031705474757680746232**.", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. 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Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 183, "source_index": null, "at": "2026-10-14T04:21:33Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00167685522907132188620645677227459261951244873951047526280336519105115665521200964951578469164138454299292754381039421806310169652882028512229353918717571864509128612830494687936330582554446814903439815232715335011391445072917865378699803673653448606937592861929493520281339747942762829041141584064119827165305262609678040145750788396458013231207613085484523168448523567069817042680204269623160169827089822176849542568808893053045639627892165202346049883082847363034918", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1629", "evidence_excerpt": "Complete local finite verification passed for conditional kappa **0.001676855229071321886206456772274592619512448739510475262803365191051156655212009649515784691641384542992927543810394218063101696528820285122293539187175718645091286128304946879363305825544468149034398152327153350113914450729178653786998036736534486069375928619294935202813397479427628290411415840641198271653052626096780401457507883964580132312076130854845231684485235670698170426802042696231601698270898221768495425688088930530456", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1629-gaussian-only-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1629/priority-manifest.json", "sha256": "56574b1bce84d89b54ec4481ac06bd3cf16377ba1b5079801e988a1d6b4690c2" } ], "source_head": "9388d269c1a1405f9808c5c4e609fe983c60a07e" } }, { "pr": 1673, "title": "Conditional kappa = 0.001677160151714381 via capped phase-cell fusion", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1673", "author": "Vlado-V", "created_at": "2026-10-14T06:15:44Z", "accepted_at": "2026-10-16T13:49:47Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001677160151714381", "kappa_fraction": "1677160151714381/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1673-explicit-core-gaussian-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint.", "This is a new direct Gaussian/Fermat realization of the explicitly selected1661 core, not a cost proof or validation of every theorem of the original capped phase-cell fusion outer algorithm. No optional matrix9/4 premise or original BIT supplier is consumed.", "Concrete normalized Gaussian/finite-LDU/narrow-gap/cyclic-border/fine-prime/recovery and repaired reference correctness/finite-kernel halting remain the closed component interfaces; no arbitrary-scale accretive theorem is used." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 156, "source_index": 248, "at": "2026-10-14T06:15:44Z", "until": "2026-10-14T06:27:38Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001677160151714381", "dashboard_float_text": "0.001677160151714381", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1673", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 186, "source_index": null, "at": "2026-10-14T06:15:44Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001677160151714381", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1673", "evidence_excerpt": "$$T(n)=O(n(\\log n)^{1-\\kappa}),\\qquad \\kappa=1677160151714381/10^{18}=0.001677160151714381.$$", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "23/10000", "status": "Maintainer-reviewed conditional productive-helper construction; see integration receipt for publication state", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier4359.json", "path": "certificates/checkpoints/frontier4359.json", "commit": null, "at": null, "scope": "Productive-helper p3 construction under retained analytic decomposition, exact recovery, native ordered movement, fixed-tape execution, fine-prime padding and gauge-free outer estimates. Changed interfaces reviewed with AI assistance; no formal or independent human verification of the full theorem. Winning uniform templates are algorithm-defined, not materialized. Frozen claim publication booleans describe submission time. Unrelated H-branch research is not selected." }, { "stream": "all_selected_result_history", "record_kappa": "60403/20000000", "status": "Selected maintainer-reviewed conditional joint-helper construction; source-bound foundation reuse is explicit", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/4f19cedcd8d81e4a2359449309fa6e9f17dfd22e/certificates/selected-result.json", "path": null, "commit": "4f19cedcd8d81e4a2359449309fa6e9f17dfd22e", "at": "2026-10-22T12:16:48Z", "scope": "Maintainer-reviewed conditional PR4470 construction. Inherited native/all-column, owned-erasure, whole-job, compiler, precision/tape, analytic, prime and recovery hypotheses remain. Uniform words are not materialized." }, { "stream": "all_selected_result_history", "record_kappa": "23/10000", "status": "Maintainer-reviewed conditional productive-helper construction; see integration receipt for publication state", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/ae87507c0767c00f5a55ee9062c496191e978632/certificates/selected-result.json", "path": null, "commit": "ae87507c0767c00f5a55ee9062c496191e978632", "at": "2026-10-21T19:10:46Z", "scope": "Productive-helper p3 construction under retained analytic decomposition, exact recovery, native ordered movement, fixed-tape execution, fine-prime padding and gauge-free outer estimates. Changed interfaces reviewed with AI assistance; no formal or independent human verification of the full theorem. Winning uniform templates are algorithm-defined, not materialized. Frozen claim publication booleans describe submission time. Unrelated H-branch research is not selected." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint.", "This is a new direct Gaussian/Fermat realization of the explicitly selected1661 core, not a cost proof or validation of every theorem of the original capped phase-cell fusion outer algorithm. No optional matrix9/4 premise or original BIT supplier is consumed.", "Concrete normalized Gaussian/finite-LDU/narrow-gap/cyclic-border/fine-prime/recovery and repaired reference correctness/finite-kernel halting remain the closed component interfaces; no arbitrary-scale accretive theorem is used." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1673-explicit-core-gaussian-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1673/priority-manifest.json", "sha256": "138e9a62edf6bc4e5633bb195f325efc75776705649309b235b1188fda2f0292" } ], "source_head": "85ddaa312e463cfaca98d49a2a262994551cec4e" } }, { "pr": 1718, "title": "Conditional kappa 0.001676938111022438: compose signed pivot554 resto\u2026", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1718", "author": "Pseudoataraxia", "created_at": "2026-10-14T07:44:04Z", "accepted_at": "2026-10-16T13:49:47Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676938111022438", "kappa_fraction": "838469055511219/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t74-p554-signed-restoration/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/t74-p554-signed-restoration/PROOF.md, research/t74-p554-signed-restoration/README.md, research/t74-p554-signed-restoration/RESULT.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/t74-p554-signed-restoration/PROOF.md, research/t74-p554-signed-restoration/README.md, research/t74-p554-signed-restoration/RESULT.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/t74-p554-signed-restoration/RESULT.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/1718-manifest.json", "sha256": "387c5179ce2f8ae5dd7f7146bfea56342715e17a8567cd69e8d8b7ad7dd814c4" }, { "file": "remaining-record-audit/artifacts/1718/priority-manifest.json", "sha256": "bfe0a1c446cb1665cf9aa87d59f63fb39e64c6390bb03cf2337f9dfd9f54694a" } ], "source_head": "cd1294ebef686ff2f3cbdba1476d5f9136cb41d2" } }, { "pr": 1828, "title": "Verified conditional kappa: positive slack refinement over PR1800 (+2.00336e-64)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1828", "author": "rohanarun", "created_at": "2026-10-14T11:22:19Z", "accepted_at": "2026-10-16T13:49:47Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001679754956125544521335670993920702576998311438502580295", "kappa_fraction": "3359509912251089042671341987841405153996622877005160590920655040325599999999999999999999999995993280980173497821914657316024317/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1828-selected-k554-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 168, "source_index": 266, "at": "2026-10-14T11:22:19Z", "until": "2026-10-14T13:07:40.625172Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.0016797549561255445213356709939207025769983114385025802954603275201627999999999999999999999999979966404900867489109573286580121585", "dashboard_float_text": "0.0016797549561255445", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1828", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 198, "source_index": null, "at": "2026-10-14T11:22:19Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.0016797549561255445213356709939207025769983114385025802954603275201627999999999999999999999999979966404900867489109573286580121585", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1828", "evidence_excerpt": "Verified conditional arithmetic refinement of PR1800: kappa = **0.0016797549561255445213356709939207025769983114385025802954603275201627999999999999999999999999979966404900867489109573286580121585**.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 472, "source_index": null, "at": "2026-10-14T11:22:19Z", "until": null, "date_basis": "body-version", "fraction": "3359509912251089042671341987841405153996622877005160590920655040325599999999999999999999999995993280980173497821914657316024317/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "value_decimal": "0.0016797549561255445213356709939207025769983114385025802954603275201627999999999999999999999999979966404900867489109573286580121585", "dashboard_float_text": null, "expression": "0.0016797549561255445213356709939207025769983114385025802954603275201627999999999999999999999999979966404900867489109573286580121585", "historical_title": "Draft conditional kappa: positive slack refinement over PR1800 (+2.00336e-64)", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1828", "evidence_excerpt": "Draft conditional arithmetic refinement of PR1800: kappa = 0.0016797549561255445213356709939207025769983114385025802954603275201627999999999999999999999999979966404900867489109573286580121585.\n\nThe exact gain over PR1800 at 46d865ab92e58098538b8c5348b6a131c99abf45 is 2.00335950991325108904267134198782137240490086748910957328658E-64. This changes positive free slacks on", "automated_comparable": true, "body_sha256": "203cdd04b6c94b0157e909be36cb506572bed38b7e1b0c394962fae7b9b511d7" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr1828-selected-k554-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 7, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1828/priority-manifest.json", "sha256": "2e19a4d358676640e1ea09dbd40154124861780deb1921ef2d865801da9677bd" } ], "source_head": "5273aef05e2d554b1a4a9235d75039e2d1ec1aa9" } }, { "pr": 1875, "title": "Conditional \u03ba = 0.0016797549561255445213356709939207025769983114385025802954603275201628645482603256388263056561\u2026: supplier endpoint recertified to 1e-300 with 1e-310 slacks (+6.56e-91 over PR1839)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1875", "author": "rohanarun", "created_at": "2026-10-14T12:52:22Z", "accepted_at": "2026-10-16T13:49:47Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001679754956125544521335670993920702576998311438502580295", "kappa_fraction": "8398774780627722606678354969603512884991557192512901477301637600814322741301628194131528280664223161372256584542931104860352240600827060713856503183464783578674812636953114638574227090497768781685562377794069883920702765193372789409782809399003446270856098837437418473378465284913944613786596277824999999998998320245043374455478664329006079297/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1875-selected-k554-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "recovered_literal_highwater", "stream_row": 473, "source_index": null, "at": "2026-10-14T12:52:22Z", "until": null, "date_basis": "body-version", "fraction": "8398774780627722606678354969603512884991557192512901477301637600814322741301628194131528280664223161372256584542931104860352240600827060713856503183464783578674812636953114638574227090497768781685562377794069883920702765193372789409782809399003446270856098837437418473378465284913944613786596277824999999998998320245043374455478664329006079297/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "value_decimal": "0.0016797549561255445213356709939207025769983114385025802954603275201628645482603256388263056561328446322744513169085862209720704481201654121427713006366929567157349625273906229277148454180995537563371124755588139767841405530386745578819565618798006892541712197674874836946756930569827889227573192555649999999997996640490086748910957328658012158594", "dashboard_float_text": null, "expression": "0.0016797549561255445213356709939207025769983114385025802954603275201628645482603256388263056561328446322744513169085862209720704481201654121427713006366929567157349625273906229277148454180995537563371124755588139767841405530386745578819565618798006892541712197674874836946756930569827889227573192555649999999997996640490086748910957328658012158594", "historical_title": "Conditional \u03ba = 0.0016797549561255445213356709939207025769983114385025802954603275201628645482603256388263056561\u2026: supplier endpoint recertified to 1e-300 with 1e-310 slacks (+6.56e-91 over PR1839)", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1875", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.0016797549561255445213356709939207025769983114385025802954603275201628645482603256388263056561328446322744513169085862209720704481201654121427713006366929567157349625273906229277148454180995537563371124755588139767841405530386745578819565618798006892541712197674874836946756930569827889227573192555649999999997996640490086748910957328658012158594\n\nThis is +6.5613e-91 over PR1839 (jeremykothe2, 836ef6a1, the current leader) on the identical construction: the pivot-566 ", "automated_comparable": true, "body_sha256": "c5e09bc103d8d30488e07c99dd24cfe7a912394d3409bfe853dca0240965dad3" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr1875-selected-k554-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1875/priority-manifest.json", "sha256": "501f1656450f87215f7de5cc0cb0ee812a37191b2ba29cc74af9f559afe4e853" } ], "source_head": "bb40dfc8e155d0b4daad1d910ba3ee751669b52c" } }, { "pr": 2077, "title": "Research: four helper placements improve selected T16 kappa", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2077", "author": "lydakis", "created_at": "2026-10-14T18:47:43Z", "accepted_at": "2026-10-16T13:49:47Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672664045494084", "kappa_fraction": "418166011373521/250000000000000000", "kappa_status": "authenticated_actual_merged_source_selection", "kappa_scope": "The costed \u03ba comes from the explicitly selected source included at this merge. The original parser quote is retained and visibly distinguished. Own immutable MANIFEST/verify/build reconstruct all3complete data bytes; own SPEC and CANDIDATE.expected_updates select actual target, while CANDIDATE baseline is the preserved frozen parser quote.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr2077-vacancy-chain-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "frozen_kappa_metadata": { "kappa_fraction": "836330098538459/500000000000000000", "kappa_decimal": "0.001672660197076918", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement." }, "source_selected_kappa_correction": true, "source_selected_kappa_correction_basis": "Own immutable MANIFEST/verify/build reconstruct all3complete data bytes; own SPEC and CANDIDATE.expected_updates select actual target, while CANDIDATE baseline is the preserved frozen parser quote.", "source_kappa_correction_primary_receipt": "data/operation-audit/pr2077-source-chronology/chronology.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr2077-vacancy-chain-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 6, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/2077/priority-manifest.json", "sha256": "247467bd0b4c84788c3c4d1ddffebca48fbfdd6cb86495a261b1a976508197cb" } ], "source_head": "407712103b605a662a89a56f9c42b93dca69126b" } }, { "pr": 2482, "title": "Research: verified pure44/q518/506 composition and latest-source comparison", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2482", "author": "mdumitrean", "created_at": "2026-10-15T12:28:03Z", "accepted_at": "2026-10-16T13:49:47Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001696599961051819247369999999999799660680007689636150526", "kappa_fraction": "42414999026295481184249999999994991517000192240903763150000000001/25000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_own_source_selector_required; actual own source selector; expected 42414999026295481184249999999994991517000192240903763150000000001/25000000000000000000000000000000000000000000000000000000000000000000; Read actual author-head CLAIM/verifier/SOURCES/MANIFEST and identify the selected complete kernel. A missing exact claim-kappa SPEC match is a discovery limitation, not mathematical rejection. Different quoted fixtures must not override a later actual final package. All listed SPEC candidates remain unselected until independently authenticated." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/2482/priority-manifest.json", "sha256": "7d43233346405770207ba460af395266df07652a7b070fb0535aea0c9433ff53" } ], "source_head": "bbf238f3a4b9a640381015967fe1c07836ed1fd2" } }, { "pr": 2942, "title": "Conditional \u03ba \u2248 0.0017228163198632: four paired extractions at normal 45 on #2917's words (+3.16e-7 over #2930)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2942", "author": "mdumitrean", "created_at": "2026-10-16T13:09:52Z", "accepted_at": "2026-10-16T13:54:36Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001722816319863214327995999999999999999999999900000000000", "kappa_fraction": "17228163198632143279959999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 210, "source_index": 331, "at": "2026-10-16T13:09:52Z", "until": "2026-10-16T13:48:18Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001722816319863214327996", "dashboard_float_text": "0.0017228163198632143", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2942", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 245, "source_index": null, "at": "2026-10-16T13:09:52Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001722816319863214327996", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2942", "evidence_excerpt": "**\u03ba = 0.001722816319863214327996 \u2212 10\u207b\u2074\u2076 \u2212 10\u207b\u2077\u2070**, exactly `316413419939763639/10\u00b2\u2074` \u2248 **+3.1641e-7** over #2930 at `81f3b5d12977eba09e06fbff729167d59faabe90` (\u2248 +1.2277e-6 over #2917).", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 526, "source_index": null, "at": "2026-10-16T13:09:52Z", "until": null, "date_basis": "body-version", "fraction": "17228163198632143279959999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "value_decimal": "0.001722816319863214327996", "dashboard_float_text": null, "expression": "0.001722816319863214327996 - 10^-46 - 10^-70", "historical_title": "Conditional \u03ba \u2248 0.0017228163198632: four paired extractions at normal 45 on #2917's words (+3.16e-7 over #2930)", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2942", "evidence_excerpt": " (45), with a new literal T74 allocation of the changed inventory, through the complete admission:\n\n\u03ba = 0.001722816319863214327996 - 10^-46 - 10^-70, exactly 316413419939763639/10^24 \u2248 +3.1641e-7 over #2930 at 81f3b5d12977eba09e06fbff729167d59faabe90 (\u2248 +1.2277e-6 over #2917).\n\n## What changes\n\nHelpers 249, 267, 251, 265 are r", "automated_comparable": true, "body_sha256": "6a014a054013bb7ffe0aecbb54cce0baab7f56db01297a77aa76aec435a01aab" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 9, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/paired-extension-normal45/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/paired-extension-normal45/CLAIM.json, research/paired-extension-normal45/MANIFEST.json, research/paired-extension-normal45/README.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/paired-extension-normal45/CLAIM.json, research/paired-extension-normal45/MANIFEST.json, research/paired-extension-normal45/README.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/paired-extension-normal45/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2942-manifest.json", "sha256": "e0aa76b93fc778953ddb5a6893c2142ec0bb59fddbef53c5d78418c5a7fd8398" }, { "file": "remaining-record-audit/artifacts/2942/priority-manifest.json", "sha256": "e5557a6fc4c09d7128e2299a7095ec0de05829da945e1e51b70de8870869d387" } ], "source_head": "a027b0f6fdb0ab2b42ba10fc31b53960166bf2bf" } }, { "pr": 2696, "title": "Improve conditional kappa to 0.001715599770234969498857 with concentrated source-partner assignments", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2696", "author": "mason-hale", "created_at": "2026-10-15T17:40:30Z", "accepted_at": "2026-10-16T13:54:37Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001715599770234969498857", "kappa_fraction": "1715599770234969498857/1000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 193, "source_index": 306, "at": "2026-10-15T17:40:30Z", "until": "2026-10-15T19:43:14Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001715599770234969498857", "dashboard_float_text": "0.0017155997702349695", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2696", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 226, "source_index": null, "at": "2026-10-15T17:40:30Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001715599770234969498857", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2696", "evidence_excerpt": "Improve conditional kappa to 0.001715599770234969498857 with concentrated source-partner assignments", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 503, "source_index": null, "at": "2026-10-15T17:40:30Z", "until": null, "date_basis": "body-version", "fraction": "1715599770234969498857/1000000000000000000000000", "value_decimal": "0.001715599770234969498857", "dashboard_float_text": null, "expression": "0.001715599770234969498857", "historical_title": "Improve conditional kappa to 0.001715599770234969498857 with concentrated source-partner assignments", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2696", "evidence_excerpt": "## Result\n\nProposes conditional \u03ba = 0.001715599770234969498857, about 0.05829% above PR2673's outer \u03ba and 2.5671% above the selected PR1094 point. The selected record is unchanged.\n\nThe new construction assigns all eight recovered source-part", "automated_comparable": true, "body_sha256": "45731dec1f0fdab6aaaf224f18a64dbb7d394802f1899e8ea37e0a7a429cb6cf" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 12, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t74-concentrated-source-partners/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Recompute the complete own productive/paid histogram from research/t74-concentrated-source-partners/CLAIM.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/t74-concentrated-source-partners/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2696-manifest.json", "sha256": "284f646c5c5a4213b6c6486c4b6410f02c1aad85377b551fba6915210c56fc7a" }, { "file": "remaining-record-audit/artifacts/2696/priority-manifest.json", "sha256": "95c4a952901d78b9a765bab8d39740aed7dcdb575210be41c23db38a218a743d" } ], "source_head": "5a42add713e09a8798a84d0be7a8276626d9e785" } }, { "pr": 2751, "title": "Conditional kappa \u2248 0.00171714158635 via joint twelve-source recovery", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2751", "author": "tekuuu", "created_at": "2026-10-15T20:10:14Z", "accepted_at": "2026-10-16T13:54:37Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001717141586348426338109", "kappa_fraction": "1717141586348426338109/1000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 195, "source_index": 308, "at": "2026-10-15T20:10:14Z", "until": "2026-10-15T20:18:28.785050Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001717141586348426338109", "dashboard_float_text": "0.0017171415863484263", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2751", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 228, "source_index": null, "at": "2026-10-15T20:10:14Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001717141586348426338109", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2751", "evidence_excerpt": "This jointly reassigns all twelve T74 source aliases, including the four older recovery paths held fixed by PR2720. All eight central recursive children remain rank8. After composing PR2679's six pre-life hosts/refit and PR2673's complete owner allocation, the new conditional \u03ba is **0.001717141586348426338109\u2026**, about **0.05834% above PR2733 and PR2745**. The exact rational is `0.001717141586348426338109 - 10^-46 - 10^-70`; the selected frontier is unchanged.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 507, "source_index": null, "at": "2026-10-15T20:10:14Z", "until": null, "date_basis": "body-version", "fraction": "1717141586348426338109/1000000000000000000000000", "value_decimal": "0.001717141586348426338109", "dashboard_float_text": null, "expression": "0.001717141586348426338109", "historical_title": "Conditional kappa \u2248 0.00171714158635 via joint twelve-source recovery", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2751", "evidence_excerpt": "osing PR2679's six pre-life hosts/refit and PR2673's complete owner allocation, the new conditional \u03ba is 0.001717141586348426338109\u2026, about 0.05834% above PR2733 and PR2745. The exact rational is 0.001717141586348426338109 - 10^-46 - 10^-70; the selected frontier is unchanged.\n\nThe four changed (removed helper", "automated_comparable": true, "body_sha256": "87a6130a562e915602af1059a848c0d65535947ed418fa9308747734aade44e4" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t74-joint-twelve/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/t74-joint-twelve/CLAIM.json, research/t74-joint-twelve/PROOF.md, research/t74-joint-twelve/README.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/t74-joint-twelve/CLAIM.json, research/t74-joint-twelve/PROOF.md, research/t74-joint-twelve/README.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/t74-joint-twelve/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2751-manifest.json", "sha256": "3677365858a329b5758a8e1e4c41e7ccf414abecc3192ce264a900c300f26f46" }, { "file": "remaining-record-audit/artifacts/2751/priority-manifest.json", "sha256": "027973387b46e69388a30838dc61b48c5cf4efba17370453e830861de5ea48a9" } ], "source_head": "4cfbb0cc8314d7fb4e8e754545a49a42eb590a69" } }, { "pr": 2766, "title": "Improve conditional \u03ba to 0.001717256973467 with credited routing-frame fusion", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2766", "author": "DavidAriasC", "created_at": "2026-10-15T20:53:17Z", "accepted_at": "2026-10-16T13:54:37Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00171725697346700230827", "kappa_fraction": "171725697346700230827/100000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 196, "source_index": 310, "at": "2026-10-15T20:53:17Z", "until": "2026-10-15T20:54:00Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001717256973467002308270", "dashboard_float_text": "0.0017172569734670022", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2766", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 229, "source_index": null, "at": "2026-10-15T20:53:17Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001717256973467002308270", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2766", "evidence_excerpt": "The resulting conditional bound is **\u03ba \u2248 0.001717256973467002308270**, an absolute gain of `0.000000115387118575970161` and a relative gain of **0.006719720697%** over the pinned twelve-source predecessor. This is a small, fully priced improvement; the refit itself is credited work, not a new mechanism.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 508, "source_index": null, "at": "2026-10-15T20:53:17Z", "until": null, "date_basis": "body-version", "fraction": "171725697346700230827/100000000000000000000000", "value_decimal": "0.001717256973467002308270", "dashboard_float_text": null, "expression": "0.001717256973467002308270", "historical_title": "Improve conditional \u03ba to 0.001717256973467 with credited routing-frame fusion", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2766", "evidence_excerpt": "passes full finite native, supplier and modern outer admission.\n\nThe resulting conditional bound is \u03ba \u2248 0.001717256973467002308270, an absolute gain of 0.000000115387118575970161 and a relative gain of 0.006719720697% over the pinned twelve-source predecessor. This is a small, fully priced improvement; the re", "automated_comparable": true, "body_sha256": "ac34a290fd3dc1e064c230e90f781a4d5c327b79b0804ad92a0ae30ea29f65a8" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/complex-routing-leaf-fusion/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/complex-routing-leaf-fusion/CLAIM.json, research/complex-routing-leaf-fusion/PROOF.md, research/complex-routing-leaf-fusion/RESULT.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/complex-routing-leaf-fusion/RESULT.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/complex-routing-leaf-fusion/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2766-manifest.json", "sha256": "93cecc245901e3241f7ce6c4e7778d0845871c56ab2c4273811efbef5b38c654" }, { "file": "remaining-record-audit/artifacts/2766/priority-manifest.json", "sha256": "7f4d91f241ae10b5c8963500ea9914916e0ca890c7965cf109cded9b25029dde" } ], "source_head": "e6df920cd0110e4b629e2ad84eddcb539001e174" } }, { "pr": 2802, "title": "Conditional \u03ba \u2248 0.001717794984118634663827: two hostee moves and seven retired-lender aliases on #2751's joint twelve-source words", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2802", "author": "mdumitrean", "created_at": "2026-10-15T22:23:09Z", "accepted_at": "2026-10-16T13:54:37Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001717794984118634663826999", "kappa_fraction": "1717794984118634663826999/1000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "recovered_literal_highwater", "stream_row": 510, "source_index": null, "at": "2026-10-15T22:23:09Z", "until": null, "date_basis": "body-version", "fraction": "1717794984118634663826999/1000000000000000000000000000", "value_decimal": "0.001717794984118634663826999", "dashboard_float_text": null, "expression": "0.001717794984118634663826999", "historical_title": "Conditional \u03ba \u2248 0.001717794984118634663827: two hostee moves and seven retired-lender aliases on #2751's joint twelve-source words", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2802", "evidence_excerpt": "other\ntwo are opened by moving two existing borrows onto free retired lenders.\n\nThe new conditional \u03ba is 0.001717794984118634663826999\u2026. The exact rational is 0.001717794984118634663827 - 10^-46 - 10^-70;\nthe selected frontier is unchanged.\n\n| over | margin |\n|---|---|\n| #2751 (tekuuu) | +6.53397770208325718e-7 (", "automated_comparable": true, "body_sha256": "b0780e18bdc59903261e984066d81e25e023e6c17f20e0894298c09de87517e0" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 12, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t74-joint-twelve-retired7/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/t74-joint-twelve-retired7/CLAIM.json, research/t74-joint-twelve-retired7/PROOF.md, research/t74-joint-twelve-retired7/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/t74-joint-twelve-retired7/CLAIM.json, research/t74-joint-twelve-retired7/PROOF.md, research/t74-joint-twelve-retired7/SOURCES.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/t74-joint-twelve-retired7/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2802-manifest.json", "sha256": "787c403c31e204092a5a2d8af81208da7e820972ff41159387c7b6f10d8a6408" }, { "file": "remaining-record-audit/artifacts/2802/priority-manifest.json", "sha256": "28022fb4d8e1d9c03f3fc89aa2e0b98deca33944d4706ce468785f76fdbe23c4" } ], "source_head": "17b2ee6ef3cf1468e78a6267f0ecbc9a0e6f60dd" } }, { "pr": 2804, "title": "Independent verification (no \u03ba): #2530's source-partner words exact through cleanup and endpoint; stock, endpoint enclosure and \u03ba composition reproduce; no defect found", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2804", "author": "thakrarsagar", "created_at": "2026-10-15T22:26:53Z", "accepted_at": "2026-10-16T13:54:37Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0017137379", "kappa_fraction": "17137379/10000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep the actual named multiplier/changedprogram as a distinct costing target. This contribution is validation, a restricted theorem or an unimplementedtarget; it defines no new fullruntime point. Its target-specific scope/negative controls/constant qualifications must be checked when a complete supplier is priced." ], "source_manifest": [ { "file": "individual-primary-interface-source/2804-manifest.json", "sha256": "2477c5779c805bf388e08ebfa931144a6e5bb944c8f7eb71df817f00fbfefcfd" }, { "file": "remaining-record-audit/artifacts/2804/priority-manifest.json", "sha256": "fe9e88c46f9b721ebeb381c9061f099aff338445480e580fda61fa44e4774468" } ], "source_head": "feb727ba471b5dc3f057f867804aa70ae58b2e71" } }, { "pr": 2824, "title": "T94 retained-tail allocation on PR2802: conditional kappa 0.001717795160032012107407", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2824", "author": "Dugongue", "created_at": "2026-10-15T23:59:46Z", "accepted_at": "2026-10-16T13:54:37Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001717795160032012107407", "kappa_fraction": "1717795160032012107407/1000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 198, "source_index": 313, "at": "2026-10-15T23:59:46Z", "until": "2026-10-16T00:26:58Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.0017177951600320121074069999999999999999999998999999999999999999999999", "dashboard_float_text": "0.0017177951600320122", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2824", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 232, "source_index": null, "at": "2026-10-15T23:59:46Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.0017177951600320121074069999999999999999999998999999999999999999999999", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2824", "evidence_excerpt": "The complete T94 allocation raises the conditional finite-supplier headline from PR2802's 0.001717794984118634663827 lower certificate to 0.0017177951600320121074069999999999999999999998999999999999999999999999. The exact gain is 8795668872179/50000000000000000000000. Increasing replicas 74 to 94 amortizes the same explicitly charged positive residue; 345,168 literal owner roles compose with the credited retired7 native construction.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 512, "source_index": null, "at": "2026-10-15T23:59:46Z", "until": null, "date_basis": "opening-title", "fraction": "1717795160032012107407/1000000000000000000000000", "value_decimal": "0.0017177951600320121074069999999999999999999998999999999999999999999999", "dashboard_float_text": null, "expression": "0.001717795160032012107407", "historical_title": "T94 retained-tail allocation on PR2802: conditional kappa 0.001717795160032012107407", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2824", "evidence_excerpt": "T94 retained-tail allocation on PR2802: conditional kappa 0.001717795160032012107407", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 12, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/replica-tail-gain/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/replica-tail-gain/CLAIM.json, research/replica-tail-gain/validation/NATIVE.json, research/replica-tail-gain/PROOF.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/replica-tail-gain/CLAIM.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/replica-tail-gain/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2824-manifest.json", "sha256": "5c895c26951a4c9da07344b2eb41f6e07f7e45a9aa594743272a5e60730936e6" }, { "file": "remaining-record-audit/artifacts/2824/priority-manifest.json", "sha256": "561b28bf01ccdf93b9244776ed945f63eab7d3f0144f864a12ec6979209a0eb3" } ], "source_head": "f1826afe1f487333f2c1e5bf862bae2211ce8dd9" } }, { "pr": 2827, "title": "T104 paid allocation and exact prefix reserve: conditional \u03ba \u2248 0.001717795222616587743198", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2827", "author": "Dugongue", "created_at": "2026-10-16T00:26:58Z", "accepted_at": "2026-10-16T13:54:37Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001717795222616587743198", "kappa_fraction": "858897611308293871599/500000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 199, "source_index": 314, "at": "2026-10-16T00:26:58Z", "until": "2026-10-16T00:56:10Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.0017177952226165877431979999999999999999999998999999999999999999999999", "dashboard_float_text": "0.0017177952226165877", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2827", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 233, "source_index": null, "at": "2026-10-16T00:26:58Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.0017177952226165877431979999999999999999999998999999999999999999999999", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2827", "evidence_excerpt": "The complete T104 allocation raises the conditional \u03ba from PR2824's delivered T94 point to 0.0017177952226165877431979999999999999999999998999999999999999999999999. The exact gain is 62584575635791/1000000000000000000000000 (6.2584575635791e-11). It retains PR2802's credited native words and one charged positive residue.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 513, "source_index": null, "at": "2026-10-16T00:26:58Z", "until": null, "date_basis": "opening-title", "fraction": "858897611308293871599/500000000000000000000000", "value_decimal": "0.0017177952226165877431979999999999999999999998999999999999999999999999", "dashboard_float_text": null, "expression": "0.001717795222616587743198", "historical_title": "T104 paid allocation and exact prefix reserve: conditional \u03ba \u2248 0.001717795222616587743198", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2827", "evidence_excerpt": "T104 paid allocation and exact prefix reserve: conditional \u03ba \u2248 0.001717795222616587743198", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 12, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/superior-replica-kappa/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/superior-replica-kappa/CLAIM.json, research/superior-replica-kappa/validation/NATIVE.json, research/superior-replica-kappa/PROOF.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/superior-replica-kappa/CLAIM.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/superior-replica-kappa/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2827-manifest.json", "sha256": "e67059065c660b65ed892b1be58ee2476a9b3e08a75d2e641450a3e7379dfa52" }, { "file": "remaining-record-audit/artifacts/2827/priority-manifest.json", "sha256": "9ffa4a74948e21763d51d2f1b38162839843668c6c1a21bdaabb1fd373ce0ecf" } ], "source_head": "4dc1286a476874447f76826885c6af99409a1d46" } }, { "pr": 2863, "title": "Attain the fixed-word packing optimum: conditional \u03ba \u2248 0.0017201008054", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2863", "author": "Dugongue", "created_at": "2026-10-16T04:47:29Z", "accepted_at": "2026-10-16T13:54:37Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001720100805416885927943999999999999999999999900000000000", "kappa_fraction": "17201008054168859279439999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 206, "source_index": 325, "at": "2026-10-16T04:47:29Z", "until": "2026-10-16T05:13:35Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001720100805416885927944", "dashboard_float_text": "0.001720100805416886", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2863", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 240, "source_index": null, "at": "2026-10-16T04:47:29Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001720100805416885927944", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2863", "evidence_excerpt": "Combines the complete shared-kernel words from PR #2857 with a width 9 vacancy relay inspired by PR #2856 and five-copy concentration from PR #2848 / PR #2855. The literal T185 construction raises conditional \u03ba to **0.001720100805416885927944 \u2212 10\u207b\u2074\u2076 \u2212 10\u207b\u2077\u2070**, an exact gain of **4.176732053326972 \u00d7 10\u207b\u2079** over the full pinned PR #2857 claim.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 520, "source_index": null, "at": "2026-10-16T04:47:29Z", "until": null, "date_basis": "manual-source-reconciliation", "fraction": "17201008054168859279439999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "value_decimal": "0.001720100805416885927944", "dashboard_float_text": null, "expression": "0.001720100805416885927944-10^-46-10^-70", "historical_title": "Attain the fixed-word packing optimum: conditional \u03ba \u2248 0.0017201008054", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2863", "evidence_excerpt": "", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/shared-kernel-packing/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/shared-kernel-packing/CLAIM.json, research/shared-kernel-packing/MANIFEST.json, research/shared-kernel-packing/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/shared-kernel-packing/CLAIM.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/shared-kernel-packing/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2863-manifest.json", "sha256": "415b040c69345e21c6bfd462163ed6d7a94c1e75486f0e49b517469b3a096452" }, { "file": "remaining-record-audit/artifacts/2863/priority-manifest.json", "sha256": "bfa5047cccb6bb255d9cba6743baa360c0cc9cad857b9f3f293ac197eb3e2724" } ], "source_head": "34328b1d5e5bebac62d5cabec993dfbfd7b2123f" } }, { "pr": 2865, "title": "Audit #2751 independently and reconcile it with #2720's T74 centre floor (no \u03ba; no defect found)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2865", "author": "thakrarsagar", "created_at": "2026-10-16T05:12:07Z", "accepted_at": "2026-10-16T13:54:37Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0017171416", "kappa_fraction": "2146427/1250000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/2865-manifest.json", "sha256": "78ce5036c3608c67e195d8218cf13916b85978c665c3ae16b53be1b6ca74572b" }, { "file": "remaining-record-audit/artifacts/2865/priority-manifest.json", "sha256": "9c4528a7b84a5a6cfa12950fc07683ca04da46af06a992c69cfc13422911add1" } ], "source_head": "867d8add1c3be9a1a50a447789c46256d81bb790" } }, { "pr": 2866, "title": "Research: verified T74 residue concentration (superseded by #2863)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2866", "author": "digitalis-p", "created_at": "2026-10-16T05:13:35Z", "accepted_at": "2026-10-16T13:54:37Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001720097402339781716059999999999999999999999900000000000", "kappa_fraction": "17200974023397817160599999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/shared-kernel-pair-concentration/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/shared-kernel-pair-concentration/CLAIM.json, research/shared-kernel-pair-concentration/evidence/baseline-pinned/RESULT.json, research/shared-kernel-pair-concentration/evidence/baseline-pinned/candidate/RESULT.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/shared-kernel-pair-concentration/evidence/candidate-admission/discovery/RESULT.json#/independent and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/shared-kernel-pair-concentration/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2866-manifest.json", "sha256": "140b2f63d9bab97c8d09a2b554b2144b92ed02854762b567fd8653ea7c3d53f0" }, { "file": "remaining-record-audit/artifacts/2866/priority-manifest.json", "sha256": "b486a50503708cf87e30e0b73a254922f4acbb770a48379316a6111fe4d9bf39" } ], "source_head": "f40b1e92c15018af96293ee830e0cb0fd03db2ce" } }, { "pr": 2930, "title": "Conditional \u03ba \u2248 0.0017224999064433: cap-attaining allocation of #2917's unchanged words (+9.11e-7)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2930", "author": "mdumitrean", "created_at": "2026-10-16T12:18:36Z", "accepted_at": "2026-10-16T13:54:37Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001722499906443274564356999999999999999999999900000000000", "kappa_fraction": "17224999064432745643569999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 209, "source_index": 330, "at": "2026-10-16T12:18:36Z", "until": "2026-10-16T13:09:52Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001722499906443274564357", "dashboard_float_text": "0.0017224999064432746", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2930", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 244, "source_index": null, "at": "2026-10-16T12:18:36Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001722499906443274564357", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2930", "evidence_excerpt": "**\u03ba = 0.001722499906443274564357 \u2212 10\u207b\u2074\u2076 \u2212 10\u207b\u2077\u2070**, exactly `113907405684085469/125000000000000000000000` \u2248 **+9.1126e-7** over #2917 at `224bd5e56041c40078ff6b5fa7393733a215de5c` (about 0.053%).", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 525, "source_index": null, "at": "2026-10-16T12:18:36Z", "until": null, "date_basis": "body-version", "fraction": "17224999064432745643569999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "value_decimal": "0.001722499906443274564357", "dashboard_float_text": null, "expression": "0.001722499906443274564357 - 10^-46 - 10^-70", "historical_title": "Conditional \u03ba \u2248 0.0017224999064433: cap-attaining allocation of #2917's unchanged words (+9.11e-7)", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2930", "evidence_excerpt": "ry. This package packs PR2917's unchanged words at that optimum and passes the complete admission:\n\n\u03ba = 0.001722499906443274564357 - 10^-46 - 10^-70, exactly 113907405684085469/125000000000000000000000 \u2248 +9.1126e-7 over #2917 at 224bd5e56041c40078ff6b5fa7393733a215de5c (about 0.053%).\n\n## What changes\n\nOnly the literal allocat", "automated_comparable": true, "body_sha256": "45437742a566dfb43644bcc00d6064d4f1863549f6b8f70dd50b1dd358db3458" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 9, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/paired-extension-cap-fill/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/paired-extension-cap-fill/CLAIM.json, research/paired-extension-cap-fill/MANIFEST.json, research/paired-extension-cap-fill/README.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/paired-extension-cap-fill/CLAIM.json, research/paired-extension-cap-fill/MANIFEST.json, research/paired-extension-cap-fill/README.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/paired-extension-cap-fill/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2930-manifest.json", "sha256": "eba6fadcfb6502923eb6e54ca495ffc0b35e5a41cc39a981977f969f11af9cdf" }, { "file": "remaining-record-audit/artifacts/2930/priority-manifest.json", "sha256": "6acb6cdf1625bf8cf299316acbbc4b86a1672c633cfc35e45f07a19263367add" } ], "source_head": "81f3b5d12977eba09e06fbff729167d59faabe90" } }, { "pr": 1536, "title": "Conditional \u03ba = 0.001676855229071321: finer certified endpoints (1e-200) and deeper outer witness on PR1424 (82 bootstrap steps, eta=beta=1e-210, kappa grid 1e-199); construction unchanged", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1536", "author": "jeremykothe2", "created_at": "2026-10-14T02:24:14Z", "accepted_at": "2026-10-16T14:06:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676855229071321886206456772274592619512448739510475263", "kappa_fraction": "16768552290713218862064567722745926195124487395104752628033651910511566552120096495157846916413845429929275438103942180631016965288202851222935391871757186450912861283049468793633058255444681490343/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1536-gaussian-only-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 179, "source_index": null, "at": "2026-10-14T02:24:14Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.0016768552290713218862064567722745926195124487395104752628033651910511566552120096495157846916413845429929275438103942180631016965288202851222935391871757186450912861283049468793633058255444681490343", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1536", "evidence_excerpt": "Conditional \u03ba = **0.0016768552290713218862064567722745926195124487395104752628033651910511566552120096495157846916413845429929275438103942180631016965288202851222935391871757186450912861283049468793633058255444681490343", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1536-gaussian-only-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1536/priority-manifest.json", "sha256": "468ae9a6271a7945a0cc7599fffa2aa21fa0372990b1246235a69e6e398af466" } ], "source_head": "527d7623009f295b7311e98ae36f5e2fbdbbc3e5" } }, { "pr": 1601, "title": "Conditional \u03ba = 0.001676855229071321886206456772274592619512448739510475262803365191051156655212009649515784691641384542992927543810394218063101696528820285122293539187175718645091286128304946879363305825544468149034398152327153350113914450729178653786998036736534486069375928619294935202813397479427628290411415840641: finer certified endpoints (1e-400) and deeper outer witness on PR1424 (148 bootstrap steps, eta=beta=1e-405, kappa grid 1e-395); construction unchanged", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1601", "author": "jeremykothe2", "created_at": "2026-10-14T03:48:21Z", "accepted_at": "2026-10-16T14:06:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676855229071321886206456772274592619512448739510475263", "kappa_fraction": "4192138072678304715516141930686481548781121848776188157008412977627891638030024123789461729103461357482318859525985545157754241322050712805733847967939296612728215320762367198408264563861170372585995380817883375284786126822946634467495091841336215173439821548237338007033493698569070726028539601602995679132631565241951003643769709911450330780190327137113079211213089176745426067005106740579/2500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1601-gaussian-only-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 182, "source_index": null, "at": "2026-10-14T03:48:21Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.0016768552290713218862064567722745926195124487395104752628033651910511566552120096495157846916413845429929275438103942180631016965288202851222935391871757186450912861283049468793633058255444681490343981523271533501139144507291786537869980367365344860693759286192949352028133974794276282904114158406411982716530526260967804014575078839645801323120761308548452316844852356706981704268020426962316", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1601", "evidence_excerpt": "Conditional \u03ba = **0.0016768552290713218862064567722745926195124487395104752628033651910511566552120096495157846916413845429929275438103942180631016965288202851222935391871757186450912861283049468793633058255444681490343981523271533501139144507291786537869980367365344860693759286192949352028133974794276282904114158406411982716530526260967804014575078839645801323120761308548452316844852356706981704268020426962316", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1601-gaussian-only-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1601/priority-manifest.json", "sha256": "15305798a9c83fbd452457e19f8d5781d0239e66cedce8d5c92e1807fd9de6db" } ], "source_head": "6986056504a372b8a2dd74c66000da108a549be6" } }, { "pr": 1644, "title": "Conditional \u03ba = 0.0016768966690212993: pivot-566 helper-donor kernel (PR1625) on the T74 exact fill with certified 1e-400 endpoints and a 1e-395 outer witness", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1644", "author": "jeremykothe2", "created_at": "2026-10-14T04:54:13Z", "accepted_at": "2026-10-16T14:06:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676896669021299307750710997267962671611490016339159611", "kappa_fraction": "33537933380425986155014219945359253432229800326783192213169281110298673603459706163329665915797520678218701299211456271548826432677658295931657193791562920984105784745217696422385398714479277544968453414772033493372169367078156499518480327645874504365738204887153552163687338864241214294743928488251436018263025236927183355949981660265363464492686936318041530634356948094604590286323620537151/20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1644-selected-p566-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. 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Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1644-selected-p566-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1644/priority-manifest.json", "sha256": "7bca955eb149691d8dd831cbd036f704222cbae58cc181cd42b6297ca7a7a8f8" } ], "source_head": "025afe4c5f7aa6b51efbc0383d2672818481c313" } }, { "pr": 1661, "title": "Conditional \u03ba = 0.0016768966690212993077...99432: pivot-566 kernel with 400-digit grid refinement over PR1644", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1661", "author": "midhatn", "created_at": "2026-10-14T05:38:14Z", "accepted_at": "2026-10-16T14:06:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676896669021299307750710997267962671611490016339159611", "kappa_fraction": "2096120836276624134688388746584953339514362520423949513323080069393667100216231635208104119737345042388668831200716016971801652042353643495728574611972682561506611546576106026399087419654954846560528338423252093335760585442384781219905020477867156522858637805447097010230458679015075893421495530515714751141439077307948959746873853766585216530792933519877595664647309255912786892895226283571949929/1250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1661-selected-p566-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1661-selected-p566-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1661/priority-manifest.json", "sha256": "33e4c978626f4a166c7089be25e62258bf222eed0ccf28db205e6b18a0165f6a" } ], "source_head": "f852af5e178ce035cd46181a29d9330bcbcaa206" } }, { "pr": 1677, "title": "Conditional \u03ba = 0.0016768966690212993077...159193: pivot-566 kernel with 470-digit grid and 450-digit endpoints over PR1661", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1677", "author": "midhatn", "created_at": "2026-10-14T06:27:38Z", "accepted_at": "2026-10-16T14:06:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676896669021299307750710997267962671611490016339159611", "kappa_fraction": "167689666902129930775071099726796267161149001633915961065846405551493368017298530816648329578987603391093506496057281357744132163388291479658285968957814604920528923726088482111926993572396387724842267073860167466860846835390782497592401638229372521828691024435767760818436694321206071473719642441257180091315126184635916779749908301326817322463434681590207653171784740473022951431618102685755994326607285095814925855357959732116035535244417050872462468224313198159193/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1677-selected-p566-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1677-selected-p566-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1677/priority-manifest.json", "sha256": "a88b586e07053253cae62affb0dfde99e54c10a0229f2e770fe48be74e9bee76" } ], "source_head": "be7362c7c7007390a07cf207483c1dbe3b3ab2e6" } }, { "pr": 2265, "title": "Outer retune of #2260: #1673 capped phase-cell fusion outer on the selective-borrowing supplier, conditional \u03ba = 0.00168341258854\u2026", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2265", "author": "DreamingOfClouds", "created_at": "2026-10-15T02:48:56Z", "accepted_at": "2026-10-16T14:06:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00168341258854260746233031974039993696", "kappa_fraction": "5260664339195648319782249188749803/3125000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 170, "source_index": 276, "at": "2026-10-15T02:48:56Z", "until": "2026-10-15T03:26:50.665059Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.0016834125885426074623303197403999369605037", "dashboard_float_text": "0.0016834125885426075", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2265", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 202, "source_index": null, "at": "2026-10-15T02:48:56Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.0016834125885426074623303197403999369605037", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2265", "evidence_excerpt": "- Final conditional \u03ba = C \u2212 10^-246 \u2212 10^-222 = **0.0016834125885426074623303197403999369605037\u2026**", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 480, "source_index": null, "at": "2026-10-15T02:48:56Z", "until": null, "date_basis": "body-version", "fraction": "5260664339195648319782249188749803/3125000000000000000000000000000000000", "value_decimal": "0.0016834125885426074623303197403999369605037", "dashboard_float_text": null, "expression": "0.00168341258854260746233031974039993696", "historical_title": "Outer retune of #2260: #1673 capped phase-cell fusion outer on the selective-borrowing supplier, conditional \u03ba = 0.00168341258854\u2026", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2265", "evidence_excerpt": "## Outer retune of #2260 (no new construction): conditional \u03ba = 0.00168341258854260746233031974039993696\u2026\n\nWhat this is. #2260 (Dugongue) built a new finite complex supplier and assembled it with the retained balanced-prefix outer, whose final \u03ba \u2248 b/(1+b): 3361/2000000. #2220 (jeremy", "automated_comparable": true, "body_sha256": "52bf8ae6cbbdfefaa4249e6476df63993eb2d28c354feb1be30c1e007148a143" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_own_source_selector_required; actual own source selector; expected 5260664339195648319782249188749803/3125000000000000000000000000000000000; Read actual author-head CLAIM/verifier/SOURCES/MANIFEST and identify the selected complete kernel. A missing exact claim-kappa SPEC match is a discovery limitation, not mathematical rejection. Different quoted fixtures must not override a later actual final package. All listed SPEC candidates remain unselected until independently authenticated." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/2265/priority-manifest.json", "sha256": "d2cb69b32564eb0bf4c2a31899bb2f328db9135a8d1b9b210bbd5c3669a4e7b6" } ], "source_head": "6b09c565887c400ca01fafb067bc9d855f1ef9fc" } }, { "pr": 2269, "title": "Conditional \u03ba = 0.001696247139058474: capped phase-cell fusion outer (PR1673) on the T74 supplier with anticipatory dirty borrowing (PR2226, 43 high-helper aliases) on the T74 pivot-566+554 supplier: conditional kappa 0.0016962471390584742\u2026", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2269", "author": "jeremykothe2", "created_at": "2026-10-15T02:59:11Z", "accepted_at": "2026-10-16T14:06:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0016962471390584742207696225394800943861", "kappa_fraction": "16962471390584742207696225394800943861/10000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 203, "source_index": null, "at": "2026-10-15T03:26:50.665059+00:00", "until": null, "date_basis": "observed_revision", "fraction": null, "value_decimal": "0.0016962471390584742207696225394800943861", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2269", "evidence_excerpt": "Conditional \u03ba = **0.0016962471390584742207696225394800943861\u2026(136 digits)**. Adds the exact helper-donor kernel borrow43 (pivot None, found by Cinna Davis (1337isnot1337), PR2226 anticipatory dirty borrowing; adapted to the T74 words) to the previous record's T74 local words (re-solved frames, fresh natives, PLAN rebound, SPEC refrozen) under the PR1673 capped phase-cell fusion outer, with certified 1e-90 complex endpoints (accept at the endpoint, reject at endpoint + 1e-90), grid_digits 85, mar", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 481, "source_index": null, "at": "2026-10-15T02:59:11Z", "until": null, "date_basis": "body-version", "fraction": "16962471390584742207696225394800943861284603706821716607210815258272261945561178592716719999999997996607505720883051558460754921039811/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "value_decimal": "0.0016962471390584742207696225394800943861", "dashboard_float_text": null, "expression": "0.0016962471390584742207696225394800943861284603706821716607210815258272261945561178592716719999999997996607505720883051558460754921039811", "historical_title": "Conditional \u03ba = 0.001696247139058474: capped phase-cell fusion outer (PR1673) on the T74 supplier with anticipatory dirty borrowing (PR2226, 43 high-helper aliases) on the T74 pivot-566+554 supplier: conditional kappa 0.0016962471390584742\u2026", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2269", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.0016962471390584742207696225394800943861284603706821716607210815258272261945561178592716719999999997996607505720883051558460754921039811. Adds the exact helper-donor kernel borrow43 (pivot None, found by Cinna Davis (1337isnot1337), PR2226 anticipatory dirty borrowing; adapted to the T74 words) to the previous reco", "automated_comparable": true, "body_sha256": "bb5646561a9d626e6404e5dfeb49ac6d0f0e4926efbe013284c7c07930787324" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_own_source_selector_required; actual own source selector; expected 16962471390584742207696225394800943861/10000000000000000000000000000000000000000; Read actual author-head CLAIM/verifier/SOURCES/MANIFEST and identify the selected complete kernel. A missing exact claim-kappa SPEC match is a discovery limitation, not mathematical rejection. Different quoted fixtures must not override a later actual final package. All listed SPEC candidates remain unselected until independently authenticated." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/2269/priority-manifest.json", "sha256": "7dc29490986b67d1321c6ee19c254450ac71da2deb7937a7aff72440e768bac3" } ], "source_head": "b479fc5567bc09ab9185bffe89b62594f36d74e5" } }, { "pr": 2281, "title": "Conditional \u03ba = 0.0016962471390584742: recertified 1e-3000 supplier endpoint, fixed-grid-maximum kappa C - 1/F - B at 1e-3080 slacks (PR2180 / PR2161 retune) and exact-integer coarse exponential (PR2168): conditional kappa 0.00169624713905\u2026", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2281", "author": "jeremykothe2", "created_at": "2026-10-15T03:19:59Z", "accepted_at": "2026-10-16T14:06:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0016962471390584742207696225394800943861", "kappa_fraction": "16962471390584742207696225394800943861/10000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "reconstructed_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 171, "source_index": 277, "at": "2026-10-15T03:26:50.665059Z", "until": "2026-10-15T03:27:40.564787Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": null, "dashboard_float_text": "0.0016962471390584743", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2281", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_own_source_selector_required; actual own source selector; expected 16962471390584742207696225394800943861/10000000000000000000000000000000000000000; Read actual author-head CLAIM/verifier/SOURCES/MANIFEST and identify the selected complete kernel. A missing exact claim-kappa SPEC match is a discovery limitation, not mathematical rejection. Different quoted fixtures must not override a later actual final package. All listed SPEC candidates remain unselected until independently authenticated." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/2281/priority-manifest.json", "sha256": "44138dad7ae07d00327b1246883c7334a3a33e9812eaccbb21aa5df493e1a50c" } ], "source_head": "9c71e6194841d7355efa343b7cd5646359fad364" } }, { "pr": 2288, "title": "Conditional \u03ba = 0.001696310950415050: exact frame refit of the borrowed gauge44 word (WildIdeas), 1e-3000 certified supplier endpoint, fixed-grid-maximum kappa C - 1/F - B at 1e-3080 slacks (PR2180 / PR2161 retune) and exact-integer coarse\u2026", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2288", "author": "jeremykothe2", "created_at": "2026-10-15T03:40:50Z", "accepted_at": "2026-10-16T14:06:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001696310950415050335545972294892837228", "kappa_fraction": "424077737603762583886493073723209307/250000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 204, "source_index": null, "at": "2026-10-15T04:26:04.370351+00:00", "until": null, "date_basis": "observed_revision", "fraction": null, "value_decimal": "0.001696310950415050335545972294892837228092172196872456176222", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2288", "evidence_excerpt": "Conditional \u03ba = **0.001696310950415050335545972294892837228092172196872456176222\u2026** (3046 decimals; the exact value is `kappa` in `research/gmx-t74-borrow43-refit/outer/OUTER-CLAIM.json`, SHA-256 of the decimal string `d490066cb24700cb844ffe31a58e00a6f1c6d28a10fe39676b189e027eae0f43`). Applies PR2226's anticipatory dirty borrowing (Cinna Davis / 1337isnot1337) to our T74 local words: 43 helpers per call are removed by borrowing dirty space from other registers (480 to 437 helpers, local mass 559", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 482, "source_index": null, "at": "2026-10-15T03:40:50Z", "until": null, "date_basis": "body-version", "fraction": "424077737603762583886493073723209307/250000000000000000000000000000000000000", "value_decimal": "0.001696310950415050335545972294892837228092172196872456176222", "dashboard_float_text": null, "expression": "0.0016963109504150503355459722948928372280", "historical_title": "Conditional \u03ba = 0.001696310950415050: exact frame refit of the borrowed gauge44 word (WildIdeas), 1e-3000 certified supplier endpoint, fixed-grid-maximum kappa C - 1/F - B at 1e-3080 slacks (PR2180 / PR2161 retune) and exact-integer coarse\u2026", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2288", "evidence_excerpt": "the PR1956 carried bootstrap cutoffs and PR1964 Lemma G label stage are retained. Conditional final kappa = 0.0016963109504150503355459722948928372280\u2026(3046 digits) (supplier strict-assembly kappa 0.0016934383523940315190092442195145690007\u2026(2995 digits)). Retuned to the fixed-grid maximum of PR2180 / PR2161 (dataisfire): kappa =", "automated_comparable": true, "body_sha256": "34f2bbbb3c73176f4613687ec0c5846103771206e983ea4c5b3794e7205c4b03" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_own_source_selector_required; actual own source selector; expected 424077737603762583886493073723209307/250000000000000000000000000000000000000; Read actual author-head CLAIM/verifier/SOURCES/MANIFEST and identify the selected complete kernel. A missing exact claim-kappa SPEC match is a discovery limitation, not mathematical rejection. Different quoted fixtures must not override a later actual final package. All listed SPEC candidates remain unselected until independently authenticated." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/2288/priority-manifest.json", "sha256": "316f95cb60ec9337663d6069e16985b6e0b1c2615926453b1249a2e3e4f88c4f" } ], "source_head": "ba5e316fe247355397f63b6fcb3cfef78c11fa82" } }, { "pr": 2302, "title": "Conditional \u03ba = 0.001696395766736081: exact pivot-518 and 506 helper-donor kernel(s) (PR1625 shape, KernelsOnBorrow) on the borrowed words, exact frame refit (WildIdeas), 1e-3000 certified supplier endpoint, fixed-grid-maximum kappa C - 1/\u2026", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2302", "author": "jeremykothe2", "created_at": "2026-10-15T04:15:16Z", "accepted_at": "2026-10-16T14:06:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0016963957667360813401512017553615279117", "kappa_fraction": "16963957667360813401512017553615279117/10000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 172, "source_index": 281, "at": "2026-10-15T04:26:04.370351Z", "until": "2026-10-15T04:29:18Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": null, "dashboard_float_text": "0.0016963957667360814", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2302", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 205, "source_index": null, "at": "2026-10-15T04:26:04.370351+00:00", "until": null, "date_basis": "observed_revision", "fraction": null, "value_decimal": "0.001696395766736081340151201755361527911765706899936336210617", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2302", "evidence_excerpt": "Conditional \u03ba = **0.001696395766736081340151201755361527911765706899936336210617\u2026** (3046 decimals; the exact value is `kappa` in `research/gmx-t74-borrow43-k518-506/outer/OUTER-CLAIM.json`, SHA-256 of the decimal string `4921e9d2f65f912a2ecde54842170f357c1fd452bfdcd402e12f48b2c0ef39ac`). Applies PR2226's anticipatory dirty borrowing (Cinna Davis / 1337isnot1337) to our T74 local words: 43 helpers per call are removed by borrowing dirty space from other registers (480 to 437 helpers, local mass ", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 483, "source_index": null, "at": "2026-10-15T04:15:16Z", "until": null, "date_basis": "body-version", "fraction": "16963957667360813401512017553615279117/10000000000000000000000000000000000000000", "value_decimal": "0.001696395766736081340151201755361527911765706899936336210617", "dashboard_float_text": null, "expression": "0.0016963957667360813401512017553615279117", "historical_title": "Conditional \u03ba = 0.001696395766736081: exact pivot-518 and 506 helper-donor kernel(s) (PR1625 shape, KernelsOnBorrow) on the borrowed words, exact frame refit (WildIdeas), 1e-3000 certified supplier endpoint, fixed-grid-maximum kappa C - 1/\u2026", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2302", "evidence_excerpt": "the PR1956 carried bootstrap cutoffs and PR1964 Lemma G label stage are retained. Conditional final kappa = 0.0016963957667360813401512017553615279117\u2026(3046 digits) (supplier strict-assembly kappa 0.0016935228816887139163412051031782853465\u2026(2995 digits)). Retuned to the fixed-grid maximum of PR2180 / PR2161 (dataisfire): kappa =", "automated_comparable": true, "body_sha256": "8ea401ff41bf50eb00841fb57414fb1bb5ee5800fa1c415f1b161c6cb6aaf1de" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_own_source_selector_required; actual own source selector; expected 16963957667360813401512017553615279117/10000000000000000000000000000000000000000; Read actual author-head CLAIM/verifier/SOURCES/MANIFEST and identify the selected complete kernel. A missing exact claim-kappa SPEC match is a discovery limitation, not mathematical rejection. Different quoted fixtures must not override a later actual final package. All listed SPEC candidates remain unselected until independently authenticated." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/2302/priority-manifest.json", "sha256": "a1b74b1ca710e29680aa2f84aec6c323e6262f6e828a170cecb2c1d48f0dbeea" } ], "source_head": "9f67406e9972be9a97139f68ca29ea27a7545655" } }, { "pr": 2312, "title": "Conditional \u03ba = 0.001696891067241618: helper width exchange on the borrowed T74 words", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2312", "author": "jeremykothe2", "created_at": "2026-10-15T04:50:12Z", "accepted_at": "2026-10-16T14:06:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0016968910672416183217741664253306608313", "kappa_fraction": "16968910672416183217741664253306608313/10000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 174, "source_index": 284, "at": "2026-10-15T04:50:12Z", "until": "2026-10-15T05:15:03Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001696891067241618321774166425330660831398187109259160678591", "dashboard_float_text": "0.0016968910672416184", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2312", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 207, "source_index": null, "at": "2026-10-15T04:50:12Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001696891067241618321774166425330660831398187109259160678591", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2312", "evidence_excerpt": "Conditional \u03ba = **0.001696891067241618321774166425330660831398187109259160678591\u2026** (3046 decimals; the exact value is `kappa` in `research/gmx-t74-borrow43-width-exchange/outer/OUTER-CLAIM.json`, SHA-256 of the decimal string `45a8f009d5537ff7386138e8e3d8d4c0c207e9ce18b2a906b726bb499e4ff444`). Applies PR2226's anticipatory dirty borrowing (Cinna Davis / 1337isnot1337) to our T74 local words: 42 helpers per call are removed by borrowing dirty space from other registers (480 to 438 helpers, local", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 485, "source_index": null, "at": "2026-10-15T04:50:12Z", "until": null, "date_basis": "body-version", "fraction": "16968910672416183217741664253306608313/10000000000000000000000000000000000000000", "value_decimal": "0.001696891067241618321774166425330660831398187109259160678591", "dashboard_float_text": null, "expression": "0.0016968910672416183217741664253306608313", "historical_title": "Conditional \u03ba = 0.001696891067241618: width exchange (alias 651 re-lent from 530, alias 653 dropped), exact owner fill, frame refit and two exact helper-donor kernels (pivots 518 and 506) on the PR2226 anticipatory-dirty-borrowing T74 word\u2026", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2312", "evidence_excerpt": "the PR1956 carried bootstrap cutoffs and PR1964 Lemma G label stage are retained. Conditional final kappa = 0.0016968910672416183217741664253306608313\u2026(3046 digits) (supplier strict-assembly kappa 0.0016940165057652254512814651321488010600\u2026(2995 digits)). Retuned to the fixed-grid maximum of PR2180 / PR2161 (dataisfire): kappa =", "automated_comparable": true, "body_sha256": "01558d3c413593f5caa96d78a02f0f08970df9f09401970fc616e75edb8bcbd5" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_own_source_selector_required; actual own source selector; expected 16968910672416183217741664253306608313/10000000000000000000000000000000000000000; Read actual author-head CLAIM/verifier/SOURCES/MANIFEST and identify the selected complete kernel. A missing exact claim-kappa SPEC match is a discovery limitation, not mathematical rejection. Different quoted fixtures must not override a later actual final package. All listed SPEC candidates remain unselected until independently authenticated." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/2312/priority-manifest.json", "sha256": "ba12dbbccc7ecf59fb3e6ea04e94b4ec4fd3e1cfd3cb43e2aef024596eb1f0a9" } ], "source_head": "2900774d7e3b40dc2d0e7e96579d543699dded3e" } }, { "pr": 2833, "title": "Conditional \u03ba = 0.001718657437166855: dirt-entry rewrite of helpers 530 and 542 on #2802's construction", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2833", "author": "jeremykothe2", "created_at": "2026-10-16T00:56:10Z", "accepted_at": "2026-10-16T14:06:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0017186574371668559556934576143242804099", "kappa_fraction": "17186574371668559556934576143242804099/10000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 200, "source_index": 315, "at": "2026-10-16T00:56:10Z", "until": "2026-10-16T01:34:08Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001718657437166855955693457614324280409964974692938405744766", "dashboard_float_text": "0.001718657437166856", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2833", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 234, "source_index": null, "at": "2026-10-16T00:56:10Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001718657437166855955693457614324280409964974692938405744766", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2833", "evidence_excerpt": "Conditional \u03ba = **0.001718657437166855955693457614324280409964974692938405744766\u2026** (3046 decimals; the exact value is `kappa` in `research/gmx-t74-borrow43-handoff/outer/OUTER-CLAIM.json`, SHA-256 of the decimal string `962260755185e3077435dfac7af940dfc047c520f12a4e26b86f349a219dfe2e`). This package takes PR2802's (mdumitrean, Marius-Paul Dumitrean) construction as its base: seven retired-lender aliases and two hostee moves on PR2751's (tekuuu) twelve-alias words with PR2766's (DavidAriasC) fra", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 514, "source_index": null, "at": "2026-10-16T00:56:10Z", "until": null, "date_basis": "body-version", "fraction": "17186574371668559556934576143242804099/10000000000000000000000000000000000000000", "value_decimal": "0.001718657437166855955693457614324280409964974692938405744766", "dashboard_float_text": null, "expression": "0.0017186574371668559556934576143242804099", "historical_title": "Conditional \u03ba = 0.001718657437166855: dirt-entry rewrite of helpers 530 and 542 on #2802's construction", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2833", "evidence_excerpt": "uu) exact sparse native replay, the stale-bytecode guard (PR2788, jeremydiviney). Conditional final kappa = 0.0017186574371668559556934576143242804099\u2026(3046 digits) (supplier strict-assembly kappa 0.0017157087216124446887789003618932350021\u2026(2995 digits)). It exceeds PR2824 (exact kappa_decimal from its claim) by 8.62277E-7 (exac", "automated_comparable": true, "body_sha256": "27442e192623dc32514dfd2988c2bc15c9ce15f409a10387eef70cc66464d969" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_own_source_selector_required; actual own source selector; expected 17186574371668559556934576143242804099/10000000000000000000000000000000000000000; Read actual author-head CLAIM/verifier/SOURCES/MANIFEST and identify the selected complete kernel. A missing exact claim-kappa SPEC match is a discovery limitation, not mathematical rejection. Different quoted fixtures must not override a later actual final package. All listed SPEC candidates remain unselected until independently authenticated." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/2833/priority-manifest.json", "sha256": "690448f8b486ae5908523182681ba27d085087acd36eef87a1b0334149ad41ad" } ], "source_head": "e9307b48d7d1b690939935ecef0f8e524e6d92f4" } }, { "pr": 2853, "title": "Conditional \u03ba = 0.0017193776586975866590: dirt-entry rewrite of A-phase helpers 460/462/478/480 on #2833", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2853", "author": "philippeVV", "created_at": "2026-10-16T02:50:53Z", "accepted_at": "2026-10-16T14:06:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001719377658697586659", "kappa_fraction": "1719377658697586659/1000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 203, "source_index": 320, "at": "2026-10-16T02:50:53Z", "until": "2026-10-16T03:04:24.474338Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.0017193776586975866590", "dashboard_float_text": "0.0017193776586975867", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2853", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 237, "source_index": null, "at": "2026-10-16T02:50:53Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.0017193776586975866590", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2853", "evidence_excerpt": "Conditional \u03ba = 0.0017193776586975866590: dirt-entry rewrite of A-phase helpers 460/462/478/480 on #2833", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 517, "source_index": null, "at": "2026-10-16T02:50:53Z", "until": null, "date_basis": "body-version", "fraction": "1719377658697586659/1000000000000000000000", "value_decimal": "0.0017193776586975866590", "dashboard_float_text": null, "expression": "0.0017193776586975866590", "historical_title": "Conditional \u03ba = 0.0017193776586975866590: dirt-entry rewrite of A-phase helpers 460/462/478/480 on #2833", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2853", "evidence_excerpt": "Conditional \u03ba = 0.0017193776586975866590\u2026, which is +7.20222e-7 over #2833 and +7.19381e-7 over #2843. It is stacked on #2833's head e9307b48d and updates research/gmx-t74-borrow43-handoff in place, following the same co", "automated_comparable": true, "body_sha256": "3fc16d4516375c0ff59d8e4bbe49ee5d79ef20b608123c58535442771e36a8a4" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_own_source_selector_required; actual own source selector; expected 1719377658697586659/1000000000000000000000; Read actual author-head CLAIM/verifier/SOURCES/MANIFEST and identify the selected complete kernel. A missing exact claim-kappa SPEC match is a discovery limitation, not mathematical rejection. Different quoted fixtures must not override a later actual final package. All listed SPEC candidates remain unselected until independently authenticated." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/2853/priority-manifest.json", "sha256": "892496d1ca64563d1bf8869ed15fa6ac36ddc85e73c8c226ffff14a63b180d9c" } ], "source_head": "d01045dfb67428679618027dff552f1d032fa999" } }, { "pr": 2856, "title": "Conditional \u03ba \u2248 0.00171937887049554: P53 width-7 vacancy relay", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2856", "author": "mdumitrean", "created_at": "2026-10-16T03:47:13Z", "accepted_at": "2026-10-16T14:06:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001719378870495538841811999999999999999999999900000000000", "kappa_fraction": "17193788704955388418119999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 204, "source_index": 323, "at": "2026-10-16T03:47:13Z", "until": "2026-10-16T03:50:54Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001719378870495538841812", "dashboard_float_text": "0.0017193788704955389", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2856", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 238, "source_index": null, "at": "2026-10-16T03:47:13Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001719378870495538841812", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2856", "evidence_excerpt": "`\u03ba = 0.001719378870495538841812 \u2212 10^-46 \u2212 10^-70`", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 518, "source_index": null, "at": "2026-10-16T03:47:13Z", "until": null, "date_basis": "body-version", "fraction": "17193788704955388418119999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "value_decimal": "0.001719378870495538841812", "dashboard_float_text": null, "expression": "0.001719378870495538841812 - 10^-46 - 10^-70", "historical_title": "Conditional \u03ba \u2248 0.00171937887049554: P53 width-7 vacancy relay", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2856", "evidence_excerpt": "g all native words, 666 calls and physical stock 66794.\n\nThe fully replayed conditional target is:\n\n\u03ba = 0.001719378870495538841812 - 10^-46 - 10^-70\n\nThis exceeds #2853\u2019s full exact rational by 1.21179795218276466e-9, or 0.0000704788704%. The complete paid delta is H14 - 2H7 < 0 for every 0 < a < 1. All 271,728 helper placemen", "automated_comparable": true, "body_sha256": "3b045b8213fda6dbaccb71f4aff53b151fa3658dba996e9e50e1c8bfcf744cf3" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 12, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t248-dirtentry-residue/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Recompute the complete own productive/paid histogram from research/aphase-residue-composition/CLAIM.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/aphase-residue-composition/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2856-manifest.json", "sha256": "ae7d3af9db26f19a086891186d761dcbb4f192f0f8b4abeda26a0d3195ac61ff" }, { "file": "remaining-record-audit/artifacts/2856/priority-manifest.json", "sha256": "464e1b6bebbdb088f8a82fadc163439010fb128bb39357b319988d873ed4071d" } ], "source_head": "7a43b24c4b6729d171f3a2a11ef3b7dc77aabaa4" } }, { "pr": 2948, "title": "Conditional \u03ba = 0.001723356487244355: nine declared gate rewrites on #2917's words with #2930's cap-attaining fill", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2948", "author": "jeremykothe2", "created_at": "2026-10-16T13:48:18Z", "accepted_at": "2026-10-16T14:06:49Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00172335648724435579890999999999999999", "kappa_fraction": "172335648724435579890999999999999999/100000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 211, "source_index": 332, "at": "2026-10-16T13:48:18Z", "until": "2026-10-16T14:21:12Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001723356487244355798909999999999999999999999899999999999999", "dashboard_float_text": "0.0017233564872443559", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2948", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 246, "source_index": null, "at": "2026-10-16T13:48:18Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001723356487244355798909999999999999999999999899999999999999", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2948", "evidence_excerpt": "Conditional \u03ba = **0.001723356487244355798909999999999999999999999899999999999999\u2026** (70 decimals; the exact value is `kappa` in `research/paired-extension-cap-fill-rewrites/outer/OUTER-CLAIM.json`, SHA-256 of the decimal string `03548b4355a6d507c554991e79b6ef63c4b210bbfca3ac9c3c04995ce76897f1`). This package takes PR2930's (mdumitrean, Marius-Paul Dumitrean) cap-attaining T74 allocation of PR2917's (mason-hale) nine paired extractions on PR2908's (jeremydiviney) construction as its base: its lit", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 527, "source_index": null, "at": "2026-10-16T13:48:18Z", "until": null, "date_basis": "body-version", "fraction": "172335648724435579890999999999999999/100000000000000000000000000000000000000", "value_decimal": "0.001723356487244355798909999999999999999999999899999999999999", "dashboard_float_text": null, "expression": "0.00172335648724435579890999999999999999", "historical_title": "Conditional \u03ba = 0.001723356487244355: nine declared gate rewrites on #2917's words with #2930's cap-attaining fill", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2948", "evidence_excerpt": "h natives for both changed words, complete admission and the modern outer release pass. Conditional kappa = 0.00172335648724435579890999999999999999..., above PR2930 by 8.566e-7 (exact gate in verify_release.py).\n\n## Verification\n\nFresh checkout of 34e1080739e5e8a4349f8582c31dca798c308d4a. Manifest: 9f9add122c7cb07fa5952a7e928", "automated_comparable": true, "body_sha256": "626b71b03d75546ae9fb4440c5d1c1736eef40294b8d113a3e60853484e4595e" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 9, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/paired-extension-cap-fill-rewrites/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/paired-extension-cap-fill-rewrites/CLAIM.json, research/paired-extension-cap-fill-rewrites/MANIFEST.json, research/paired-extension-cap-fill-rewrites/README.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/paired-extension-cap-fill-rewrites/CLAIM.json, research/paired-extension-cap-fill-rewrites/MANIFEST.json, research/paired-extension-cap-fill-rewrites/README.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/paired-extension-cap-fill-rewrites/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2948-manifest.json", "sha256": "bda599327c3661bb96bcd25fd51e40ec2cdc18f121d04395890a905071956f6d" }, { "file": "remaining-record-audit/artifacts/2948/priority-manifest.json", "sha256": "6965594865db4c55b8472d0b7bd496e9f0b0a4a31014da9c9e57eccf9bf4a60e" } ], "source_head": "34e1080739e5e8a4349f8582c31dca798c308d4a" } }, { "pr": 1104, "title": "Conditional \u03ba = 0.001672691689152441: rank-seven helper ends and T16 owner packing on the seven-slot k8 word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1104", "author": "jeremykothe2", "created_at": "2026-10-13T18:15:35Z", "accepted_at": "2026-10-16T14:06:50Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672691689152441", "kappa_fraction": "1672691689152441/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1104-ends7-selected-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 133, "source_index": 188, "at": "2026-10-13T18:15:35Z", "until": "2026-10-13T18:19:42Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001672691689152441", "dashboard_float_text": "0.001672691689152441", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1104", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 150, "source_index": null, "at": "2026-10-13T18:15:35Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001672691689152441", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1104", "evidence_excerpt": "Conditional \u03ba = **0.001672691689152441**. Ports #1030\u2019s rank-seven helper-end mechanism to the seven-slot k8 word, with a new T16 owner map. Changes include the local construction, its recipe and independent controls, native locals and packing.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 439, "source_index": null, "at": "2026-10-13T18:15:35Z", "until": null, "date_basis": "body-version", "fraction": "1672691689152441/1000000000000000000", "value_decimal": "0.001672691689152441", "dashboard_float_text": null, "expression": "0.001672691689152441", "historical_title": "Conditional \u03ba = 0.001672691689152441: rank-seven helper ends and T16 owner packing on the seven-slot k8 word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1104", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001672691689152441. Ports #1030\u2019s rank-seven helper-end mechanism to the seven-slot k8 word, with a new T16 owner map. Changes include the local construction, its recipe and independent controls, na", "automated_comparable": true, "body_sha256": "f05494922ef35f643d966fa8e8b71c787da95a01cc1dfb313ec236660badf8b7" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1104-ends7-selected-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1104/priority-manifest.json", "sha256": "6e269509ccc673edb4a134adda9dc6f781dfe9bbc3ddf9e50e4df8e410a4cf16" } ], "source_head": "d8982686afd7ef6ce52ddeaa17011ccda558d666" } }, { "pr": 1172, "title": "research/gauge44-ends7-t16: cross-replica exchange extinguishing remainders 5 and 6 (kappa = 0.001672802407467250)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1172", "author": "midhatn", "created_at": "2026-10-13T19:34:59Z", "accepted_at": "2026-10-16T14:06:50Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00167280240746725", "kappa_fraction": "6691209629869/4000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1172-ends7-exchange-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1172-ends7-exchange-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1172/priority-manifest.json", "sha256": "c476b569aeb7030037fa57bd6cac5302f887ec3cf66ea4169216d9fa7a2edc8e" } ], "source_head": "4d2cc9df55ed5a17786b7c0a200d70332afbe41e" } }, { "pr": 1261, "title": "Conditional \u03ba = 0.001675809683500501757384: finer 1e-24 outer-grid certification of PR1218's global mixed X54 fusion construction (same construction, no new circuit)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1261", "author": "jeremykothe2", "created_at": "2026-10-13T21:22:16Z", "accepted_at": "2026-10-16T14:06:50Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001675809683500501757384", "kappa_fraction": "209476210437562719673/125000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 148, "source_index": 218, "at": "2026-10-13T21:22:16Z", "until": "2026-10-13T21:34:13Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001675809683500501757384", "dashboard_float_text": "0.0016758096835005017", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1261", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 165, "source_index": null, "at": "2026-10-13T21:22:16Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001675809683500501757384", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1261", "evidence_excerpt": "Conditional \u03ba = **0.001675809683500501757384**. The identical PR1218 construction (125 base and 208 extra-group calls, X54, source-holder fusions, PR1193 global T37 allocation), replayed completely with the retained assembler's outer objective grid refined from 10^-18 to 10^-24, as PR1019 did for the T37 construction. No local word, owner map, profile or endpoint changes; only the final rounding grid of the nominated kappa does. The 1e-18 floor of the new value equals PR1218's 0.0016758096835005", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 456, "source_index": null, "at": "2026-10-13T21:22:16Z", "until": null, "date_basis": "body-version", "fraction": "209476210437562719673/125000000000000000000000", "value_decimal": "0.001675809683500501757384", "dashboard_float_text": null, "expression": "0.001675809683500501757384", "historical_title": "Conditional \u03ba = 0.001675809683500501757384: finer 1e-24 outer-grid certification of PR1218's global mixed X54 fusion construction (same construction, no new circuit)", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1261", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001675809683500501757384. The identical PR1218 construction (125 base and 208 extra-group calls, X54, source-holder fusions, PR1193 global T37 allocation), replayed completely with the retained assembler'", "automated_comparable": true, "body_sha256": "8bd23b97dab297789d5c42309d692f87e2b741de7bfc5fcc6a3baa672beda29f" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_selected_full_program_bytes_missing; extra; required full program 820aac386d3f651eb976baa991075b267ab7dd42997a966c18bbea2b277dfb46; both orientations {\"backward\": \"d0a8c0d082e5f079c8b9bbae2000971691d2586be0d985435a22cdcd488eb05b\", \"forward\": \"f7db7b1f9b0b048ee678abc49e3798831edd01aad7ea34fe058d53dda714ffdd\"}; Recover exact actual complete selected program bytes, by own immutable primary source or deterministic pinned constructor/recipe with mandatory complete semantic and orientation commitments. A matching profile, scalar saving or another provider does not fill this gap. Missing canonical catalogue may remain a separately stated endpoint premise only after the actual selected program and complete own physical/invoice are bound.", "Source-specific frozen V10 discovery snapshot: actual_selected_full_program_bytes_missing; gauge44; required full program 3cf9daa25562d324d3eaf4b854e78aff98bc254891e8aaafef4ac66e0c731517; both orientations {\"backward\": \"f15c1600543ada5b5e4e3c68bf2f171ea35ca520a571d91bf29f8f612361771a\", \"forward\": \"66632cb2270b40618c0f013d71ef600b3809b51de7e2f4833c266dfce4afe77c\"}; Recover exact actual complete selected program bytes, by own immutable primary source or deterministic pinned constructor/recipe with mandatory complete semantic and orientation commitments. A matching profile, scalar saving or another provider does not fill this gap. Missing canonical catalogue may remain a separately stated endpoint premise only after the actual selected program and complete own physical/invoice are bound." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1261/priority-manifest.json", "sha256": "2a17adbe08b5e098341e1f053295fc9353d536ecff88c80b35edb78dc4f1ed6f" } ], "source_head": "f8fede235d45ea3aada5cbb28704c8a2ecd0f3d7" } }, { "pr": 1274, "title": "Conditional \u03ba = 0.001676070884699375: exact helper-donor cold kernel for pivot 531 on the global mixed X54 fusions word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1274", "author": "jeremykothe2", "created_at": "2026-10-13T21:34:13Z", "accepted_at": "2026-10-16T14:06:50Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676070884699375", "kappa_fraction": "2681713415519/1600000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 149, "source_index": 219, "at": "2026-10-13T21:34:13Z", "until": "2026-10-13T21:45:05Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001676070884699375", "dashboard_float_text": "0.001676070884699375", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1274", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 166, "source_index": null, "at": "2026-10-13T21:34:13Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001676070884699375", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1274", "evidence_excerpt": "Conditional \u03ba = **0.001676070884699375**. Replaces the three early gates of the pivot-531 cold kernel (output-target donors 115/179 and partner 507) with an exact helper-donor kernel (donors 636 and 351 at frame [30]), found by an exact backward output-sensitivity relation search and kept legal by the unchanged k8 frame model, with one exact tail-gate endpoint correction (351 += 531) in the refactored cleanup. Local paid profile changes by H1 -3, H3 +1 per call in both providers (widths, ports, ", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 458, "source_index": null, "at": "2026-10-13T21:34:13Z", "until": null, "date_basis": "body-version", "fraction": "2681713415519/1600000000000000", "value_decimal": "0.001676070884699375", "dashboard_float_text": null, "expression": "0.001676070884699375", "historical_title": "Conditional \u03ba = 0.001676070884699375: exact helper-donor cold kernel for pivot 531 on the global mixed X54 fusions word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1274", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001676070884699375. Replaces the three early gates of the pivot-531 cold kernel (output-target donors 115/179 and partner 507) with an exact helper-donor kernel (donors 636 and 351 at frame [30]), f", "automated_comparable": true, "body_sha256": "59df9f5b41869e2566cdb732447a025bca9f73b8c24869002139c52709938472" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_selected_full_program_bytes_missing; extra; required full program 609e6e8f4fe3ee6a6843605257cff06235e2b1d96ae129bba1831b47aaa7002c; both orientations {\"backward\": \"102916ac72093e83aeae90ffd404a981e8b1b09248407f779bcce2c2c816e041\", \"forward\": \"272129996c0da641eadf2e476bfead5a4abda76c6e488052f9643fe326331976\"}; Recover exact actual complete selected program bytes, by own immutable primary source or deterministic pinned constructor/recipe with mandatory complete semantic and orientation commitments. A matching profile, scalar saving or another provider does not fill this gap. Missing canonical catalogue may remain a separately stated endpoint premise only after the actual selected program and complete own physical/invoice are bound.", "Source-specific frozen V10 discovery snapshot: actual_selected_full_program_bytes_missing; gauge44; required full program 5735e841c66a456efea127fc7c66c7bfe5cc2f1216a4de5d6fb9f892c47cfa6e; both orientations {\"backward\": \"f6066b015d25617dc434274adccd2cfc3e95952070faae19e6d8d8c503c32a7a\", \"forward\": \"1d813c6def542014d3a22fb20aff1f9e8d44f7417467b3cffd4205062943e6c9\"}; Recover exact actual complete selected program bytes, by own immutable primary source or deterministic pinned constructor/recipe with mandatory complete semantic and orientation commitments. A matching profile, scalar saving or another provider does not fill this gap. Missing canonical catalogue may remain a separately stated endpoint premise only after the actual selected program and complete own physical/invoice are bound." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1274/priority-manifest.json", "sha256": "21e80340240729e0e8055db186ce2c9f5ea722dea2cdefc00f4a3a4a4f0ff3e1" } ], "source_head": "336d0ee3ea8026f9388ccafee91c923a434d0328" } }, { "pr": 1377, "title": "Conditional \u03ba = 0.001676855229071321886144: finer 1e-24 kappa grid on PR1319's 74-replica exact-fill construction (same construction, only the final grid is refined)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1377", "author": "jeremykothe2", "created_at": "2026-10-13T23:46:56Z", "accepted_at": "2026-10-16T14:06:50Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676855229071321886144", "kappa_fraction": "26200862954239404471/15625000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1377-gaussian-only-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 153, "source_index": 223, "at": "2026-10-13T23:46:56Z", "until": "2026-10-14T00:22:40Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001676855229071321886144", "dashboard_float_text": "0.001676855229071322", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1377", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 170, "source_index": null, "at": "2026-10-13T23:46:56Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001676855229071321886144", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1377", "evidence_excerpt": "Conditional \u03ba = 0.001676855229071321886144: finer 1e-24 kappa grid on PR1319's 74-replica exact-fill construction (same construction, only the final grid is refined)", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1377-gaussian-only-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1377/priority-manifest.json", "sha256": "c6ee920e2fb0c7f56226a393ade32750f6bca6d18bcabffbdf065ffff8ad6879" } ], "source_head": "7b6b538212812e01c45a51966837598a197a799b" } }, { "pr": 1444, "title": "Conditional \u03ba = 0.001676855229071321: deeper outer-witness refinement of #1424's construction (unchanged)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1444", "author": "jeremykothe2", "created_at": "2026-10-14T00:52:56Z", "accepted_at": "2026-10-16T14:06:50Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676855229071321886206381217337894076302355284707188159", "kappa_fraction": "8384276145356609431031906086689470381511776423535940796712693058763/5000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1444-gaussian-only-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 172, "source_index": null, "at": "2026-10-14T00:52:56Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.0016768552290713218862063812173378940763023552847071881593425386117526", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1444", "evidence_excerpt": "Conditional \u03ba = **0.0016768552290713218862063812173378940763023552847071881593425386117526**. PR1424's construction (PR1319 74-replica exact fill of PR1297's four cold kernels) is unchanged. Only the three outer-witness settings in SPEC.json:outer_refinement are deepened (bootstrap steps 26, eta = beta = 1e-76 with target backoff 1e-79, final kappa grid 1e-70); all 47 strict outer inequalities, the rejection controls and next-grid rejection hold, so kappa moves from 0.001676855229071321886206381", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1444-gaussian-only-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1444/priority-manifest.json", "sha256": "9fb630979fcea6946ad7eb47f0932d6334bc2950b870059cb19a5b0546ab268d" } ], "source_head": "e8281be5d0123527bd467e92c4f7005d2ab33b3f" } }, { "pr": 1458, "title": "Conditional \u03ba = 0.001676855229071321: finer 1e-60 certified endpoints and a deeper outer witness on #1424's construction (unchanged)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1458", "author": "jeremykothe2", "created_at": "2026-10-14T00:57:12Z", "accepted_at": "2026-10-16T14:06:50Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676855229071321886206456772274592619512448739510475263", "kappa_fraction": "16768552290713218862064567722745926195124487395104752628031703388673/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1458-gaussian-only-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 173, "source_index": null, "at": "2026-10-14T00:57:12Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.0016768552290713218862064567722745926195124487395104752628031703388673", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1458", "evidence_excerpt": "Conditional \u03ba = **0.0016768552290713218862064567722745926195124487395104752628031703388673**. PR1424's construction is unchanged. The certified complex endpoints (native and conservative) are refined from the inherited 1e-24 bracket to 1e-60, each checked as accepted at the endpoint and rejected at endpoint+1e-60 by both rational moment engines (the retained Mercator engine and a finer-constant copy of the base-two engine), and the outer witness settings are deepened (bootstrap steps 26, eta = b", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1458-gaussian-only-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1458/priority-manifest.json", "sha256": "c669c9c06c8efbc7e672cb11307acb5dba9900ba6cf23e64dcf07ef25aac005f" } ], "source_head": "fec30ff23f972fdc59aeec24bc5bd64b8638d8aa" } }, { "pr": 1479, "title": "Conditional \u03ba = 0.001676855229071321: finer certified endpoints (1e-120) and deeper outer witness on PR1424 (46 bootstrap steps, eta=beta=1e-124, kappa grid 1e-67); construction unchanged", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1479", "author": "jeremykothe2", "created_at": "2026-10-14T01:26:06Z", "accepted_at": "2026-10-16T14:06:50Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676855229071321886206456772274592619512448739510475263", "kappa_fraction": "1676855229071321886206456772274592619512448739510475262803365191/1000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1479-gaussian-only-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 175, "source_index": null, "at": "2026-10-14T01:26:06Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001676855229071321886206456772274592619512448739510475262803365191", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1479", "evidence_excerpt": "Conditional \u03ba = **0.001676855229071321886206456772274592619512448739510475262803365191**. PR1424's construction is unchanged. The certified complex endpoints (native and conservative) are refined from the inherited 1e-24 bracket to 1e-120: the retained engines still certify the 1e-24 bracket, and finer-constant copies of both rational engines certify accept at the endpoint and reject at endpoint+1e-120. The outer witness settings are deepened (bootstrap steps 46, eta = beta = 1e-124, backoff 1e-", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1479-gaussian-only-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1479/priority-manifest.json", "sha256": "4fbf64046f08afecaea88b96031790255d105a4e4832357212769e20e333babf" } ], "source_head": "0a211a4608d2c3d295f8bb94b12ca446714186ab" } }, { "pr": 1510, "title": "Conditional \u03ba = 0.001676855229071321: finer certified endpoints (1e-200) and deeper outer witness on PR1424 (60 bootstrap steps, eta=beta=1e-130, kappa grid 1e-122); construction unchanged", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1510", "author": "jeremykothe2", "created_at": "2026-10-14T02:00:28Z", "accepted_at": "2026-10-16T14:06:50Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676855229071321886206456772274592619512448739510475263", "kappa_fraction": "83842761453566094310322838613729630975622436975523763140168259552557832760600482475789234582069227149646377190519710903/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1510-gaussian-only-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 177, "source_index": null, "at": "2026-10-14T02:00:28Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00167685522907132188620645677227459261951244873951047526280336519105115665521200964951578469164138454299292754381039421806", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1510", "evidence_excerpt": "Conditional \u03ba = **0.00167685522907132188620645677227459261951244873951047526280336519105115665521200964951578469164138454299292754381039421806**. PR1424's construction is unchanged. The certified complex endpoints (native and conservative) are refined from the inherited 1e-24 bracket to 1e-200: the retained engines still certify the 1e-24 bracket, and finer-constant copies of both rational engines certify accept at the endpoint and reject at endpoint+1e-200. The outer witness settings are deepen", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1510-gaussian-only-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1510/priority-manifest.json", "sha256": "19b82d5c77316ce20eb54249a8bba37e1c561a9a6867f34d842434e07a8dd633" } ], "source_head": "4adcd51fd74f6cf64970e2dd87b33b1a7864e408" } }, { "pr": 1513, "title": "Conditional \u03ba = 0.001676855229071321: finer certified endpoints (1e-200) and deeper outer witness on PR1424 (80 bootstrap steps, eta=beta=1e-205, kappa grid 1e-195); construction unchanged", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1513", "author": "jeremykothe2", "created_at": "2026-10-14T02:06:56Z", "accepted_at": "2026-10-16T14:06:50Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676855229071321886206456772274592619512448739510475263", "kappa_fraction": "1676855229071321886206456772274592619512448739510475262803365191051156655212009649515784691641384542992927543810394218063101696528820285122293539187175718645091286128304946879363305825544468149/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1513-gaussian-only-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 178, "source_index": null, "at": "2026-10-14T02:06:56Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001676855229071321886206456772274592619512448739510475262803365191051156655212009649515784691641384542992927543810394218063101696528820285122293539187175718645091286128304946879363305825544468149", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1513", "evidence_excerpt": "Conditional \u03ba = **0.001676855229071321886206456772274592619512448739510475262803365191051156655212009649515784691641384542992927543810394218063101696528820285122293539187175718645091286128304946879363305825544468149**. PR1424's construction is unchanged. The certified complex endpoints (native and conservative) are refined from the inherited 1e-24 bracket to 1e-200: the retained engines still certify the 1e-24 bracket, and finer-constant copies of both rational engines certify accept at the endp", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1513-gaussian-only-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1513/priority-manifest.json", "sha256": "91bd0f789a58b6e043b4f4d56f88e2a9e292fdbda58252bd669049f7fe04d197" } ], "source_head": "968d7ea2be07c376ceaee24d659b4298628e9767" } }, { "pr": 1578, "title": "Conditional \u03ba = 0.001676855229071321: finer certified endpoints (1e-300) and deeper outer witness on PR1424 (112 bootstrap steps, eta=beta=1e-305, kappa grid 1e-295); construction unchanged", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1578", "author": "jeremykothe2", "created_at": "2026-10-14T03:16:23Z", "accepted_at": "2026-10-16T14:06:50Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676855229071321886206456772274592619512448739510475263", "kappa_fraction": "8384276145356609431032283861372963097562243697552376314016825955255783276060048247578923458206922714964637719051971090315508482644101425611467695935878593225456430641524734396816529127722340745171990761635766750569572253645893268934990183682672430346879643096474676014066987397138141452057079/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1578-gaussian-only-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1578-gaussian-only-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1578/priority-manifest.json", "sha256": "a89be63c2fce3888a0b3a92b4afa898f41c2cbf632734fad050f9ea7d5b25ae0" } ], "source_head": "3218fe01c9405e82c79e97a36224bcd34de41afc" } }, { "pr": 1586, "title": "T74 outer210: verified conditional arithmetic refinement (superseded by #1578)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1586", "author": "dataisfire", "created_at": "2026-10-14T03:30:30Z", "accepted_at": "2026-10-16T14:06:50Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676855229071321886206456772274592619512448739510475263", "kappa_fraction": "419213807267830471551614193068648154878112184877618815700841297762789163803002412378946172910346135748231885952598554515775424132205071280573384796793929661272821532076236719840826456386117037258598487922871/250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1586-source-retuned-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1586-source-retuned-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1586/priority-manifest.json", "sha256": "715aa5f45d4b89598c91f733530700ff619223ed15f6a1f7842b4b73deccd0de" } ], "source_head": "18009ebf530ccd4b197c13333e651b7218df13ed" } }, { "pr": 1640, "title": "Conditional \u03ba = 0.001676855229071321886...1141584064: 300-digit grid refinement over PR1578", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1640", "author": "midhatn", "created_at": "2026-10-14T04:44:44Z", "accepted_at": "2026-10-16T14:06:50Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676855229071321886206456772274592619512448739510475263", "kappa_fraction": "2620086295423940447197588706679050967988201155485117598130258111017432273768765077368413580689663348426449287203740965723596400826281695503583654979962060382955134575476479499005165352413231482866247113011177109552991329264341646542184432400835134483399888467648336254395933561605669203767837251/1562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1640-gaussian-only-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1640-gaussian-only-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1640/priority-manifest.json", "sha256": "b42d93ec6f0e4ccd32bf8e6ae73f0cd2edfd5fb9eea1a5fb253b93e9d42a10a6" } ], "source_head": "3339744de1bbcc82844c890101856c31e3610d02" } }, { "pr": 1672, "title": "Conditional \u03ba = 0.001676938111022438: pivot 554 helper-donor kernel (k554-signed-001) stacked on the previous record", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1672", "author": "jeremykothe2", "created_at": "2026-10-14T06:11:21Z", "accepted_at": "2026-10-16T14:06:50Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676938111022438771190100017020725032555691674761792048", "kappa_fraction": "1676938111022438771190100017020725032555691674761792047536039179/1000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1672-selected-k554-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 155, "source_index": 247, "at": "2026-10-14T06:11:21Z", "until": "2026-10-14T06:15:44Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001676938111022438771190100017020725032555691674761792047536039179", "dashboard_float_text": "0.0016769381110224389", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1672", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 185, "source_index": null, "at": "2026-10-14T06:11:21Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001676938111022438771190100017020725032555691674761792047536039179", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1672", "evidence_excerpt": "Conditional \u03ba = **0.001676938111022438771190100017020725032555691674761792047536039179**. Adds the exact helper-donor kernel k554-signed-001 (pivot 554, found by LeverRank/kernel566) to the previous record's local words: re-solved frames, fresh natives, PLAN rebound, SPEC refrozen, certified fine endpoints and exact outer witness of the base package. kappa 0.001676938111022438771190100017020725032555691674761792047536039179.", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1672-selected-k554-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1672/priority-manifest.json", "sha256": "7155893fe9da1e097c27ee38c5db9886b6f9609ab381d6968b70a9476f1c3616" } ], "source_head": "b8ab040dbb7638e79249e763c60e877765d9d3b7" } }, { "pr": 2220, "title": "Conditional \u03ba = 0.001679754956125544521335670993920702576998311438502580295460327520162864548260325638826305656132844: recertified 1e-60000 supplier endpoint, fixed-grid-maximum kappa C - 1/F - B at 1e-60080 slacks (PR2180 / PR2161 retune)\u2026", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2220", "author": "jeremykothe2", "created_at": "2026-10-15T00:25:46Z", "accepted_at": "2026-10-16T14:06:50Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001679754956125544521335670993920702576998311438502580295", "kappa_fraction": "419938739031386130333917748480175644249577859625645073865081880040716137065081409706576414033211/250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_own_source_selector_required; actual own source selector; expected 419938739031386130333917748480175644249577859625645073865081880040716137065081409706576414033211/250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000; Read actual author-head CLAIM/verifier/SOURCES/MANIFEST and identify the selected complete kernel. A missing exact claim-kappa SPEC match is a discovery limitation, not mathematical rejection. Different quoted fixtures must not override a later actual final package. All listed SPEC candidates remain unselected until independently authenticated." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/2220/priority-manifest.json", "sha256": "4bdb8325d3242ff6ebe11ec8ab152cbb80db4f4330ac7e64ce467793ac708b9c" } ], "source_head": "fc09a70baf7d6bcff935df226f6fc9e6c6c0131d" } }, { "pr": 1117, "title": "Conditional \u03ba = 0.001672846995880185: rank-seven helper ends and T16 owner packing on the seven-slot k8 word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1117", "author": "jeremykothe2", "created_at": "2026-10-13T18:31:49Z", "accepted_at": "2026-10-16T14:21:05Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672846995880185", "kappa_fraction": "334569399176037/200000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1117-ends7-selected-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 136, "source_index": 191, "at": "2026-10-13T18:31:49Z", "until": "2026-10-13T18:38:03Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001672846995880185", "dashboard_float_text": "0.001672846995880185", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1117", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 153, "source_index": null, "at": "2026-10-13T18:31:49Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001672846995880185", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1117", "evidence_excerpt": "Conditional \u03ba = **0.001672846995880185**. Ports #1030\u2019s rank-seven helper-end mechanism to the seven-slot k8 word, with a new T16 owner map. Changes include the local construction, its recipe and independent controls, native locals and packing.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 442, "source_index": null, "at": "2026-10-13T18:31:49Z", "until": null, "date_basis": "body-version", "fraction": "334569399176037/200000000000000000", "value_decimal": "0.001672846995880185", "dashboard_float_text": null, "expression": "0.001672846995880185", "historical_title": "Conditional \u03ba = 0.001672846995880185: rank-seven helper ends and T16 owner packing on the seven-slot k8 word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1117", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001672846995880185. Ports #1030\u2019s rank-seven helper-end mechanism to the seven-slot k8 word, with a new T16 owner map. Changes include the local construction, its recipe and independent controls, na", "automated_comparable": true, "body_sha256": "ef0694a86f7ad86f5b6a2c93ee91571916e121e4f9a134d0138faa0c6f7d9f55" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1117-ends7-selected-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1117/priority-manifest.json", "sha256": "66f3ad321a0ef5f9bf7ffabe940147c5f5d1f8d0efba78ffe2558a8c98de2d21" } ], "source_head": "342b67f23dfa8f41a520a0d58978b2875e9eb0dd" } }, { "pr": 1121, "title": "Conditional \u03ba = 0.001672965558289236: rank-seven helper ends and T16 owner packing on the seven-slot k8 word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1121", "author": "jeremykothe2", "created_at": "2026-10-13T18:38:03Z", "accepted_at": "2026-10-16T14:21:05Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672965558289236", "kappa_fraction": "418241389572309/250000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1121-ends7-selected-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 137, "source_index": 192, "at": "2026-10-13T18:38:03Z", "until": "2026-10-13T18:41:41Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001672965558289236", "dashboard_float_text": "0.001672965558289236", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1121", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 154, "source_index": null, "at": "2026-10-13T18:38:03Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001672965558289236", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1121", "evidence_excerpt": "Conditional \u03ba = **0.001672965558289236**. Ports #1030\u2019s rank-seven helper-end mechanism to the seven-slot k8 word, with a new T16 owner map. Changes include the local construction, its recipe and independent controls, native locals and packing.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 443, "source_index": null, "at": "2026-10-13T18:38:03Z", "until": null, "date_basis": "body-version", "fraction": "418241389572309/250000000000000000", "value_decimal": "0.001672965558289236", "dashboard_float_text": null, "expression": "0.001672965558289236", "historical_title": "Conditional \u03ba = 0.001672965558289236: rank-seven helper ends and T16 owner packing on the seven-slot k8 word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1121", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001672965558289236. Ports #1030\u2019s rank-seven helper-end mechanism to the seven-slot k8 word, with a new T16 owner map. Changes include the local construction, its recipe and independent controls, na", "automated_comparable": true, "body_sha256": "a9ccbc568fafb729e0a0f69c80d3b02faa74a40864113fc50dd9913f23606364" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1121-ends7-selected-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1121/priority-manifest.json", "sha256": "61bf7734bc47b4cae124a3fc9095dc9aa27d8339f8f1ffdf9b67f45fd786f171" } ], "source_head": "61e816c29165a94f6cfc57d9e195063a5b027bc2" } }, { "pr": 1130, "title": "Conditional \u03ba = 0.001673006105142741: eighth triangle slot X54, rank-seven helper ends and T16 owner packing on the eight-slot k8 word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1130", "author": "jeremykothe2", "created_at": "2026-10-13T18:47:31Z", "accepted_at": "2026-10-16T14:21:05Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001673006105142741", "kappa_fraction": "1673006105142741/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1130-dispatched-finite-controller-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1130-dispatched-finite-controller-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1130/priority-manifest.json", "sha256": "ad6224231595951f9aea746347c4ee282c77493797cb40e5fce3a881db4082d7" } ], "source_head": "1558508e5cbff0b7c534d1c4cc7a0fb1b7145c1c" } }, { "pr": 1157, "title": "Conditional \u03ba = 0.001674137810105185: X54 slot on the seven-slot k8 word with the exact T37 owner optimum", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1157", "author": "rohanarun", "created_at": "2026-10-13T19:19:14Z", "accepted_at": "2026-10-16T14:21:05Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001674137810105185", "kappa_fraction": "334827562021037/200000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1157-gaussian-only-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1157-gaussian-only-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 7, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1157/priority-manifest.json", "sha256": "221cde7fa43c9f579e1aaeaaed69f4dd80925fa275348e4b1a0c9b34a585ba98" } ], "source_head": "c5647aecc8ff44e49776860bb75520bfe3e88f1e" } }, { "pr": 1549, "title": "Conditional \u03ba = 0.001676855229071321886...03439: 200-digit outer refinement over PR1536", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1549", "author": "midhatn", "created_at": "2026-10-14T02:46:46Z", "accepted_at": "2026-10-16T14:21:05Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676855229071321886206456772274592619512448739510475263", "kappa_fraction": "167685522907132188620645677227459261951244873951047526280336519105115665521200964951578469164138454299292754381039421806310169652882028512229353918717571864509128612830494687936330582554446814903439/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1549-gaussian-only-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 180, "source_index": null, "at": "2026-10-14T02:46:46Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00167685522907132188620645677227459261951244873951047526280336519105115665521200964951578469164138454299292754381039421806310169652882028512229353918717571864509128612830494687936330582554446814903439", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1549", "evidence_excerpt": "Conditional \u03ba = **0.00167685522907132188620645677227459261951244873951047526280336519105115665521200964951578469164138454299292754381039421806310169652882028512229353918717571864509128612830494687936330582554446814903439**, an exact rational increase of **9.000000e-200** (+9/10^200) over PR #1536 (`527d7623009f295b7311e98ae36f5e2fbdbbc3e5`).", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1549-gaussian-only-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1549/priority-manifest.json", "sha256": "4b2165dffb82357d724d8dca63ed8412922c529344045a0d0bac37ef8616a66d" } ], "source_head": "f98c217351ff1a5e5d831d75070c3adb4422c1bf" } }, { "pr": 1582, "title": "Conditional \u03ba = 0.001676855229071321886...03439815: 220-digit certified endpoints and outer refinement over PR1549", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1582", "author": "midhatn", "created_at": "2026-10-14T03:23:27Z", "accepted_at": "2026-10-16T14:21:05Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676855229071321886206456772274592619512448739510475263", "kappa_fraction": "16768552290713218862064567722745926195124487395104752628033651910511566552120096495157846916413845429929275438103942180631016965288202851222935391871757186450912861283049468793633058255444681490343981523271533501139143/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1582-gaussian-only-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1582-gaussian-only-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1582/priority-manifest.json", "sha256": "3f7113e2e5c7cb5b524c4f2005022b705ea5b844166789bfed4d8a0894eb92d2" } ], "source_head": "5d3f2c9789aeb16e09c213869ec05e5ab72da464" } }, { "pr": 1625, "title": "Conditional \u03ba = 0.001676896669021299: pivot-566 helper-donor kernel on PR1319's T74 exact fill (+4.14e-8)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1625", "author": "mdumitrean", "created_at": "2026-10-14T04:17:30Z", "accepted_at": "2026-10-16T14:21:05Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001676896669021299", "kappa_fraction": "1676896669021299/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1625-pivot566-kernel-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1625-pivot566-kernel-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1625/priority-manifest.json", "sha256": "5b16bf84e47825ff9e4f1a2009a435f79465bed1f8917c4fee11f97130bbeb13" } ], "source_head": "c7cac07823caabefb2439a9fc5c222639b487cbd" } }, { "pr": 2621, "title": "Conditional \u03ba = 0.001714270081226977: half-stage timing and evacuated #2588 hosting", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2621", "author": "themilkman216", "created_at": "2026-10-15T16:15:10Z", "accepted_at": "2026-10-16T14:21:05Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001714270081226977", "kappa_fraction": "1714270081226977/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 190, "source_index": 303, "at": "2026-10-15T16:15:10Z", "until": "2026-10-15T16:58:17Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001714270081226977", "dashboard_float_text": "0.001714270081226977", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2621", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 223, "source_index": null, "at": "2026-10-15T16:15:10Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001714270081226977", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2621", "evidence_excerpt": "Certify conditional **\u03ba \u2248 0.001714270081226977**, improving #2588's `0.001714252039260245` by **1.8041966731709573\u00d710\u207b\u2078**. The complete literal witness, exact rational claim, source manifests and admission receipts are in [`research/half-stage-evacuation`](https://github.com/themilkman216/integer-mult-bounds/tree/codex/kappa-sourcepartner/research/half-stage-evacuation).", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 500, "source_index": null, "at": "2026-10-15T16:15:10Z", "until": null, "date_basis": "body-version", "fraction": "1714270081226977/1000000000000000000", "value_decimal": "0.001714270081226977", "dashboard_float_text": null, "expression": "0.001714270081226977", "historical_title": "Conditional \u03ba = 0.001714270081226977: half-stage timing and evacuated #2588 hosting", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2621", "evidence_excerpt": "## Change and mathematical scope\n\nCertify conditional \u03ba \u2248 0.001714270081226977, improving #2588's 0.001714252039260245 by 1.8041966731709573*10^-8. The complete literal witness, exact rational claim, source manifests and admission receipts are in [research/h", "automated_comparable": true, "body_sha256": "589b8703971210adfc77c97d9a0045364660bbf6a41c7c0d0e45fff9a51589e7" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_own_source_selector_required; actual own source selector; expected 1714270081226977/1000000000000000000; Read actual author-head CLAIM/verifier/SOURCES/MANIFEST and identify the selected complete kernel. A missing exact claim-kappa SPEC match is a discovery limitation, not mathematical rejection. Different quoted fixtures must not override a later actual final package. All listed SPEC candidates remain unselected until independently authenticated." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/2621/priority-manifest.json", "sha256": "5d2b6830617ebda385847592a50d8c4362f76af75c89bdaf605ece2eb908c94a" } ], "source_head": "07c0e3000e8538058b80e309440f29652edff0b4" } }, { "pr": 962, "title": "Conditional \u03ba = 0.001661960547713947: T37 owner map on PR890's U8 word (independent cross-check of #942)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/962", "author": "GamingPuzzled", "created_at": "2026-10-13T14:59:06Z", "accepted_at": "2026-10-16T14:21:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661960547713947", "kappa_fraction": "1661960547713947/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr962-generated-U8-t37-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr962-generated-U8-t37-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 6, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/962/priority-manifest.json", "sha256": "73cacd5e97c9cd56fb72658372b49a810b233a1b3616dc53855aade48647e36b" } ], "source_head": "50c6ae8151493af21d284afe34fb35f68f6d4934" } }, { "pr": 1107, "title": "Conditional \u03ba = 0.001672765980186726: rank-seven helper ends and T16 owner packing on the seven-slot k8 word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1107", "author": "jeremykothe2", "created_at": "2026-10-13T18:19:42Z", "accepted_at": "2026-10-16T14:21:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672765980186726", "kappa_fraction": "836382990093363/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1107-ends7-selected-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 134, "source_index": 189, "at": "2026-10-13T18:19:42Z", "until": "2026-10-13T18:23:15Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001672765980186726", "dashboard_float_text": "0.001672765980186726", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1107", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 151, "source_index": null, "at": "2026-10-13T18:19:42Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001672765980186726", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1107", "evidence_excerpt": "Conditional \u03ba = **0.001672765980186726**. Ports #1030\u2019s rank-seven helper-end mechanism to the seven-slot k8 word, with a new T16 owner map. Changes include the local construction, its recipe and independent controls, native locals and packing.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 440, "source_index": null, "at": "2026-10-13T18:19:42Z", "until": null, "date_basis": "body-version", "fraction": "836382990093363/500000000000000000", "value_decimal": "0.001672765980186726", "dashboard_float_text": null, "expression": "0.001672765980186726", "historical_title": "Conditional \u03ba = 0.001672765980186726: rank-seven helper ends and T16 owner packing on the seven-slot k8 word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1107", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001672765980186726. Ports #1030\u2019s rank-seven helper-end mechanism to the seven-slot k8 word, with a new T16 owner map. Changes include the local construction, its recipe and independent controls, na", "automated_comparable": true, "body_sha256": "43e1cb33e7df0b27dbc218b05493ed0b8519f419ff8d1028d96ad9583291ef94" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1107-ends7-selected-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1107/priority-manifest.json", "sha256": "f9e0a7de7d9614e3cdeff9499b788c7057b531417bc3659221751926653981c2" } ], "source_head": "6123fc5d57db16aaa3e8a26b4a11a34b46c0c391" } }, { "pr": 1124, "title": "Conditional \u03ba = 0.001673005344598825: eighth triangle slot X54, rank-seven helper ends and T16 owner packing on the eight-slot k8 word", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1124", "author": "jeremykothe2", "created_at": "2026-10-13T18:41:41Z", "accepted_at": "2026-10-16T14:21:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001673005344598825", "kappa_fraction": "66920213783953/40000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1124-dispatched-finite-controller-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 138, "source_index": 193, "at": "2026-10-13T18:41:41Z", "until": "2026-10-13T18:47:16Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001673005344598825", "dashboard_float_text": "0.001673005344598825", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1124", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 155, "source_index": null, "at": "2026-10-13T18:41:41Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001673005344598825", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1124", "evidence_excerpt": "Conditional \u03ba = **0.001673005344598825**. Adds the eighth triangle slot X54 to the rank-seven helper-end k8 construction with a new T16 owner map. The pinned composite replay rebuilds and independently controls both transformations before admitting the new locals and packing.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 444, "source_index": null, "at": "2026-10-13T18:41:41Z", "until": null, "date_basis": "body-version", "fraction": "66920213783953/40000000000000000", "value_decimal": "0.001673005344598825", "dashboard_float_text": null, "expression": "0.001673005344598825", "historical_title": "Conditional \u03ba = 0.001673005344598825: eighth triangle slot X54, rank-seven helper ends and T16 owner packing on the eight-slot k8 word", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1124", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001673005344598825. Adds the eighth triangle slot X54 to the rank-seven helper-end k8 construction with a new T16 owner map. The pinned composite replay rebuilds and independently controls both tran", "automated_comparable": true, "body_sha256": "1e9e32f08248d3cf66963d621a080686f3a3933fa37bd683523034561004c0ee" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1124-dispatched-finite-controller-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1124/priority-manifest.json", "sha256": "3d635bcef830227aee737012605ed52044106c4e0792f510b1b268cda38aafcc" } ], "source_head": "7c0e3ee0e2d4f6c00d033a4f1dfe4e793e7ecae4" } }, { "pr": 1178, "title": "Conditional \u03ba = 0.001675161536733127: X54 slot on #1148's three-demotion k8 word with its T16 owners", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1178", "author": "rohanarun", "created_at": "2026-10-13T19:45:06Z", "accepted_at": "2026-10-16T14:21:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001675161536733127", "kappa_fraction": "1675161536733127/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1178-recovered-x54-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1178-recovered-x54-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 7, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1178/priority-manifest.json", "sha256": "545a4931bd6a7e8b41ad7172a8d7e8ae0539e2d5a47e6871c8c537e5d731d465" } ], "source_head": "6d4d0dd1c2df531a3350495dd15e00105793c52d" } }, { "pr": 2571, "title": "Conditional \u03ba = 0.0017137844912361143: repacked owner fill on #2530's source-partner words", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2571", "author": "rohanarun", "created_at": "2026-10-15T14:58:55Z", "accepted_at": "2026-10-16T14:21:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001713784491236114313144999999999999999999999900000000000", "kappa_fraction": "17137844912361143131449999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 187, "source_index": 300, "at": "2026-10-15T14:58:55Z", "until": "2026-10-15T15:03:49Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.0017137844912361143131449999999999999999999998999999999999999999999999", "dashboard_float_text": "0.0017137844912361144", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2571", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 220, "source_index": null, "at": "2026-10-15T14:58:55Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.0017137844912361143131449999999999999999999998999999999999999999999999", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2571", "evidence_excerpt": "Conditional **\u03ba = 0.0017137844912361143131449999999999999999999998999999999999999999999999**. The exact rational is in `research/source-partner-repack/CLAIM.json`.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 497, "source_index": null, "at": "2026-10-15T14:58:55Z", "until": null, "date_basis": "body-version", "fraction": "17137844912361143131449999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "value_decimal": "0.0017137844912361143131449999999999999999999998999999999999999999999999", "dashboard_float_text": null, "expression": "0.0017137844912361143131449999999999999999999998999999999999999999999999", "historical_title": "Conditional \u03ba = 0.0017137844912361143: repacked owner fill on #2530's source-partner words", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2571", "evidence_excerpt": "## Result\n\nConditional \u03ba = 0.0017137844912361143131449999999999999999999998999999999999999999999999. The exact rational is in research/source-partner-repack/CLAIM.json.\n\n- Over #2530 (zxv, 0.0017137379215475043\u2026): +4.6569688609966393E-8 (exact 46569688609966393/10000000000000000", "automated_comparable": true, "body_sha256": "c7cab7b50657d6429273e2cdc99e7dd4031245b306904833dd2b691871d004ef" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_own_source_selector_required; actual own source selector; expected 17137844912361143131449999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000; Read actual author-head CLAIM/verifier/SOURCES/MANIFEST and identify the selected complete kernel. A missing exact claim-kappa SPEC match is a discovery limitation, not mathematical rejection. Different quoted fixtures must not override a later actual final package. All listed SPEC candidates remain unselected until independently authenticated." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/2571/priority-manifest.json", "sha256": "1ebfeb15ce9b165a39b1fc80346ed6f6d98bd4e5f2ea66c37190f2f2014d4835" } ], "source_head": "faff03cf5c29dadd6e0eb51e406efdc921bfa683" } }, { "pr": 685, "title": "Conditional \u03ba = 0.001660339298410333: four entrance promotions and 72 cold ends", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/685", "author": "chafreaky", "created_at": "2026-10-13T04:02:54Z", "accepted_at": "2026-10-16T14:31:20Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001660339298410333", "kappa_fraction": "1660339298410333/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr685-cold72-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 106, "source_index": 155, "at": "2026-10-13T04:02:54Z", "until": "2026-10-13T04:23:47Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001660339298410333", "dashboard_float_text": "0.001660339298410333", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/685", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 123, "source_index": null, "at": "2026-10-13T04:02:54Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001660339298410333", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/685", "evidence_excerpt": "Composes six new cold dimension-eight ends with entrance promotions on the PR659 no-triangle word, then adds a fourth promotion group and an exact physical owner assignment. The resulting **conditional \u03ba is 0.001660339298410333** (`1660339298410333/10^18`), above independently replayed #676's `0.001659319032684569` and independently replayed #671. The complex endpoint is `1663100609709845015347/10^24`; #589's bit supplier and surcharge are unchanged.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 407, "source_index": null, "at": "2026-10-13T04:02:54Z", "until": null, "date_basis": "body-version", "fraction": "1660339298410333/1000000000000000000", "value_decimal": "0.001660339298410333", "dashboard_float_text": null, "expression": "0.001660339298410333", "historical_title": "Conditional \u03ba = 0.001660339298410333: four entrance promotions and 72 cold ends", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/685", "evidence_excerpt": "hen adds a fourth promotion group and an exact physical owner assignment. The resulting conditional \u03ba is 0.001660339298410333 (1660339298410333/10^18), above independently replayed #676's 0.001659319032684569 and independently replayed #671. The complex endpoint is 1663100609709845015347/10^24; #589's bi", "automated_comparable": true, "body_sha256": "d9518d3eed9bdebb2ae9a67faa27db0197d43a081bf37c2fdeac4c56a83e48df" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "1672188119205421/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier1042.json", "path": "certificates/checkpoints/frontier1042.json", "commit": null, "at": null, "scope": "Finite composition under inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic and bit H1-H5 assumptions. 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Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_current_checkpoint_json", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier799.json", "path": "certificates/checkpoints/frontier799.json", "commit": null, "at": null, "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. Not a full Lean multiplication theorem. 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Not a full Lean multiplication theorem; Linux integration CI tracked separately." }, { "stream": "all_selected_result_history", "record_kappa": "1661634653669567/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/d6dfd8f21b1e0b7e3f93b7e30e64639390e48504/certificates/selected-result.json", "path": null, "commit": "d6dfd8f21b1e0b7e3f93b7e30e64639390e48504", "at": "2026-10-13T06:44:14Z", "scope": "Source-bound finite X4 construction and freshly rebuilt bit589/ancestral SW4 supplier checks; optional verified ancestry reuse recorded explicitly. Inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic hypotheses remain. Not a full Lean multiplication theorem. Integration Linux CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/c290b7b919790300e14004a75d8d24b55ca3c5b5/certificates/selected-result.json", "path": null, "commit": "c290b7b919790300e14004a75d8d24b55ca3c5b5", "at": "2026-10-13T06:10:31Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." }, { "stream": "all_selected_result_history", "record_kappa": "1661202643272239/1000000000000000000", "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/2cdd93d0250554e5160edbb8535c4500c4227349/certificates/selected-result.json", "path": null, "commit": "2cdd93d0250554e5160edbb8535c4500c4227349", "at": "2026-10-13T05:57:09Z", "scope": "Finite scalar, frame, phase, whole-owner, precision, moment and exact assembly checks on both freshly rebuilt suppliers. All-size/compiler/common-label/mutable-source/whole-call hosting/precision/tape/analytic assumptions remain. Not a full Lean multiplication theorem. Source PR Linux CI passed; combined integration CI status is separate." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr685-cold72-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 12, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/685-manifest.json", "sha256": "8f22ddaf9ae5ec477ef91a2d0c2fe688a40c27c7624843eb061fedcae4f22d2f" }, { "file": "remaining-record-audit/artifacts/685/priority-manifest.json", "sha256": "e9fd8cea0dab9b54dc6327c74a726ae9f77f4a0e1765e421a6feeb30212e46b2" } ], "source_head": "5fc2a0c4e10558f09f03a8e42559dcf8e381e57e" } }, { "pr": 1131, "title": "Conditional \u03ba = 0.001674097969905390: seven-slot k8 with T37 whole-owner packing", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1131", "author": "chafreaky", "created_at": "2026-10-13T18:49:02Z", "accepted_at": "2026-10-16T14:31:20Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00167409796990539", "kappa_fraction": "167409796990539/100000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1131-generated-t37-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1131-generated-t37-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1131/priority-manifest.json", "sha256": "2d1fc02100a8c0ada8fe5a52d8907b5cf5a645804d40e54ec4d7c5c25f93f50b" } ], "source_head": "fcdc42737b703323d8ed550a528141a482e68e96" } }, { "pr": 1152, "title": "Conditional \u03ba = 0.001674340686401949: rank-seven helper ends with T37 owner packing", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1152", "author": "chafreaky", "created_at": "2026-10-13T19:10:53Z", "accepted_at": "2026-10-16T14:31:20Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001674340686401949", "kappa_fraction": "1674340686401949/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr1152-generated-t37-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ] }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 140, "source_index": 197, "at": "2026-10-13T19:10:53Z", "until": "2026-10-13T19:14:18.872220Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001674340686401949", "dashboard_float_text": "0.001674340686401949", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1152", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 157, "source_index": null, "at": "2026-10-13T19:10:53Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001674340686401949", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1152", "evidence_excerpt": "Conditional **\u03ba = 0.001674340686401949** (`1674340686401949/10^18`). This improves the currently selected #1094 result `0.001672660197076918` and the submitted #1121 value `0.001672965558289236` at the comparison snapshot. It improves our #1131 construction and the concurrent #1129 construction, both at `0.001674097969905390`.", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Full partial initial/final Gaussian-subspace operator identities, tensor identity on spectators, required absolute phases and normalized completed-child interfaces remain explicit; scalar specialization or frame dimensions alone do not prove them. Actual canonical initial/final nesting and rank differences are checked, and actual nonzero initial frames, not width<9, determine entering counts." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr1152-generated-t37-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1152/priority-manifest.json", "sha256": "76efc4ecf5d8b484c97155f946d5e872218dc3e82512e6062f77911b8a724121" } ], "source_head": "d376209304f05551f975b0ddf6eaa84edc4ae31a" } }, { "pr": 1196, "title": "Conditional \u03ba = 0.001675608585476885: joint entrances and X54 with T37 owners", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1196", "author": "chafreaky", "created_at": "2026-10-13T19:56:17Z", "accepted_at": "2026-10-16T14:31:20Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001675608585476885", "kappa_fraction": "335121717095377/200000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_selected_full_program_bytes_missing; gauge44; required full program b6e6d496eefc02532f91e833561b8cb676062c57d3943afc2ae0932810a5a36b; both orientations {\"backward\": \"1e1f4ada65568b65479452e89569a7c9ec1c1900a10684ebfe3ec835800dfddb\", \"forward\": \"12960a48d39ca4e4187dbcafa0cd8ecfc43fd7a9479c1a2fb3ba8438c3ddfb5e\"}; Recover exact actual complete selected program bytes, by own immutable primary source or deterministic pinned constructor/recipe with mandatory complete semantic and orientation commitments. A matching profile, scalar saving or another provider does not fill this gap. Missing canonical catalogue may remain a separately stated endpoint premise only after the actual selected program and complete own physical/invoice are bound.", "Source-specific frozen V10 discovery snapshot: actual_selected_physical_input_unresolved; PLAN; expected 5b2cbbd3fa5aedd720f327d742721ba427b4478f046f70bf2efbf46aa7211abd; Bind the actual complete own PLAN/OWNERS bytes or reconstruct a source-equivalent complete physical realization with explicit changed-parent provenance, actual role/program/windows/stock checks and fresh full invoice. A404 under conventional local paths is not proof that an explicitly pinned parent archive is absent." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1196/priority-manifest.json", "sha256": "ebb9dfe02559313f3bcc0c81414b7b53e60b7553c6d1f2b8d60761321e3092d6" } ], "source_head": "7015903d1d01a2b50ff16f85184edc2686f69e37" } }, { "pr": 1239, "title": "Conditional \u03ba = 0.001675809683500501: source-holder fusions and X54 on #1193's mixed T37 construction (independent; equals #1218)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1239", "author": "GamingPuzzled", "created_at": "2026-10-13T20:51:29Z", "accepted_at": "2026-10-16T14:31:20Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001675809683500501", "kappa_fraction": "1675809683500501/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_selected_full_program_bytes_missing; demote3; required full program 293f63a036a5546032a3a651dfd96c7d9a8eb1f4e4fb52d435da71e6d13e8548; both orientations {\"backward\": \"feee707495945622de885acdd3b37be7258d1253a6fbc6cd2353c461aaf7c7c1\", \"forward\": \"1c219088ed8d8e54c4247eaf7ebfea10fb1a0dcbe33c08563a37994ed84fcd4a\"}; Recover exact actual complete selected program bytes, by own immutable primary source or deterministic pinned constructor/recipe with mandatory complete semantic and orientation commitments. A matching profile, scalar saving or another provider does not fill this gap. Missing canonical catalogue may remain a separately stated endpoint premise only after the actual selected program and complete own physical/invoice are bound.", "Source-specific frozen V10 discovery snapshot: actual_selected_full_program_bytes_missing; demote4; required full program 8d235fa25a5c5bf111fd4c7d8c2e44b6d4d4ee3b9abf7eca4e39ce668f24afec; both orientations {\"backward\": \"c3ac69bcf280a772c8ed3cdd83e24a6188cd90758f54f57e8d0bef5ac0afaf2d\", \"forward\": \"03a00c24e56a63b64233e05e9b3a6c79dca327d5763ffb691a7363c31ad6e520\"}; Recover exact actual complete selected program bytes, by own immutable primary source or deterministic pinned constructor/recipe with mandatory complete semantic and orientation commitments. A matching profile, scalar saving or another provider does not fill this gap. Missing canonical catalogue may remain a separately stated endpoint premise only after the actual selected program and complete own physical/invoice are bound.", "Source-specific frozen V10 discovery snapshot: actual_selected_physical_input_unresolved; PLAN; expected 6ca0d1ecf8800f02b4c721dc9c55276b3de9222a14648affb96bdfe01879b811; Bind the actual complete own PLAN/OWNERS bytes or reconstruct a source-equivalent complete physical realization with explicit changed-parent provenance, actual role/program/windows/stock checks and fresh full invoice. A404 under conventional local paths is not proof that an explicitly pinned parent archive is absent." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/1239/priority-manifest.json", "sha256": "376be022ea28d8acd263e380ef0e48ef062cd109cd1aa1459abf2272cf0cfd9a" } ], "source_head": "12e04a30d7381a2a60bf2d7260febcb37f14e454" } }, { "pr": 2957, "title": "Conditional \u03ba = 0.001723717415070738: fourteen declared gate rewrites (five classes) on #2917's words with #2930's cap-attaining fill", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2957", "author": "jeremykothe2", "created_at": "2026-10-16T14:21:12Z", "accepted_at": "2026-10-16T14:47:34Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00172371741507073817097099999999999999", "kappa_fraction": "172371741507073817097099999999999999/100000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 212, "source_index": 333, "at": "2026-10-16T14:21:12Z", "until": "2026-10-16T14:50:21Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001723717415070738170970999999999999999999999899999999999999", "dashboard_float_text": "0.0017237174150707382", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2957", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 247, "source_index": null, "at": "2026-10-16T14:21:12Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001723717415070738170970999999999999999999999899999999999999", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2957", "evidence_excerpt": "Conditional \u03ba = **0.001723717415070738170970999999999999999999999899999999999999\u2026** (70 decimals; the exact value is `kappa` in `research/paired-extension-cap-fill-swaps/outer/OUTER-CLAIM.json`, SHA-256 of the decimal string `1216af123e6a037db8ada366c4c6f0557c028c0b7d982e20d40563b0cafc24a9`). This package takes PR2930's (mdumitrean, Marius-Paul Dumitrean) cap-attaining T74 allocation of PR2917's (mason-hale) nine paired extractions on PR2908's (jeremydiviney) construction as its base: its litera", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 528, "source_index": null, "at": "2026-10-16T14:21:12Z", "until": null, "date_basis": "body-version", "fraction": "172371741507073817097099999999999999/100000000000000000000000000000000000000", "value_decimal": "0.001723717415070738170970999999999999999999999899999999999999", "dashboard_float_text": null, "expression": "0.00172371741507073817097099999999999999", "historical_title": "Conditional \u03ba = 0.001723717415070738: fourteen declared gate rewrites (five classes) on #2917's words with #2930's cap-attaining fill", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2957", "evidence_excerpt": "h natives for both changed words, complete admission and the modern outer release pass. Conditional kappa = 0.00172371741507073817097099999999999999..., above PR2930 by 1.2176e-6 (exact gate in verify_release.py).\n\n## Verification\n\nFresh checkout of b74b25f3ccc84c16e1a801d73b2f47e5ea764c78. Manifest: 9cd226a2bf7391e7fbf4a23741", "automated_comparable": true, "body_sha256": "18e528e0a59750c62f8f7d02ffad1c9b3c5d05ae28a6bc719ad8fc30ed4fd359" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 9, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/paired-extension-cap-fill-swaps/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/paired-extension-cap-fill-swaps/CLAIM.json, research/paired-extension-cap-fill-swaps/MANIFEST.json, research/paired-extension-cap-fill-swaps/README.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/paired-extension-cap-fill-swaps/CLAIM.json, research/paired-extension-cap-fill-swaps/MANIFEST.json, research/paired-extension-cap-fill-swaps/README.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/paired-extension-cap-fill-swaps/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2957-manifest.json", "sha256": "80e174cd3fd92129059818bc24b213f165c067ed8958ebd0bbaf44a9db2837f2" }, { "file": "remaining-record-audit/artifacts/2957/priority-manifest.json", "sha256": "ae841175cee5f3c33fcb2877ee230729442df4fc5d57a716a59e406a387aad17" } ], "source_head": "b74b25f3ccc84c16e1a801d73b2f47e5ea764c78" } }, { "pr": 2966, "title": "Conditional \u03ba = 0.001724034272523452: fourteen declared gate rewrites (five classes) on #2942's words and literal allocation", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2966", "author": "jeremykothe2", "created_at": "2026-10-16T14:50:21Z", "accepted_at": "2026-10-16T15:18:21Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0017240342725234521774119999", "kappa_fraction": "17240342725234521774119999/10000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 213, "source_index": 334, "at": "2026-10-16T14:50:21Z", "until": "2026-10-16T15:00:49Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001724034272523452177411999999999999999999999899999999999999", "dashboard_float_text": "0.001724034272523452", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2966", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 248, "source_index": null, "at": "2026-10-16T14:50:21Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001724034272523452177411999999999999999999999899999999999999", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2966", "evidence_excerpt": "Conditional \u03ba = **0.001724034272523452177411999999999999999999999899999999999999\u2026** (70 decimals; the exact value is `kappa` in `research/paired-extension-normal45-rewrites/outer/OUTER-CLAIM.json`, SHA-256 of the decimal string `869742d3e490308fd61beb10221325d6a2d906d571400becd028bb390b128c3e`). This package takes PR2942's (mdumitrean, Marius-Paul Dumitrean) words (PR2917's (mason-hale) nine paired extractions on PR2908's (jeremydiviney) construction plus four normal-45 paired extractions) and i", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 529, "source_index": null, "at": "2026-10-16T14:50:21Z", "until": null, "date_basis": "body-version", "fraction": "17240342725234521774119999/10000000000000000000000000000", "value_decimal": "0.001724034272523452177411999999999999999999999899999999999999", "dashboard_float_text": null, "expression": "0.0017240342725234521774119999", "historical_title": "Conditional \u03ba = 0.001724034272523452: fourteen declared gate rewrites (five classes) on #2942's words and literal allocation", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2966", "evidence_excerpt": "s for both words, complete replica admission and the modern outer release are replayed. Conditional kappa 0.0017240342725234521774119999..., 1.2180e-06 above PR2942 and 6.778e-07 above the nine-rewrite package on PR2930.\n\n## Verification\n\nFresh checkout of e62d3eb9005117d82a9babcfa937ecc53237c490. Manifest: 9e410c2", "automated_comparable": true, "body_sha256": "675587f42388d07f68598b143ba49b3ec40e4cebdd0c5b89abccc7e33ac7b75f" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/paired-extension-normal45-rewrites/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/paired-extension-normal45-rewrites/CLAIM.json, research/paired-extension-normal45-rewrites/README.md, research/paired-extension-normal45-rewrites/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/paired-extension-normal45-rewrites/CLAIM.json, research/paired-extension-normal45-rewrites/README.md, research/paired-extension-normal45-rewrites/SOURCES.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/paired-extension-normal45-rewrites/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2966-manifest.json", "sha256": "2e3a50a2e630dcfc0288ef335ccb47c5512bef12f5333600549c1f68e343a743" }, { "file": "remaining-record-audit/artifacts/2966/priority-manifest.json", "sha256": "807b4f29e6655b05772713c4a76a14144b174e78bb26e9f8f0d11aa11f482157" } ], "source_head": "e62d3eb9005117d82a9babcfa937ecc53237c490" } }, { "pr": 2969, "title": "Compose normal-45 extraction and fourteen gate rewrites: candidate \u03ba \u2248 0.0017240352247481", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2969", "author": "Dugongue", "created_at": "2026-10-16T15:00:49Z", "accepted_at": "2026-10-16T15:18:21Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0017240352247481", "kappa_fraction": "17240352247481/10000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 214, "source_index": 335, "at": "2026-10-16T15:00:49Z", "until": "2026-10-16T15:59:15Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.0017240352247481", "dashboard_float_text": "0.0017240352247481", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2969", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 249, "source_index": null, "at": "2026-10-16T15:00:49Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.0017240352247481", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2969", "evidence_excerpt": "Compose normal-45 extraction and fourteen gate rewrites: candidate \u03ba \u2248 0.0017240352247481", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 530, "source_index": null, "at": "2026-10-16T15:00:49Z", "until": null, "date_basis": "opening-title", "fraction": "17240352247481/10000000000000000", "value_decimal": "0.0017240352247481", "dashboard_float_text": null, "expression": "0.0017240352247481", "historical_title": "Compose normal-45 extraction and fourteen gate rewrites: candidate \u03ba \u2248 0.0017240352247481", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2969", "evidence_excerpt": "Compose normal-45 extraction and fourteen gate rewrites: candidate \u03ba \u2248 0.0017240352247481", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/paired-swap-normal45/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/paired-swap-normal45/CLAIM.json, research/paired-swap-normal45/MANIFEST.json, research/paired-swap-normal45/PROOF.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/paired-swap-normal45/CLAIM.json, research/paired-swap-normal45/MANIFEST.json, research/paired-swap-normal45/PROOF.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/paired-swap-normal45/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2969-manifest.json", "sha256": "7edfc96d6ccc7000882715a4180c5f7258a8d1f8a1c018e029deab7f6ca28300" }, { "file": "remaining-record-audit/artifacts/2969/priority-manifest.json", "sha256": "dbb5e8fa366164fb75445c0a2bf2af1628047c0c53a615993d3e1bdbc84ffddc" } ], "source_head": "e2ca469b08385d3d5e29a918d66dbefaf889e9f3" } }, { "pr": 1252, "title": "Idle pair exchanges improve the #1094 \u03ba candidate", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1252", "author": "Gonzalo-Mier", "created_at": "2026-10-13T21:09:53Z", "accepted_at": "2026-10-16T15:37:26Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672846574134982", "kappa_fraction": "836423287067491/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 2 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Recompute the complete own productive/paid histogram from research/frontier1094-idle-exchanges/replay/audit/PREFIX-AND-INVOICE.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/frontier1094-idle-exchanges/replay/ASSEMBLY.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/1252-manifest.json", "sha256": "7de8d67afb09ce196f6d789d11ffe1f9f19f43d727a1a23cd05ae149072f8c15" }, { "file": "remaining-record-audit/artifacts/1252/priority-manifest.json", "sha256": "f8c50d16a609005821157cf8d42b8401c7aae6b36f61fc5efe961e30e3d08a9d" } ], "source_head": "1b9db2faf82b8866b0bb0164501c9a627c7dca9b" } }, { "pr": 275, "title": "Finite assembly theorem and source-bound PR799 application", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/275", "author": "lydakis", "created_at": "2026-10-10T04:17:25Z", "accepted_at": "2026-10-16T15:51:16Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001661634653669567075843432", "kappa_fraction": "207704331708695884480429/125000000000000000000000000", "kappa_status": "authenticated_actual_merged_source_selection", "kappa_scope": "The costed \u03ba comes from the explicitly selected source included at this merge. The original parser quote is retained and visibly distinguished. Own actual merged-head799-application EXPECTED target, own manifest/verifier/UPSTREAM binding and actual merge second parent; old parser chose historical433fixture. Frozen metadata is preserved, not rewritten.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr275-supplied-cap-gaussian-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": "New direct Gaussian realization of the exact799 core explicitly selected by the actual merged PR275 source. The source-selected kappa is visibly corrected while preserving the old parsed433 fixture, and dated at actual merge inclusion. Native/operator, whole-owner/all-size, precision and analytic contracts remain conditional; this is a sufficient gate, with no natural first-crossing claim." }, "cost_status": "conditional_own_source_upper_only", "historical_streams": [ "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "recovered_literal_highwater", "stream_row": 191, "source_index": null, "at": "2026-10-10T04:17:25Z", "until": null, "date_basis": "body-version", "fraction": "8921126351038225858611/12500000000000000000000000", "value_decimal": "0.001661634653669567075843432", "dashboard_float_text": null, "expression": "8921126351038225858611 / 12500000000000000000000000", "historical_title": "Zero-frame target restores on PR271: conditional \u03ba = 0.000713690108083058", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/275", "evidence_excerpt": "package composes that selection with PR 271's current 99-helper cleanup, giving conditional finite\n\n\u03ba = 8921126351038225858611 / 12500000000000000000000000 = 0.00071369010808305806868888.\n\nThe exact gain over reproduced PR 271 ebc1defe8c13f39f86e5901c3437c1be52886a2b is 27951693448094147889/10^27 (about 0.00391665625%). This is an ad", "automated_comparable": true, "body_sha256": "d5c6f3eb3b571c6565095ac61cc196b2e4bc8de5bd56ee33d7d5a77dc9ac6abf" }, { "stream": "recovered_literal_highwater", "stream_row": 197, "source_index": null, "at": "2026-10-10T05:52:09Z", "until": null, "date_basis": "body-version", "fraction": "726214631355537156447271/1000000000000000000000000000", "value_decimal": "0.001661634653669567075843432", "dashboard_float_text": null, "expression": "726214631355537156447271 / 10^27", "historical_title": "Conditional \u03ba = 0.000726214631355537: twenty extra target pairs on gen4 composition", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/275", "evidence_excerpt": "th rank-21 children, preserving all existing helper optimizations and the bank layout.\n\nConditional \u03ba = 726214631355537156447271 / 10^27 = 0.000726214631355537156447271. This is 0.0142247% above pinned PR283 and 1.75490% above this PR's earlier zero-frame result.\n\n## Change\n\nThe new additive package is research/gen", "automated_comparable": true, "body_sha256": "1e925e84c6c973f36b2c3b0a0830cd897dcb145ca6a7fef8aafb189b789cd985" }, { "stream": "recovered_literal_highwater", "stream_row": 200, "source_index": null, "at": "2026-10-10T07:38:46Z", "until": null, "date_basis": "body-version", "fraction": "744118535019311029483079/1000000000000000000000000000", "value_decimal": "0.001661634653669567075843432", "dashboard_float_text": null, "expression": "744118535019311029483079 / 10^27", "historical_title": "Conditional \u03ba = 0.000744118535019311: gen5 source retiming and target-prefix compression", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/275", "evidence_excerpt": "ve calls and 440 scalar ADDs while preserving helper endpoints, rank mass and storage.\n\nConditional \u03ba = 744118535019311029483079 / 10^27 = 0.000744118535019311029483079, 0.1794423% above freshly reproduced PR285.\n\n## Contribution\n\nThe new additive package is research/gen5-retiming-targets/. The source search derive", "automated_comparable": true, "body_sha256": "95e03c2fdf7f3dd60d777a41dcc0d2ea8a61373a677a3098462ac122e5dfa164" }, { "stream": "recovered_literal_highwater", "stream_row": 205, "source_index": null, "at": "2026-10-10T09:28:40Z", "until": null, "date_basis": "body-version", "fraction": "46579554167366864110747/62500000000000000000000000", "value_decimal": "0.001661634653669567075843432", "dashboard_float_text": null, "expression": "745272866677869825771952 / 10^27", "historical_title": "Conditional \u03ba = 0.000745272866677870: 440 early helper restorations on gen5 kernels", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/275", "evidence_excerpt": "th PR290's actual 450-entry collective-kernel construction. It admits the conditional finite bound\n\n\u03ba = 745272866677869825771952 / 10^27 = 0.000745272866677869825771952.\n\nThat is 0.074977% above independently reproduced PR290 and 0.155127% above this PR's previous gen5 result. It also exceeds the newer advertised v", "automated_comparable": true, "body_sha256": "3e18a8d53c9d0acb6f0fcdd2308ce56aa14b498e796794c0d331cadca5cb4120" }, { "stream": "recovered_literal_highwater", "stream_row": 210, "source_index": null, "at": "2026-10-10T10:42:44Z", "until": null, "date_basis": "body-version", "fraction": "375528459906701/500000000000000000", "value_decimal": "0.001661634653669567075843432", "dashboard_float_text": null, "expression": "375528459906701 / 500000000000000000", "historical_title": "Conditional \u03ba = 0.000751056919813402: donor-weighted matching on gen5b kernels", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/275", "evidence_excerpt": "nd composes the resulting word with every PR299 kernel, restoration and terminal sink.\n\nConditional \u03ba = 375528459906701 / 500000000000000000 = 0.000751056919813402.\n\nThis is 0.154381% above independently reproduced PR299 (0.000749899215319498) and 0.776099% above this PR's previous published checkpoint. It also exceeds", "automated_comparable": true, "body_sha256": "b82194af082d2bff6d81656683a03c628e10bfe6c20144a29a80e4e825833aa0" }, { "stream": "recovered_literal_highwater", "stream_row": 211, "source_index": null, "at": "2026-10-10T11:31:42Z", "until": null, "date_basis": "body-version", "fraction": "46942230864663/62500000000000000", "value_decimal": "0.001661634653669567075843432", "dashboard_float_text": null, "expression": "46942230864663 / 62500000000000000", "historical_title": "Conditional \u03ba = 0.000751075693834608: weighted gen5b matching with second descent", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/275", "evidence_excerpt": "nd scalar descent, followed by freshly screened early restorations and terminal sinks.\n\nConditional \u03ba = 46942230864663 / 62500000000000000 = 0.000751075693834608.\n\nThis is 0.156885% above independently reproduced PR299 (0.000749899215319498), 0.154385% above PR300's advertised result (0.000749917931696438), and 0.002", "automated_comparable": true, "body_sha256": "ecdac6e6a53cbe808f7445629730ca68c8ca51535e48297924a1d497119093c9" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "frozen_kappa_metadata": { "kappa_fraction": "46942230864663/62500000000000000", "kappa_decimal": "0.000751075693834608", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews." }, "source_selected_kappa_correction": true, "source_selected_kappa_correction_basis": "Own actual merged-head799-application EXPECTED target, own manifest/verifier/UPSTREAM binding and actual merge second parent; old parser chose historical433fixture. Frozen metadata is preserved, not rewritten.", "source_kappa_correction_primary_receipt": "data/operation-audit/pr275-cap-source/chronology-primary-receipt.json", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": "New direct Gaussian realization of the exact799 core explicitly selected by the actual merged PR275 source. The source-selected kappa is visibly corrected while preserving the old parsed433 fixture, and dated at actual merge inclusion. Native/operator, whole-owner/all-size, precision and analytic contracts remain conditional; this is a sufficient gate, with no natural first-crossing claim.", "own_source_record_tail_quantified": true, "own_source_certificate": "pr275-supplied-cap-gaussian-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 12, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "individual-primary-interface-source/275-manifest.json", "sha256": "a69459b27db5d78dfa674c4145e094f694d3db580e3f53ca123734aee0f175aa" }, { "file": "remaining-record-audit/artifacts/275/priority-manifest.json", "sha256": "08166f8f184295e0e2f3609698e2a079d8504391e831faecb72f1a9c08ee0982" } ], "source_head": "524375c61b75dc10cef68a71d504e79e7e7f138c" } }, { "pr": 2979, "title": "Conditional \u03ba \u2248 0.0017290339826465: joint rank-7 end frames, five paired extractions and #2957's rewrites on #2942's words (+5.00e-6 over #2969)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2979", "author": "mdumitrean", "created_at": "2026-10-16T15:59:15Z", "accepted_at": "2026-10-16T16:02:20Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001729033982646513517716999999999999999999999900000000000", "kappa_fraction": "17290339826465135177169999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 215, "source_index": 336, "at": "2026-10-16T15:59:15Z", "until": "2026-10-16T17:54:20Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001729033982646513517717", "dashboard_float_text": "0.0017290339826465135", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2979", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 250, "source_index": null, "at": "2026-10-16T15:59:15Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001729033982646513517717", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2979", "evidence_excerpt": "**\u03ba = 0.001729033982646513517717 \u2212 10\u207b\u2074\u2076 \u2212 10\u207b\u2077\u2070**, exactly `4998757898408639167/10\u00b2\u2074` \u2248 **+4.9988e-6** over #2969 (Dugongue, `e2ca469b`; \u2248 +4.9997e-6 over #2966, +5.3166e-6 over #2957, +6.2177e-6 over #2942).", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 531, "source_index": null, "at": "2026-10-16T15:59:15Z", "until": null, "date_basis": "body-version", "fraction": "17290339826465135177169999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "value_decimal": "0.001729033982646513517717", "dashboard_float_text": null, "expression": "0.001729033982646513517717 - 10^-46 - 10^-70", "historical_title": "Conditional \u03ba \u2248 0.0017290339826465: joint rank-7 end frames, five paired extractions and #2957's rewrites on #2942's words (+5.00e-6 over #2969)", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2979", "evidence_excerpt": "s package changes them in three declared stages on #2942's words and admits the result completely:\n\n\u03ba = 0.001729033982646513517717 - 10^-46 - 10^-70, exactly 4998757898408639167/10^24 \u2248 +4.9988e-6 over #2969 (Dugongue, e2ca469b; \u2248 +4.9997e-6 over #2966, +5.3166e-6 over #2957, +6.2177e-6 over #2942).\n\n## What changes\n\n1. Joint ", "automated_comparable": true, "body_sha256": "51ab40456a5dbf7f43c319b515f2ffa758f51c52006dafcc3aa607afda7694b2" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "23/10000", "status": "Maintainer-reviewed conditional productive-helper construction; see integration receipt for publication state", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier4359.json", "path": "certificates/checkpoints/frontier4359.json", "commit": null, "at": null, "scope": "Productive-helper p3 construction under retained analytic decomposition, exact recovery, native ordered movement, fixed-tape execution, fine-prime padding and gauge-free outer estimates. Changed interfaces reviewed with AI assistance; no formal or independent human verification of the full theorem. Winning uniform templates are algorithm-defined, not materialized. Frozen claim publication booleans describe submission time. Unrelated H-branch research is not selected." }, { "stream": "all_selected_result_history", "record_kappa": "60403/20000000", "status": "Selected maintainer-reviewed conditional joint-helper construction; source-bound foundation reuse is explicit", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/4f19cedcd8d81e4a2359449309fa6e9f17dfd22e/certificates/selected-result.json", "path": null, "commit": "4f19cedcd8d81e4a2359449309fa6e9f17dfd22e", "at": "2026-10-22T12:16:48Z", "scope": "Maintainer-reviewed conditional PR4470 construction. Inherited native/all-column, owned-erasure, whole-job, compiler, precision/tape, analytic, prime and recovery hypotheses remain. Uniform words are not materialized." }, { "stream": "all_selected_result_history", "record_kappa": "23/10000", "status": "Maintainer-reviewed conditional productive-helper construction; see integration receipt for publication state", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/ae87507c0767c00f5a55ee9062c496191e978632/certificates/selected-result.json", "path": null, "commit": "ae87507c0767c00f5a55ee9062c496191e978632", "at": "2026-10-21T19:10:46Z", "scope": "Productive-helper p3 construction under retained analytic decomposition, exact recovery, native ordered movement, fixed-tape execution, fine-prime padding and gauge-free outer estimates. Changed interfaces reviewed with AI assistance; no formal or independent human verification of the full theorem. Winning uniform templates are algorithm-defined, not materialized. Frozen claim publication booleans describe submission time. Unrelated H-branch research is not selected." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 9, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/rank7-joint-endframes/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/rank7-joint-endframes/CLAIM.json, research/rank7-joint-endframes/MANIFEST.json, research/rank7-joint-endframes/README.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/rank7-joint-endframes/CLAIM.json, research/rank7-joint-endframes/MANIFEST.json, research/rank7-joint-endframes/README.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/rank7-joint-endframes/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/2979-manifest.json", "sha256": "39c44fd295a9232266c43c745befa2ddbf4d2b96aefa4610e234b026af154c23" }, { "file": "remaining-record-audit/artifacts/2979/priority-manifest.json", "sha256": "87c5c4ec75ecb813ff2bac45a27b5b125f1474206b2b40e7d1f07dd9d43442be" } ], "source_head": "be191346391661f4d35fc0d1508d0a6029572576" } }, { "pr": 3042, "title": "Conditional \u03ba = 0.001729736166387916: six restore carrier/pivot skips (R1_E42, R2_E7) on PR2979's words and literal allocation", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3042", "author": "dcharb78", "created_at": "2026-10-16T20:15:55Z", "accepted_at": "2026-10-16T23:51:01Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001729736166387915986811999999999999999999999900000000000", "kappa_fraction": "17297361663879159868119999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "recovered_literal_highwater", "stream_row": 533, "source_index": null, "at": "2026-10-16T20:15:55Z", "until": null, "date_basis": "body-version", "fraction": "17297361663879159868119999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "value_decimal": "0.001729736166387916", "dashboard_float_text": null, "expression": "0.001729736166387915986812 - 10^-46 - 10^-70", "historical_title": "Conditional \u03ba = 0.001729736166387916: six restore carrier/pivot skips (R1_E42, R2_E7) on PR2979's words and literal allocation", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3042", "evidence_excerpt": "## Summary\n\nConditional \u03ba = 0.001729736166387915986812 - 10^-46 - 10^-70 (17297361663879159868119999999999999999999998999999999999999999999999 / 10^70 in research/rank7-restore-carrier-skips/CLAIM.json), +7.0218e-7 above PR #2979 (main, be191346), +5.8", "automated_comparable": true, "body_sha256": "01226946ed3d7dbce164e04515bd3103a274accaf06e96b58964d86f25199f17" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/rank7-restore-carrier-skips/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/rank7-restore-carrier-skips/CLAIM.json, research/rank7-restore-carrier-skips/MANIFEST.json, research/rank7-restore-carrier-skips/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/rank7-restore-carrier-skips/CLAIM.json, research/rank7-restore-carrier-skips/MANIFEST.json, research/rank7-restore-carrier-skips/SOURCES.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/rank7-restore-carrier-skips/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3042-manifest.json", "sha256": "40d82b75e39a7b229e0fa8646bff099e570550878270188b390fb5d795b48ff2" }, { "file": "remaining-record-audit/artifacts/3042/priority-manifest.json", "sha256": "840326e4185ed7b9af8696fb4b654f1b424e2b17737f316d9ad95eadfeee6f01" } ], "source_head": "84cc406ad91ec53fff329a11a445d7effe564a77" } }, { "pr": 3051, "title": "Verify six-skip/T740 release: conditional kappa 0.001729737950064279", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3051", "author": "jeremydiviney", "created_at": "2026-10-16T20:52:32Z", "accepted_at": "2026-10-16T23:51:01Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001729737950064278551241999999999999999999999900000000000", "kappa_fraction": "17297379500642785512419999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 217, "source_index": 338, "at": "2026-10-16T20:52:32Z", "until": "2026-10-16T21:17:04.798911Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001729737950064278551242", "dashboard_float_text": "0.0017297379500642786", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3051", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 252, "source_index": null, "at": "2026-10-16T20:52:32Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001729737950064278551242", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3051", "evidence_excerpt": "The resulting **conditional** value is `\u03ba = 0.001729737950064278551242 \u2212 10^-46 \u2212 10^-70`, an exact gain of `178367636256443 / 10^23` (about `1.78e-9`) over pinned PR3042. This is a small integration gain from existing constructions. Credit dcharb78 for the six-skip words, Nick Petalas for the allocation and cap, and Marius-Paul Dumitrean for the joint rank-seven predecessor. Full lineage and substantial OpenAI Codex assistance are disclosed in the package.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 534, "source_index": null, "at": "2026-10-16T20:52:32Z", "until": null, "date_basis": "body-version", "fraction": "17297379500642785512419999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "value_decimal": "0.001729737950064278551242", "dashboard_float_text": null, "expression": "0.001729737950064278551242 - 10^-46 - 10^-70", "historical_title": "Verify six-skip/T740 release: conditional kappa 0.001729737950064279", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3051", "evidence_excerpt": "the complete source/native/owner/physical/prefix/outer release.\n\nThe resulting conditional value is \u03ba = 0.001729737950064278551242 - 10^-46 - 10^-70, an exact gain of 178367636256443 / 10^23 (about 1.78e-9) over pinned PR3042. This is a small integration gain from existing constructions. Credit dcharb78 for the six-skip words,", "automated_comparable": true, "body_sha256": "964689bc243951f8e2d6cd590cafbcd631ffe6fbd9e244f79bc3f8dbf2c4f976" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 12, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/rank7-six-skip-cap-release/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/rank7-six-skip-cap-release/CLAIM.json, research/rank7-six-skip-cap-release/MANIFEST.json, research/rank7-six-skip-cap-release/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/rank7-six-skip-cap-release/CLAIM.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/rank7-six-skip-cap-release/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3051-manifest.json", "sha256": "9119a0b2409a393746b93310521a9f076bcaad47ce6724751dcd57b43cc83af9" }, { "file": "remaining-record-audit/artifacts/3051/priority-manifest.json", "sha256": "46a8e04928f05d269d3f33ddbd51d2753e3c8c63628964d8fdcd666c55ea3991" } ], "source_head": "10a45bd361554709840becb5bc26016ca49944c3" } }, { "pr": 3054, "title": "feat(research): release the T740 six-skip composition", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3054", "author": "petalas", "created_at": "2026-10-16T20:54:47Z", "accepted_at": "2026-10-16T23:51:01Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001729737950064278551241999999999999999999999900000000000", "kappa_fraction": "17297379500642785512419999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 12, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/rank7-t740-carrier-skips/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/rank7-t740-carrier-skips/README.md, research/rank7-t740-carrier-skips/evidence/DISCOVERY-INVOICE.json.gz, research/rank7-t740-carrier-skips/evidence/INVOICE-PAYLOAD.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/3054-manifest.json", "sha256": "5c2fc7d4b18b73cc0de2865b501e46efdfd82c56e80c31c94bc1beec35332efe" }, { "file": "remaining-record-audit/artifacts/3054/priority-manifest.json", "sha256": "b7eadd080c4166675e34795ff9ea12b58af8ff740cc94bdfcb5846eb9a71607a" } ], "source_head": "4773c3ea67b471415870e38411fae313ec44a675" } }, { "pr": 3082, "title": "Research: exact screen for kappa > 0.1 on selected suppliers", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3082", "author": "Gonzalo-Mier", "created_at": "2026-10-16T22:27:19Z", "accepted_at": "2026-10-16T23:51:01Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.1", "kappa_fraction": "1/10", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/3082-manifest.json", "sha256": "e06d71a61dc0344c7cade70748d83ac50ed4437939ed18991311157bf3461fdd" }, { "file": "remaining-record-audit/artifacts/3082/priority-manifest.json", "sha256": "7c4062e90d1f8d9d55844c39f056c8a692d8b0c99dfc47805323c467fe048fd4" } ], "source_head": "c9c6b59ce5f526a0082d06b24470b7ac946e62da" } }, { "pr": 3015, "title": "Conditional \u03ba = 0.001729150973534224: one declared restore edit (R1) on PR2979's words and literal allocation", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3015", "author": "jeremykothe2", "created_at": "2026-10-16T17:54:20Z", "accepted_at": "2026-10-16T23:51:02Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0017291509735342244286949999999999999999", "kappa_fraction": "17291509735342244286949999999999999999/10000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 216, "source_index": 337, "at": "2026-10-16T17:54:20Z", "until": "2026-10-16T20:52:32Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001729150973534224428694999999999999999999999899999999999999", "dashboard_float_text": "0.0017291509735342244", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3015", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 251, "source_index": null, "at": "2026-10-16T17:54:20Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001729150973534224428694999999999999999999999899999999999999", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3015", "evidence_excerpt": "Conditional \u03ba = **0.001729150973534224428694999999999999999999999899999999999999\u2026** (70 decimals; the exact value is `kappa` in `research/rank7-joint-endframes-restore-edit/outer/OUTER-CLAIM.json`, SHA-256 of the decimal string `f0cbe97dd438d62a9615e6ca9708cfaf4cee432072e2c1f7e7e99438eeb49a7a`). This package takes PR2979's (mdumitrean, Marius-Paul Dumitrean) words (joint rank-7 end frames, five further paired extractions, PR2957's fourteen rewrites on PR2942) and its literal T74 allocation as it", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 532, "source_index": null, "at": "2026-10-16T17:54:20Z", "until": null, "date_basis": "body-version", "fraction": "17291509735342244286949999999999999999/10000000000000000000000000000000000000000", "value_decimal": "0.001729150973534224428694999999999999999999999899999999999999", "dashboard_float_text": null, "expression": "0.0017291509735342244286949999999999999999", "historical_title": "Conditional \u03ba = 0.001729150973534224: one declared restore edit (R1) on PR2979's words and literal allocation", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3015", "evidence_excerpt": "chains for both changed words, complete replica admission and the modern outer release. Conditional kappa 0.0017291509735342244286949999999999999999\u2026(70 digits).\n\nFull package-owned verification passed in 1571.14 seconds. The fresh receipt binds the exact package manifest and score.\n\nSee research/rank7-joint-endframes-restore-", "automated_comparable": true, "body_sha256": "f8385af3c4db074cc6d3fef47768a1389156580d46b931cb584e50896a780b73" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/rank7-joint-endframes-restore-edit/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/rank7-joint-endframes-restore-edit/CLAIM.json, research/rank7-joint-endframes-restore-edit/README.md, research/rank7-joint-endframes-restore-edit/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/rank7-joint-endframes-restore-edit/CLAIM.json, research/rank7-joint-endframes-restore-edit/README.md, research/rank7-joint-endframes-restore-edit/SOURCES.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/rank7-joint-endframes-restore-edit/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3015-manifest.json", "sha256": "7edf0cc723fa9c07c2f265ddabab81e2b05c230ae75844a9c9924ab7c2756209" }, { "file": "remaining-record-audit/artifacts/3015/priority-manifest.json", "sha256": "8b8c33529b8041ab1aeb0260cb0c46727600d1622c36ff8eb9644eef7e3e9a7c" } ], "source_head": "e244296debb45fe6f4da84d29e4d64fbab55fda0" } }, { "pr": 3028, "title": "feat(research): release the T148 restore composition", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3028", "author": "petalas", "created_at": "2026-10-16T19:08:05Z", "accepted_at": "2026-10-16T23:51:02Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001729151203983018442997999999999999999999999900000000000", "kappa_fraction": "17291512039830184429979999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/rank7-t148-restore-release/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/rank7-t148-restore-release/README.md, research/rank7-t148-restore-release/SOURCES.json, research/rank7-t148-restore-release/evidence/NATIVE-RECEIPT.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/rank7-t148-restore-release/README.md, research/rank7-t148-restore-release/SOURCES.json, research/rank7-t148-restore-release/evidence/NATIVE-RECEIPT.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/rank7-t148-restore-release/evidence/RESULT.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3028-manifest.json", "sha256": "5f8649c81b097d5142d1395fc1b50bc42e81f00551333fb3c45cc31afb63a458" }, { "file": "remaining-record-audit/artifacts/3028/priority-manifest.json", "sha256": "9b55c8c96984466acc9e62580e8e1bce777c575a651b1e60912a5382523fb9e9" } ], "source_head": "9d10633660a3dff5469f4e7a0a009a6c9994c0d7" } }, { "pr": 3030, "title": "feat(research): release the T740 R1 cap composition", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3030", "author": "petalas", "created_at": "2026-10-16T19:18:19Z", "accepted_at": "2026-10-16T23:51:02Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001729152756004330934534999999999999999999999900000000000", "kappa_fraction": "17291527560043309345349999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 12, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/rank7-t740-release/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/rank7-t740-release/SOURCES.json, research/rank7-t740-release/evidence/DISCOVERY-INVOICE.json.gz, research/rank7-t740-release/evidence/INVOICE-PAYLOAD.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/rank7-t740-release/SOURCES.json, research/rank7-t740-release/evidence/DISCOVERY-INVOICE.json.gz, research/rank7-t740-release/evidence/INVOICE-PAYLOAD.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/rank7-t740-release/TASK.json#/predecessors/2 after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3030-manifest.json", "sha256": "b22f12dec9baae30143999c7c55799500760045ecca2cf86a56d1bd38d09a1a9" }, { "file": "remaining-record-audit/artifacts/3030/priority-manifest.json", "sha256": "161ba7825bcd4acf2993dc1239f6090fa0d23c8138bb86ce044e459bfa69a38a" } ], "source_head": "78e77d820393c6b8648b47af219e991edfcc54e6" } }, { "pr": 3064, "title": "Propose conditional \u03ba \u2248 0.001729737530919310 via T148 carrier skips (full replay pending)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3064", "author": "dataisfire", "created_at": "2026-10-16T21:35:14Z", "accepted_at": "2026-10-17T02:02:19Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001729737530919309734203999999999999999999999900000000000", "kappa_fraction": "17297375309193097342039999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t148-carrier-skips/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/rank7-t148-restore-release/evidence/RESULT.json, research/rank7-t740-release/evidence/INVOICE-PAYLOAD.json, research/rank7-t740-release/evidence/NATIVE-RECEIPT.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/rank7-t148-restore-release/evidence/RESULT.json, research/rank7-t740-release/evidence/INVOICE-PAYLOAD.json, research/rank7-t740-release/evidence/NATIVE-RECEIPT.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/rank7-t148-restore-release/evidence/RESULT.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3064-manifest.json", "sha256": "e6d3b999159eac9b9e0d5e7314a58ba8b28523edc59978e307ecce878be0af0a" }, { "file": "remaining-record-audit/artifacts/3064/priority-manifest.json", "sha256": "17924a961c3aabe89cdbc473b89502a689cc7693baef3101faab029aedf6dd62" } ], "source_head": "239447f19b9365194bca2583014c947db5de8ea4" } }, { "pr": 3093, "title": "Research: audit #2979 profile against kappa=0.1", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3093", "author": "Gonzalo-Mier", "created_at": "2026-10-16T23:47:17Z", "accepted_at": "2026-10-17T02:02:19Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.1", "kappa_fraction": "1/10", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain exact local evidence and stated restrictions with the named target. A whole-input crossover needs its own source-selected complete native/owner/recursive/precision/outer invoice and all-size realization." ], "source_manifest": [ { "file": "individual-primary-interface-source/3093-manifest.json", "sha256": "c6ac17673860cc7ab511dd99f01788b36e85fb8abb5059f3d350e80ff77e8dc9" }, { "file": "remaining-record-audit/artifacts/3093/priority-manifest.json", "sha256": "3ea48a0b699c28be6995bf362be661717789b4506b5625c3b30e9224f730fda1" } ], "source_head": "d7b545b12da3fc9751c2ea36f5efbf26e12dfcaf" } }, { "pr": 3097, "title": "Research: rule out seven-owner centre information compression", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3097", "author": "Gonzalo-Mier", "created_at": "2026-10-17T00:15:02Z", "accepted_at": "2026-10-17T02:02:19Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.1", "kappa_fraction": "1/10", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain exact local evidence and stated restrictions with the named target. A whole-input crossover needs its own source-selected complete native/owner/recursive/precision/outer invoice and all-size realization." ], "source_manifest": [ { "file": "individual-primary-interface-source/3097-manifest.json", "sha256": "1f132334b1e39c0abd0c9e6f859d9157bea891915aa25df4720a009c74f515c0" }, { "file": "remaining-record-audit/artifacts/3097/priority-manifest.json", "sha256": "29fac186e5125c9ed9435eb5dcca3f0307148b72a5727370ba98ace20efa40b3" } ], "source_head": "ef7a52f4b0acf7cc8c51f9d81274d106abeffa24" } }, { "pr": 3107, "title": "Kappa 0.1 budget screens and conditional paired-plane sensitivity", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3107", "author": "Gonzalo-Mier", "created_at": "2026-10-17T01:22:00Z", "accepted_at": "2026-10-17T02:03:23Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.1", "kappa_fraction": "1/10", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/3107/priority-manifest.json", "sha256": "908a8683a61826b2a25b48ad26c8d1db885fc5a046f443ebedecced2c26bc430" } ], "source_head": "7d40236bf22109ad64ae95a1d25eff7fa40478b5" } }, { "pr": 3116, "title": "Research: source-bound weighted diagonal rank-batching screen", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3116", "author": "Gonzalo-Mier", "created_at": "2026-10-17T02:57:16Z", "accepted_at": "2026-10-17T16:50:24Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.1", "kappa_fraction": "1/10", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain exact local evidence and stated restrictions with the named target. A whole-input crossover needs its own source-selected complete native/owner/recursive/precision/outer invoice and all-size realization." ], "source_manifest": [ { "file": "individual-primary-interface-source/3116-manifest.json", "sha256": "0f1e84d9839424ad294348a717d1b281908042d3b764ae861204308f83b7a01f" }, { "file": "remaining-record-audit/artifacts/3116/priority-manifest.json", "sha256": "328a4ccb1eca09b81eb89ede81a1d622cb6b7c81d2c900ea8773a521fde3fdd5" } ], "source_head": "2ebdcfebd6d3da023dc45ddf68729f0771ccb77c" } }, { "pr": 3133, "title": "research(rank7-coupled-586-588-carrier-fold): lower helpers 586 & 588 via coupled B+restore carrier folds (\u03ba = 0.0017297760894)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3133", "author": "dcharb78", "created_at": "2026-10-17T06:55:07Z", "accepted_at": "2026-10-17T16:50:24Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001729776089405120334237999999999999999999999900000000000", "kappa_fraction": "17297760894051203342379999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 218, "source_index": 342, "at": "2026-10-17T06:55:07Z", "until": "2026-10-17T07:15:09Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001729776089405120334238", "dashboard_float_text": "0.0017297760894051204", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3133", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 254, "source_index": null, "at": "2026-10-17T06:55:07Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001729776089405120334238", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3133", "evidence_excerpt": "# Conditional \u03ba = 0.001729776089405120334238 \u2212 10\u207b\u2074\u2076 \u2212 10\u207b\u2077\u2070: Coupled `B + restore` Dying-Helper Carrier Folds Lowering Helpers `586` & `588` to Rank 7 (`width 6`) with Literal $T=74$ Allocation (`T74_optimal_idle39`)", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 536, "source_index": null, "at": "2026-10-17T06:55:07Z", "until": null, "date_basis": "body-version", "fraction": "17297760894051203342379999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "value_decimal": "0.001729776089405120334238", "dashboard_float_text": null, "expression": "0.001729776089405120334238 - 10^-46 - 10^-70", "historical_title": "research(rank7-coupled-586-588-carrier-fold): lower helpers 586 & 588 via coupled B+restore carrier folds (\u03ba = 0.0017297760894)", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3133", "evidence_excerpt": "# Conditional \u03ba = 0.001729776089405120334238 - 10^-46 - 10^-70: Coupled B + restore Dying-Helper Carrier Folds Lowering Helpers 586 & 588 to Rank 7 (width 6) with Literal T=74 Allocation (T74_optimal_idle39)\n\nSelected Frontier, Archival Base ", "automated_comparable": true, "body_sha256": "bc0b15213235bb7716d8b278ec63a7037964bfe8b0c6ed6228ffb7a4c7b5e9a2" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/rank7-coupled-586-588-carrier-fold/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/rank7-coupled-586-588-carrier-fold/CLAIM.json, research/rank7-coupled-586-588-carrier-fold/MANIFEST.json, research/rank7-coupled-586-588-carrier-fold/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/rank7-coupled-586-588-carrier-fold/CLAIM.json, research/rank7-coupled-586-588-carrier-fold/MANIFEST.json, research/rank7-coupled-586-588-carrier-fold/SOURCES.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/rank7-coupled-586-588-carrier-fold/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3133-manifest.json", "sha256": "c64cc05e4e84b97279f64df180650074c657360f2d59f8c15738f0affc87d325" }, { "file": "remaining-record-audit/artifacts/3133/priority-manifest.json", "sha256": "8e4f16097e22ce90d6e2045140baf92b1e07c58d1ec2c87d7d51ad3832fc0ed6" } ], "source_head": "51eb9c4ee9e4722010d308aa3309e039d3940cc2" } }, { "pr": 3135, "title": "research: release T740 precision35 kappa refinement", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3135", "author": "Gonzalo-Mier", "created_at": "2026-10-17T07:15:09Z", "accepted_at": "2026-10-17T16:50:24Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001729776089405120334237999999999999999999999900000000000", "kappa_fraction": "17297760894051203342379999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t740-six-skip-precision35/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/t740-six-skip-precision35/PROOF.md, research/t740-six-skip-precision35/README.md, research/t740-six-skip-precision35/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/t740-six-skip-precision35/PROOF.md, research/t740-six-skip-precision35/README.md, research/t740-six-skip-precision35/SOURCES.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/3135-manifest.json", "sha256": "c612b36a4304cfb66ee3ae89962316641e89242b8c77f93bf9f00dd8c23b814d" }, { "file": "remaining-record-audit/artifacts/3135/priority-manifest.json", "sha256": "174c1e4f49f046b5b429a709dfaed98554c04318fc3752097f164ae95977e076" } ], "source_head": "776ae75d640e6a5672e8ea798677a2cd3ae2d53c" } }, { "pr": 3148, "title": "Realize the coupled-carrier T740 packing cap: \u03ba \u2248 0.001729777494678597", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3148", "author": "jeremydiviney", "created_at": "2026-10-17T09:29:24Z", "accepted_at": "2026-10-17T16:50:24Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001729777494678597011885999999999999999999999900000000000", "kappa_fraction": "17297774946785970118859999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 219, "source_index": 344, "at": "2026-10-17T09:29:24Z", "until": "2026-10-17T10:39:16Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001729777494678597011886", "dashboard_float_text": "0.001729777494678597", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3148", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 255, "source_index": null, "at": "2026-10-17T09:29:24Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001729777494678597011886", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3148", "evidence_excerpt": "**\u03ba = 0.001729777494678597011886 \u2212 10\u207b\u2074\u2076 \u2212 10\u207b\u2077\u2070**, about **1.4052734766776475 \u00d7 10\u207b\u2079 above PR3143's precision-40 T74 claim**.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 537, "source_index": null, "at": "2026-10-17T09:29:24Z", "until": null, "date_basis": "body-version", "fraction": "17297774946785970118859999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "value_decimal": "0.001729777494678597011886", "dashboard_float_text": null, "expression": "0.001729777494678597011886 - 10^-46 - 10^-70", "historical_title": "Realize the coupled-carrier T740 packing cap: \u03ba \u2248 0.001729777494678597", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3148", "evidence_excerpt": "tion exchange for PR3133's changed helper inventory, attaining its fixed-word packing cap at T740:\n\n\u03ba = 0.001729777494678597011886 - 10^-46 - 10^-70, about 1.4052734766776475 * 10^-9 above PR3143's precision-40 T74 claim.\n\nTen interleaved copies of the literal T74 fill contain twenty 48:[4,8,9,9,9,9] and ten 48:[9] non-tight b", "automated_comparable": true, "body_sha256": "37d0b9dff0bfbd600b2942eea636ca6665fe2fb22561ea5297468eec51d6983d" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 12, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/coupled-carrier-cap740/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/coupled-carrier-cap740/CLAIM.json, research/coupled-carrier-cap740/MANIFEST.json, research/coupled-carrier-cap740/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/coupled-carrier-cap740/CLAIM.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/coupled-carrier-cap740/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3148-manifest.json", "sha256": "552100b824caec1e13f78d6483b83834a99b085cad96c14e606e08169b9efec2" }, { "file": "remaining-record-audit/artifacts/3148/priority-manifest.json", "sha256": "bc3383887b45a5f8d9647dbc8c5549a143b4aa66a21265abb911adad7feebb7d" } ], "source_head": "f2927a4b8afcf0701a6b945e14f30de1d94f5176" } }, { "pr": 3157, "title": "Conditional \u03ba \u2248 0.0017291527560043: R1 words at their packing cap (T740), +1.55e-9 over #3021", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3157", "author": "rohanarun", "created_at": "2026-10-17T10:39:16Z", "accepted_at": "2026-10-17T16:50:24Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0017291527560043", "kappa_fraction": "17291527560043/10000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/rank7-r1-t740-cap/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/rank7-r1-t740-cap/CLAIM.json, research/rank7-r1-t740-cap/README.md, research/rank7-r1-t740-cap/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/rank7-r1-t740-cap/CLAIM.json, research/rank7-r1-t740-cap/README.md, research/rank7-r1-t740-cap/SOURCES.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/rank7-r1-t740-cap/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3157-manifest.json", "sha256": "1bd9a83247ca07d208f09d289496524cd83b382ba485b920db528f2d718aa910" }, { "file": "remaining-record-audit/artifacts/3157/priority-manifest.json", "sha256": "07b497af3e96ed2a8fa99d720e157ccc4f84bc92938d7934b8f3a9dd962eba61" } ], "source_head": "313ede7cfd0002b3884e235730a564e8ec7c2e05" } }, { "pr": 3111, "title": "Selected bit profile alone exceeds the \u03ba=0.1 moment budget", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3111", "author": "Gonzalo-Mier", "created_at": "2026-10-17T02:08:15Z", "accepted_at": "2026-10-17T16:50:25Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.1", "kappa_fraction": "1/10", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/3111-manifest.json", "sha256": "702d1093a6dfa246d4f09be9be30ce43e2492b9e01105f279f7d2b27f4bd0d86" }, { "file": "remaining-record-audit/artifacts/3111/priority-manifest.json", "sha256": "0b1e52c90d8814082cde9c6af77b9aa11deb46f3109d8c020f6f458bb1643cd7" } ], "source_head": "fcba8eab38c51f4cdb685559be505222d44f8ddc" } }, { "pr": 3115, "title": "research: \u03ba = 0.001729737950064278551242895823 \u2212 10^-52 \u2212 10^-76", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3115", "author": "dataisfire", "created_at": "2026-10-17T02:46:38Z", "accepted_at": "2026-10-17T16:50:25Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001729737950064278551242895822999999999999999999999900000", "kappa_fraction": "17297379500642785512428958229999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 253, "source_index": null, "at": "2026-10-17T02:46:38Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001729737950064278551242895822999999999999999999999900000000000000000000000099", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3115", "evidence_excerpt": "research: \u03ba = 0.001729737950064278551242895823 \u2212 10^-52 \u2212 10^-76", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 535, "source_index": null, "at": "2026-10-17T02:46:38Z", "until": null, "date_basis": "body-version", "fraction": "17297379500642785512428958229999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000000000", "value_decimal": "0.001729737950064278551242895822999999999999999999999900000000000000000000000099", "dashboard_float_text": null, "expression": "0.001729737950064278551242895823 - 10^-52 - 10^-76", "historical_title": "research: \u03ba = 0.001729737950064278551242895823 \u2212 10^-52 \u2212 10^-76", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3115", "evidence_excerpt": "This releases the conditional point \u03ba = 0.001729737950064278551242895823 - 10^-52 - 10^-76, strictly above the full, unrounded PR #3054 point by approximately 8.95823e-25. This is a tiny arithmetic rounding refinement of the same T740 six-skip construction. The paid pro", "automated_comparable": true, "body_sha256": "2b0ebd4714aef31d86f63d078f686a6ce8144e66bdb8947ce1f053f4ab4b0b51" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t740-six-skip-precision30/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/t740-six-skip-precision30/PROOF.md, research/t740-six-skip-precision30/README.md, research/t740-six-skip-precision30/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/t740-six-skip-precision30/PROOF.md, research/t740-six-skip-precision30/README.md, research/t740-six-skip-precision30/SOURCES.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/3115-manifest.json", "sha256": "e36eff1f8c380326955d75d32df8e6462f7272c3d2428541dfa3bfa75f494d4a" }, { "file": "remaining-record-audit/artifacts/3115/priority-manifest.json", "sha256": "07ece5910f9c714a25c4cc35acc2ae28d7fef649ebb52d36b24f3909525bcc5b" } ], "source_head": "400bc83669f86917f69b6249cd0356d3a913293c" } }, { "pr": 3123, "title": "Correct the \u03ba=0.1 complex cost screen and bound scalar-query repairs", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3123", "author": "1337isnot1337", "created_at": "2026-10-17T03:44:10Z", "accepted_at": "2026-10-17T16:50:25Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.1", "kappa_fraction": "1/10", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/3123/priority-manifest.json", "sha256": "097bfe6dc17bb3d6dfc14fb213fc4c905851743aeee7f7fcefebd11394803fc5" } ], "source_head": "195dcb14fb2e2b4de72d8e573ab6cbe120c844ba" } }, { "pr": 3328, "title": "Research: isolate orthogonal remainder overlays (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3328", "author": "1337isnot1337", "created_at": "2026-10-17T21:48:51Z", "accepted_at": "2026-10-17T21:58:37Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/3328-manifest.json", "sha256": "9a70a48f9f2be94211215779fcc99920113a7c37a8fa400ec28b5436c8b82f6f" }, { "file": "remaining-record-audit/artifacts/3328/priority-manifest.json", "sha256": "19a880d8fbafa44fa41c7ab6017d680a896561c4814f775aa5527b1ce2501931" } ], "source_head": "e3ef128540fcce9a325359e55b35ccc3d1587ea9" } }, { "pr": 3308, "title": "Verified T16 packing gain with OR-Tools: conditional \u03ba = 0.001673618490895016", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3308", "author": "Gonzalo-Mier", "created_at": "2026-10-17T21:26:40Z", "accepted_at": "2026-10-17T21:58:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001673618490895016", "kappa_fraction": "209202311361877/125000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr3308-gaussian-only-finite-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own authenticated rank73/v112/h9 complete native provider program/orientation bytes, full required entry/output-frame/absolute-phase/all-column/owned/whole-helper and bounded monomial grammar.", "Own complete numeric physical owner/invoice/profile, positive outward-enclosed moment, halving73\u00b2>2rmax\u00b2, G<2^30000/E_literal<2^100000/C0<=2^210000, row<20161 and corrected full stopped stock.", "Concrete normalized shifted Gaussian accretivity and finite-LDU/narrow row-gap/cyclic-border analytic interfaces; not a false general scale-free accretive claim.", "Same repaired reference correctness and finite-kernel halting.", "The exact own selected source core is realized by this new direct Gaussian/Fermat circuit; original optional BIT admission is neither assumed nor executed. Missing canonical catalogue is explicit; scalar specialization does not prove the operator endpoint." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr3308-gaussian-only-finite-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 4, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/3308/priority-manifest.json", "sha256": "cb78044e83735d34cd09a7f715338782cf6e9ce35b82efd32388a4f86f47416c" } ], "source_head": "8bc0555b484bf4aec4b91c680763d930d6754974" } }, { "pr": 3321, "title": "Research: one all-five toggle has no favorable price (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3321", "author": "1337isnot1337", "created_at": "2026-10-17T21:42:59Z", "accepted_at": "2026-10-17T21:58:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/3321-manifest.json", "sha256": "e69448bb59c05c9ed097ecb5dfa2597a439797d574b62f152d96b1a9c94bc23e" }, { "file": "remaining-record-audit/artifacts/3321/priority-manifest.json", "sha256": "f8276b5c517151712e7b77bbba68e8c00ad8beee49e861c5c096833922f79616" } ], "source_head": "5c1958c1bb01de8c192d19d7b7ac23d445386e02" } }, { "pr": 3337, "title": "Research: refine selected1094 conditional kappa on a 24-digit grid", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3337", "author": "petalas", "created_at": "2026-10-17T22:15:14Z", "accepted_at": "2026-10-18T04:49:35Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918658752", "kappa_fraction": "26135315579326854043/15625000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/selected1094-release-grid/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 2 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/selected1094-release-grid/CERTIFICATE.json, research/selected1094-release-grid/README.md, research/selected1094-release-grid/SOURCES.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/selected1094-release-grid/CERTIFICATE.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3337-manifest.json", "sha256": "869bd0d17f6a28ab75c13ecaca425d8180f6ba6512ea64e817a5a687030bebfc" }, { "file": "remaining-record-audit/artifacts/3337/priority-manifest.json", "sha256": "bb96bb38a6686d3627a524294ee57f84f0d543f84f5b9505cb3d4b4ff6db1f2f" } ], "source_head": "7ed071d5ba741ffd05f1b68c6fd7f8dcc6a12ad7" } }, { "pr": 3338, "title": "Conditional \u03ba = 0.001673619538656538 from a verified two-role T16 swap", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3338", "author": "petalas", "created_at": "2026-10-17T22:16:36Z", "accepted_at": "2026-10-18T04:49:35Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001673619538656538", "kappa_fraction": "836809769328269/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr3338-dispatched-finite-controller-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr3338-dispatched-finite-controller-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/3338/priority-manifest.json", "sha256": "eca0d61af2c215d9485bba022017845f02999969d40ca1643f8f0d4487a6f7bf" } ], "source_head": "f2e33dd2c07caf5dac2ee42505852a081d8fa7ca" } }, { "pr": 3342, "title": "Research: bound PR2979 selected-contract admission allowance", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3342", "author": "petalas", "created_at": "2026-10-17T22:28:06Z", "accepted_at": "2026-10-18T04:49:35Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001697", "kappa_fraction": "1697/1000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 9, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain exact local evidence and stated restrictions with the named target. A whole-input crossover needs its own source-selected complete native/owner/recursive/precision/outer invoice and all-size realization." ], "source_manifest": [ { "file": "individual-primary-interface-source/3342-manifest.json", "sha256": "47ffe111d503c45274d481ecccff6833ca32c5585c10c1ed1af7385bdc92445b" }, { "file": "remaining-record-audit/artifacts/3342/priority-manifest.json", "sha256": "6328584f117e4950199dedc623dfe1df9d099eb2b6ee7a68d41041328c920445" } ], "source_head": "7c069c6898ff4f3c2c1820086f2cb60f37538ca3" } }, { "pr": 3344, "title": "Research: complex copy budgets for 3-6 unpaid coordinates with large local children (planning screen; no \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3344", "author": "Matarener", "created_at": "2026-10-17T22:39:14Z", "accepted_at": "2026-10-18T04:49:35Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.1", "kappa_fraction": "1/10", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/3344-manifest.json", "sha256": "f242a5dee59ac7e4fc22044d6e258abb98c5bae52b52712d463ec5c0701fcbe0" }, { "file": "remaining-record-audit/artifacts/3344/priority-manifest.json", "sha256": "19ea9f86b3c929caa3d1a584b6be5e70e3d9b8b9f6a22143c262535ec7a82187" } ], "source_head": "c574f2e48d21679cd9994894a5e44d84bbbd2c91" } }, { "pr": 3354, "title": "Research: conditional \u03ba = 0.001673620586419375 via a three-helper T16 cycle", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3354", "author": "petalas", "created_at": "2026-10-17T22:50:16Z", "accepted_at": "2026-10-18T04:49:35Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001673620586419375", "kappa_fraction": "2677792938271/1600000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t16-three-helper-cycle/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 2 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Recompute the complete own productive/paid histogram from research/t16-three-helper-cycle/RESULT.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/t16-three-helper-cycle/RESULT.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3354-manifest.json", "sha256": "ed15878ce54c6db1bf91cbb48ed98e9027c0c411dcb69962d27179c88a1c4268" }, { "file": "remaining-record-audit/artifacts/3354/priority-manifest.json", "sha256": "2b348b59a0c95b20dfa25a6f8f52b9ba4d1fadbb5748f41d164e44099bbfbc8b" } ], "source_head": "2007d0d1efe82b341e51a32d8b68ebaf8218b394" } }, { "pr": 3359, "title": "Conditional \u03ba = 0.001673626873024029 by composing six cycles on PR3354", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3359", "author": "hexapode", "created_at": "2026-10-17T22:59:50Z", "accepted_at": "2026-10-18T04:49:35Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001673626873024029", "kappa_fraction": "1673626873024029/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t16-composed-cycles/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/t16-composed-cycles/PROOF.md, research/t16-composed-cycles/README.md, research/t16-composed-cycles/RESULT.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/t16-composed-cycles/RESULT.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/t16-composed-cycles/RESULT.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3359-manifest.json", "sha256": "885ec6417ef8337a7f659c0bd42c2c033ae14bd3d6a3f4af8fe3256ebd34b902" }, { "file": "remaining-record-audit/artifacts/3359/priority-manifest.json", "sha256": "d4c8002d07886e05a6125b815b6cdc6e4f4ae0e8b620a2e4b132e43e577d393e" } ], "source_head": "3bdc260e996fd3a94dcb7560b68f2c61d2253d80" } }, { "pr": 3366, "title": "Research: conditional \u03ba = 0.001673627634134309 via five interacting helpers", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3366", "author": "petalas", "created_at": "2026-10-17T23:23:09Z", "accepted_at": "2026-10-18T04:49:35Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001673627634134309", "kappa_fraction": "1673627634134309/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t16-neutral-unlock/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 2 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Recompute the complete own productive/paid histogram from research/t16-neutral-unlock/INVOICE.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/t16-neutral-unlock/RESULT.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3366-manifest.json", "sha256": "3baffbde8cfe7ac0162beb69abdddfb0627fcbf92c30b8ec697c66b4b491fc4a" }, { "file": "remaining-record-audit/artifacts/3366/priority-manifest.json", "sha256": "f4df7756315316ec35a033ee140457d1821ae854c57c13b70f21a3415c4daed6" } ], "source_head": "3f59a00257b3e29ad54e349f826d5ffdc59f7cfb" } }, { "pr": 3367, "title": "Improve selected T16 packing with five cross-call cycles", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3367", "author": "Gonzalo-Mier", "created_at": "2026-10-17T23:23:35Z", "accepted_at": "2026-10-18T04:49:35Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001673623729715781", "kappa_fraction": "1673623729715781/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t16-cross-call-cycle-packing-improvement/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/t16-cross-call-cycle-packing-improvement/README.md, research/t16-cross-call-cycle-packing-improvement/RESULT.json, research/t16-cross-call-cycle-packing-improvement/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/t16-cross-call-cycle-packing-improvement/README.md, research/t16-cross-call-cycle-packing-improvement/RESULT.json, research/t16-cross-call-cycle-packing-improvement/SOURCES.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/t16-cross-call-cycle-packing-improvement/RESULT.json#/independent_check/price_new_conservative after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3367-manifest.json", "sha256": "1d49725cdf817a9a30b5310696db40453cdd09d996dcfa7559d83afa89eb741b" }, { "file": "remaining-record-audit/artifacts/3367/priority-manifest.json", "sha256": "e66f4a9a4c15c1f8a8aa2eae13fbdfc914f05d567759eab47dcf13939c057718" } ], "source_head": "5b4baf2ba864fe137921105c2427249ea4cef8fc" } }, { "pr": 3375, "title": "Conditional \u03ba = 0.001673628681907313 by composing a cycle with PR3366", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3375", "author": "hexapode", "created_at": "2026-10-17T23:45:11Z", "accepted_at": "2026-10-18T04:49:35Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001673628681907313", "kappa_fraction": "1673628681907313/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t16-post-unlock-cycle/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/t16-post-unlock-cycle/PROOF.md, research/t16-post-unlock-cycle/README.md, research/t16-post-unlock-cycle/RESULT.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/t16-post-unlock-cycle/RESULT.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/t16-post-unlock-cycle/RESULT.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3375-manifest.json", "sha256": "40ac1745a820f8eb578f3fcbaeb2048384b4bfc0d9623d7b49003d71618145e6" }, { "file": "remaining-record-audit/artifacts/3375/priority-manifest.json", "sha256": "9df934d94590979a545c0c0fc9d9dd2a4ce12b3fc002a2c27497b92327268911" } ], "source_head": "62fd8039cc40749cea6238e7807db9a63b4d6765" } }, { "pr": 3381, "title": "Conditional \u03ba = 0.001673636244951726 via reordered T16 augmenting chain", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3381", "author": "hexapode", "created_at": "2026-10-18T00:00:34Z", "accepted_at": "2026-10-18T04:49:35Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001673636244951726", "kappa_fraction": "836818122475863/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t16-reordered-augmenting-chain/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/t16-reordered-augmenting-chain/PROOF.md, research/t16-reordered-augmenting-chain/README.md, research/t16-reordered-augmenting-chain/RESULT.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/t16-reordered-augmenting-chain/RESULT.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/t16-reordered-augmenting-chain/RESULT.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3381-manifest.json", "sha256": "d03894f80571d6d5390c93bbdf46bce60bbb57dfe32690de78a62415699e293d" }, { "file": "remaining-record-audit/artifacts/3381/priority-manifest.json", "sha256": "1987f882421b96242ffc32a4edb98bc76293e696dc376a6cca2c4e044f0dca26" } ], "source_head": "ef1f7b1f9cb582767e448dc047b2359ded28076f" } }, { "pr": 3384, "title": "Research: fixed-order T16 gain via a ten-helper repack", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3384", "author": "petalas", "created_at": "2026-10-18T00:03:51Z", "accepted_at": "2026-10-18T04:49:35Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00167362886792694", "kappa_fraction": "83681443396347/50000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t16-ten-helper-repack/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 2 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Recompute the complete own productive/paid histogram from research/t16-ten-helper-repack/INVOICE.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/t16-ten-helper-repack/RESULT.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3384-manifest.json", "sha256": "9ecfc74a8b5055a94c9f15b5e457fbb33cfcddd24f1b5d6540be11edb87f2c2a" }, { "file": "remaining-record-audit/artifacts/3384/priority-manifest.json", "sha256": "6634e66c0148343d0e9a22c71d048c27957bb5fb20d2a48e975880854740432c" } ], "source_head": "ee9f8d822bbb3a1efd6872f03c48c3357e4c5f3b" } }, { "pr": 3388, "title": "Conditional \u03ba = 0.001673648366462479 by concentrating T16 buffers", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3388", "author": "hexapode", "created_at": "2026-10-18T00:08:57Z", "accepted_at": "2026-10-18T04:49:35Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001673648366462479", "kappa_fraction": "1673648366462479/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t16-buffer-concentration/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/t16-buffer-concentration/PROOF.md, research/t16-buffer-concentration/README.md, research/t16-buffer-concentration/RESULT.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/t16-buffer-concentration/RESULT.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/t16-buffer-concentration/RESULT.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3388-manifest.json", "sha256": "a6f5cbbaee6e7e00925469d78f32e87365663b57b417e4baf4c9f50de8d3e46c" }, { "file": "remaining-record-audit/artifacts/3388/priority-manifest.json", "sha256": "5197fe87ae5dc40db177112608f96ab1816a11918d67e3679706c379ae381200" } ], "source_head": "684d347c0e6e578b8ab600d2e680ad6701cf7fa0" } }, { "pr": 3390, "title": "Conditional \u03ba = 0.001673677688974651 through repeated T16 augmentations", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3390", "author": "hexapode", "created_at": "2026-10-18T00:17:22Z", "accepted_at": "2026-10-18T04:49:35Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001673677688974651", "kappa_fraction": "1673677688974651/1000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t16-repeated-augmentations/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/t16-repeated-augmentations/PROOF.md, research/t16-repeated-augmentations/RESULT.json, research/t16-repeated-augmentations/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/t16-repeated-augmentations/RESULT.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/t16-repeated-augmentations/RESULT.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3390-manifest.json", "sha256": "51c8e92460da87d4ffa38ca61ca13baf1f20af2e4f0be1ab5b00c627a03b68b0" }, { "file": "remaining-record-audit/artifacts/3390/priority-manifest.json", "sha256": "36953af6ed8f420dc84c99651cc4cb8a7a4ebd144646128e1aff6d8b15b74cf1" } ], "source_head": "dd9c46f721864683144e76605c143795b61f06eb" } }, { "pr": 3413, "title": "Research: admit sharp T16 profile at conditional kappa 0.001674088611862992", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3413", "author": "petalas", "created_at": "2026-10-18T01:10:37Z", "accepted_at": "2026-10-18T04:49:35Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001674088611862992", "kappa_fraction": "104630538241437/62500000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": { "input_bits": "2^(2^18014398509484968)", "log2log2_input_bits": "18014398509484968", "plot_triple_log": { "exact_log2log2_integer": "18014398509484968" }, "source": "data/operation-audit/pr3413-dispatched-finite-controller-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ] }, "cost_status": "conditional_own_source_upper_only", "own_source_cost_extension": true, "early_effective_kappa": "1/5000", "own_source_scope": [ "Own full required physical entry/output-frame and absolute-phase operator-valued native endpoint, including normalized monomial wrappers and ascending typed helper paths; not inferred from scalar specialization or profiles", "All unexpanded adapter/phase operations are bounded73-axis binary affine/even-quadratic Z4 monomial grammar, with no hidden arbitrary scalar coefficients or denominators; each full operation is charged the universal64*74^3 source tariff", "Common-label/mutable-source/owned restore and all-size occupied-row interface", "Fixed constructive group/compiler and direct analytic transfer contracts", "Own complete dyadic scalar/phase grammar and actual selected source costs are separately bound; missing canonical catalogue is explicit, not a claimed native GF2 or phase replay.", "Completed native child maps have norm one under that full endpoint contract. Fixed all-size occupied-row, constructive group/compiler, analytic fine-prime/boundary/recovery and repaired unlimited GMP correctness/halting contracts remain explicit." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr3413-dispatched-finite-controller-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/3413/priority-manifest.json", "sha256": "e77718fc3447f4399321405246246750151cec02592f6998b63fd3a3a73ecdf6" } ], "source_head": "391d02ced8e620d8f06aeda1ebe02f099d37af92" } }, { "pr": 3361, "title": "Conditional T740 kappa refinement: +9.04e-25 over PR3148", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3361", "author": "dataisfire", "created_at": "2026-10-17T23:03:53Z", "accepted_at": "2026-10-18T04:49:36Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001729777494678597011886903656817799999999999999999999999", "kappa_fraction": "1729777494678597011886903656817799999999999999999999998999999999999999999999999/1000000000000000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 256, "source_index": null, "at": "2026-10-17T23:03:53Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001729777494678597011886903656817799999999999999999999999999999999999999999999999999", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3361", "evidence_excerpt": "`kappa = 0.0017297774946785970118869036568178 - 10^-57 - 10^-81`.", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/coupled-cap740-grid35/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/coupled-cap740-grid35/CLAIM.json, research/coupled-cap740-grid35/PROOF.md, research/coupled-cap740-grid35/README.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/coupled-cap740-grid35/CLAIM.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/coupled-cap740-grid35/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/3361/priority-manifest.json", "sha256": "7f1099d34dc9b9a19fa575a63785d6a59a4ff97d322dbba1c7dd9e15c5e732f1" } ], "source_head": "f9de2024916a347d939ed256a7a2e9e68d633684" } }, { "pr": 3494, "title": "Improve T8 kappa with two certified chronology swaps", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3494", "author": "hexapode", "created_at": "2026-10-18T03:38:58Z", "accepted_at": "2026-10-18T04:51:46Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001729097946885651030612999999999999999999999900000000000", "kappa_fraction": "17290979468856510306129999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 9, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t8-rank7-two-swaps/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/t8-rank7-two-swaps/CERTIFICATE.json, research/t8-rank7-two-swaps/EXPECTED.json, research/t8-rank7-two-swaps/PROOF.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/t8-rank7-two-swaps/EXPECTED.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/t8-rank7-two-swaps/source-inputs/research/community-frontier1094-audit/ASSEMBLY.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3494-manifest.json", "sha256": "d91846824543779fc0f1e484b703d333e902449258e01659c398168499b572bb" }, { "file": "remaining-record-audit/artifacts/3494/priority-manifest.json", "sha256": "9e4c136116d2540062f62d7b6f4b79b526051f63c8976341f44f38063236f77b" } ], "source_head": "5c139955cc707b4a362cd20779ef361a930648f4" } }, { "pr": 3465, "title": "Improve T16 kappa with bounded full-bin reallocation", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3465", "author": "hexapode", "created_at": "2026-10-18T02:49:45Z", "accepted_at": "2026-10-18T04:51:47Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001727254340596650594392999999999999999999999900000000000", "kappa_fraction": "17272543405966505943929999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 9, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t16-rank7-provider-composition/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/t16-rank7-provider-composition/CERTIFICATE.json, research/t16-rank7-provider-composition/EXPECTED.json, research/t16-rank7-provider-composition/PROOF.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/t16-rank7-provider-composition/EXPECTED.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/t16-rank7-provider-composition/source-inputs/research/community-frontier1094-audit/ASSEMBLY.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3465-manifest.json", "sha256": "0e1b88565e3f386e13b1623d218118a688a278a1ed8117a02084c830d4d14f1d" }, { "file": "remaining-record-audit/artifacts/3465/priority-manifest.json", "sha256": "f106311dd3dd45afe876b23e9afa1e980b84e7ce3e3c364e8d8151eda005afaf" } ], "source_head": "52c8434c4b184dbbd3e080aff43b0a9714fe8bf1" } }, { "pr": 3468, "title": "Improve kappa with an eight-replica rank-seven construction", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3468", "author": "hexapode", "created_at": "2026-10-18T03:05:24Z", "accepted_at": "2026-10-18T04:51:47Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001728992447095271166655999999999999999999999900000000000", "kappa_fraction": "17289924470952711666559999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 9, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t8-rank7-provider-composition/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/t8-rank7-provider-composition/CERTIFICATE.json, research/t8-rank7-provider-composition/EXPECTED.json, research/t8-rank7-provider-composition/PROOF.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/t8-rank7-provider-composition/EXPECTED.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/t8-rank7-provider-composition/source-inputs/research/community-frontier1094-audit/ASSEMBLY.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3468-manifest.json", "sha256": "c6c6495fd360356fdf79ee9b68df0020b88a8908ba9d278c3731de095b0f6654" }, { "file": "remaining-record-audit/artifacts/3468/priority-manifest.json", "sha256": "884078f4f63060c984fceafceaa4eaac20e60d9e535ca85a6816fa18c5791c18" } ], "source_head": "dbeac6cf5c1190459fb5ed7a6020bdc50641577d" } }, { "pr": 3485, "title": "Improve T8 kappa with one source-window swap", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3485", "author": "hexapode", "created_at": "2026-10-18T03:25:45Z", "accepted_at": "2026-10-18T04:51:47Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001728996308346386172129999999999999999999999900000000000", "kappa_fraction": "17289963083463861721299999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 9, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/t8-rank7-dual-swap/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/t8-rank7-dual-swap/CERTIFICATE.json, research/t8-rank7-dual-swap/EXPECTED.json, research/t8-rank7-dual-swap/PROOF.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/t8-rank7-dual-swap/EXPECTED.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/t8-rank7-dual-swap/source-inputs/research/community-frontier1094-audit/ASSEMBLY.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3485-manifest.json", "sha256": "6dd15b88a15bca20966288b2aa2b6690f92073b70846628d018bfa05769de153" }, { "file": "remaining-record-audit/artifacts/3485/priority-manifest.json", "sha256": "9495222574656bdb5257e9a6ccd43a136e0652771a12c8bc9079c46184a1cb3a" } ], "source_head": "1ee2ac4be28f284d75eac0869f2049025f94b94b" } }, { "pr": 3563, "title": "Name the checkpoint behind the #1042 status link", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3563", "author": "jwr404", "created_at": "2026-10-18T06:05:09Z", "accepted_at": "2026-10-20T04:59:18Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "individual-primary-interface-source/3563-manifest.json", "sha256": "9607e69cf24ab12b06a4581ecf6337b362e35462d1fc056809ae17eaa0dda102" }, { "file": "remaining-record-audit/artifacts/3563/priority-manifest.json", "sha256": "7bda160695d42649af779082f0e662820fc5657d950387814ca6ea423792a90e" } ], "source_head": "d11655a9fd1c7eedc52e0e9720158bd17d29192a" } }, { "pr": 3594, "title": "Rule out four-read retiming after removing helper 584", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3594", "author": "RossRichardson", "created_at": "2026-10-18T07:14:40Z", "accepted_at": "2026-10-20T04:59:18Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00173", "kappa_fraction": "173/100000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/3594-manifest.json", "sha256": "bdc75e33f10e24c8315372c5d2f9a4c9a4b18cf9201281ab0697bebac3fb8583" }, { "file": "remaining-record-audit/artifacts/3594/priority-manifest.json", "sha256": "f2596e1d61ff0144da8ba3a6a7a56984a4d3e4fcf68af67b12d51788bd68eaa9" } ], "source_head": "e3dc9c1660bfec0501dd7522f44a21746f9b89e2" } }, { "pr": 3531, "title": "Certify a tiny conditional T740 kappa rounding-slack refinement", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3531", "author": "SovereignSteak", "created_at": "2026-10-18T04:57:25Z", "accepted_at": "2026-10-20T04:59:19Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001729777494678597011886903656817803609000000000000000000", "kappa_fraction": "172977749467859701188690365681780360899999999999999999999998999999999999999999999999/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 257, "source_index": null, "at": "2026-10-18T04:57:25Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001729777494678597011886903656817803609", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3531", "evidence_excerpt": "kappa = 0.001729777494678597011886903656817803609 - 10^-62 - 10^-86.", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/coupled-cap740-binomial40/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/coupled-cap740-binomial40/CLAIM.json, research/coupled-cap740-binomial40/PROOF.md, research/coupled-cap740-binomial40/README.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/coupled-cap740-binomial40/RESULT.json#/outer and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/coupled-cap740-binomial40/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/3531/priority-manifest.json", "sha256": "a1d2dd56d1aa1bdceaa3ef8457d68d3528e0af6e97ffda93c3cec53017593f4d" } ], "source_head": "550a660a97308d3aeb3620ee1f4218f77e2c2742" } }, { "pr": 3682, "title": "Consume retimed staged releases with smaller T360 stock", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3682", "author": "zxv", "created_at": "2026-10-18T14:18:22Z", "accepted_at": "2026-10-20T05:06:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001730418899766071163803999999999999999999999900000000000", "kappa_fraction": "17304188997660711638039999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 263, "source_index": null, "at": "2026-10-18T14:18:22Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001730418899766071163804", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3682", "evidence_excerpt": "Compose the two commuting staged-release retimings with the literal T360 allocation. The complete conditional finite release supports **\u03ba = 0.001730418899766071163804 \u2212 10^-46 \u2212 10^-70**, matching the endpoint reported by [PR3653](https://github.com/CrocSwap/integer-mult-bounds/pull/3653) with **323,069 instead of 437,757 physical families**, 3,240 instead of 4,392 calls, and 1,321,920 instead of 1,791,936 helper roles. The normalized profiles are identical; smaller stock changes finite constant", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/staged-donor-release/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Recompute the complete own productive/paid histogram from research/staged-donor-release/evidence/complete/PREFIX-AND-INVOICE.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/staged-donor-release/evidence/complete/RESULT.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3682-manifest.json", "sha256": "e04c4a575eebcd6acb4e834049f8c1062153f9db45d2c2ec97932f57b817662d" }, { "file": "remaining-record-audit/artifacts/3682/priority-manifest.json", "sha256": "992b0df377c7c938872693849a7e3acaf45e8d29f05d31a4ee3cba34706f9f9d" } ], "source_head": "431e6c6023ef352c41696469de7fb614cd4ded8c" } }, { "pr": 3687, "title": "Independent verification: PR3605's staged 644/660 words pass an exact audit against the PR3133 control (no \u03ba claim)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3687", "author": "thakrarsagar", "created_at": "2026-10-18T14:46:45Z", "accepted_at": "2026-10-20T05:06:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00173", "kappa_fraction": "173/100000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/3687-manifest.json", "sha256": "56caa2f011a2b9a30258a6c239ee36e0b70fbe2c25a707f86bd96758505cefe0" }, { "file": "remaining-record-audit/artifacts/3687/priority-manifest.json", "sha256": "b75817ade7ff3c8a3ed6a05ddb06dad65dfd344ec83780e59edbabd459d9d8ee" } ], "source_head": "f798838eb8ede4178e94f240e7b7e54b3f80c82d" } }, { "pr": 3694, "title": "Independent verification (no \u03ba): PR3633's T488 journal, fixed-inventory ceiling and endpoint reproduce; inherited owner-audit controls cannot fail", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3694", "author": "thakrarsagar", "created_at": "2026-10-18T16:21:04Z", "accepted_at": "2026-10-20T05:06:38Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001730096363528623534229999999999999999999999900000000000", "kappa_fraction": "17300963635286235342299999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/3694-manifest.json", "sha256": "0f49cc017949f06941d784d83d0d24d6147d7d7dbdaae97d8dc7ac7af932dfe4" }, { "file": "remaining-record-audit/artifacts/3694/priority-manifest.json", "sha256": "177eca4718d1d3b92668168e3bdb8de08dd4f250468390e3e83dc245963854fc" } ], "source_head": "cfee00c832d799b2fde891047734eb15cfbd1102" } }, { "pr": 3633, "title": "Combine T37, T8 and T16: conditional \u03ba > 0.00173009636352", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3633", "author": "hexapode", "created_at": "2026-10-18T11:40:10Z", "accepted_at": "2026-10-20T05:06:39Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001730096363528623534229999999999999999999999900000000000", "kappa_fraction": "17300963635286235342299999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 223, "source_index": 371, "at": "2026-10-18T11:40:10Z", "until": "2026-10-18T11:58:31Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001730096363528623534230", "dashboard_float_text": "0.0017300963635286236", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3633", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 261, "source_index": null, "at": "2026-10-18T11:40:10Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001730096363528623534230", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3633", "evidence_excerpt": "The endpoint is `0.001730096363528623534230 \u2212 10^-46 \u2212 10^-70`. All inherited all-size, compiler, analytic and other conditional premises remain. This does not change the selected result or claim an unconditional multiplication theorem.", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/staged-width-t488/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Recompute the complete own productive/paid histogram from research/staged-width-t488/CLAIM.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/staged-width-t488/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3633-manifest.json", "sha256": "a360f7ca88965f84f79f334915b955ec74d01b0394e513963dfc16d8afaec64f" }, { "file": "remaining-record-audit/artifacts/3633/priority-manifest.json", "sha256": "d62c77df746587cfc42988b078ef354413647da9c801222833d81db6e3023c4c" } ], "source_head": "2969dce9739c4043330ddf76f395ca0dd3a90baa" } }, { "pr": 3650, "title": "Add a source-shaped Lean bridge for compiler retention", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3650", "author": "PellaML", "created_at": "2026-10-18T13:04:51Z", "accepted_at": "2026-10-20T05:06:39Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "individual-primary-interface-source/3650-manifest.json", "sha256": "4d0aa1132069ba6f166aad272a160d35b703001be7cc2e300dac5d3f414e24be" }, { "file": "remaining-record-audit/artifacts/3650/priority-manifest.json", "sha256": "29930e3ea1cec55cf0bf30e0838cee84cdb4a56f5f9cd9ee763d44732a4c3058" } ], "source_head": "7bd54e91748eb9fc6b13d61d232b6a91e8158aba" } }, { "pr": 3815, "title": "Research: certify the staged544 packing ceiling and reach it on PR3734's T360 clock (no new \u03ba; same value as #3802)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3815", "author": "ChaloupeMusic", "created_at": "2026-10-18T21:44:40Z", "accepted_at": "2026-10-20T05:20:11Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001730578437266246818739999999999999999999999900000000000", "kappa_fraction": "17305784372662468187399999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_own_source_selector_required; actual own source selector; expected 17305784372662468187399999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000; Read actual author-head CLAIM/verifier/SOURCES/MANIFEST and identify the selected complete kernel. A missing exact claim-kappa SPEC match is a discovery limitation, not mathematical rejection. Different quoted fixtures must not override a later actual final package. All listed SPEC candidates remain unselected until independently authenticated." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/3815/priority-manifest.json", "sha256": "105ca2cef0e27fba363b0c4b13edb7ad2b71a49ae7689083df9b75880325d155" } ], "source_head": "77ffbf287b6ca198b4a31e3835db3bae60718b93" } }, { "pr": 3772, "title": "Research: bit endpoint and owned-scratch negative results", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3772", "author": "Gonzalo-Mier", "created_at": "2026-10-18T20:20:47Z", "accepted_at": "2026-10-20T05:20:12Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/3772/priority-manifest.json", "sha256": "3fefc5cc0731c93a78782bcdb992048ef893dbf2a8a4f4008f8fb733e1bdcfa7" } ], "source_head": "5b1d4c2ade90dfa0d8b837148cc5b9cc4be1cdab" } }, { "pr": 3795, "title": "Improve conditional kappa with PR3734 T488 chronological allocation", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3795", "author": "hexapode", "created_at": "2026-10-18T21:20:21Z", "accepted_at": "2026-10-20T05:20:12Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001730512921319457636693999999999999999999999900000000000", "kappa_fraction": "17305129213194576366939999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 226, "source_index": 378, "at": "2026-10-18T21:20:21Z", "until": "2026-10-18T21:26:50Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001730512921319457636694", "dashboard_float_text": "0.0017305129213194576", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3795", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 265, "source_index": null, "at": "2026-10-18T21:20:21Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001730512921319457636694", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3795", "evidence_excerpt": "This combines PR3734\u2019s unchanged staged-helper544 supplier with the preserved T37/T8/T16 chronological order and a new exact T488 allocation. Conditional \u03ba improves from `0.001730448360207635461740 \u2212 10^-46 \u2212 10^-70` to `0.001730512921319457636694 \u2212 10^-46 \u2212 10^-70`, a gain of `6.4561111822174954e-8`.", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_own_source_selector_required; actual own source selector; expected 17305129213194576366939999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000; Read actual author-head CLAIM/verifier/SOURCES/MANIFEST and identify the selected complete kernel. A missing exact claim-kappa SPEC match is a discovery limitation, not mathematical rejection. Different quoted fixtures must not override a later actual final package. All listed SPEC candidates remain unselected until independently authenticated." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/3795/priority-manifest.json", "sha256": "d292e4f103a674aa3af2d7beefc367f7eb5ad72366f24b2bd7d09baa5b4e7e76" } ], "source_head": "fcffda7c6c68bcf6e417175c5aaab747341da90b" } }, { "pr": 3802, "title": "Improve conditional kappa beyond T488 with a T385 combined-clock allocation", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3802", "author": "hexapode", "created_at": "2026-10-18T21:26:50Z", "accepted_at": "2026-10-20T05:20:12Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001730578437266246818739999999999999999999999900000000000", "kappa_fraction": "17305784372662468187399999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 227, "source_index": 379, "at": "2026-10-18T21:26:50Z", "until": "2026-10-18T21:44:40Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001730578437266246818740", "dashboard_float_text": "0.0017305784372662468", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3802", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 266, "source_index": null, "at": "2026-10-18T21:26:50Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001730578437266246818740", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3802", "evidence_excerpt": "Conditional **\u03ba = 0.001730578437266246818740 \u2212 10^-46 \u2212 10^-70** improves on our just-published [PR3795](https://github.com/CrocSwap/integer-mult-bounds/pull/3795) by **0.000000065515946789182046**, and on PR3734 by 0.000000130077058611357000. Its 1,413,720 helper roles and 345,469 physical families also use less stock than PR3795\u2019s 437,757 families.", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_own_source_selector_required; actual own source selector; expected 17305784372662468187399999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000; Read actual author-head CLAIM/verifier/SOURCES/MANIFEST and identify the selected complete kernel. A missing exact claim-kappa SPEC match is a discovery limitation, not mathematical rejection. Different quoted fixtures must not override a later actual final package. All listed SPEC candidates remain unselected until independently authenticated." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/3802/priority-manifest.json", "sha256": "a66a35c227abcd062e9f517b7b5b71b0d714a4c5f6f80ec609ca2d18aacf8f76" } ], "source_head": "de2cd5c58009205210e3bf328b0ef5cadf3903af" } }, { "pr": 3804, "title": "Independent direct certification of the two batched moment bounds, with sharp thresholds (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3804", "author": "petalas", "created_at": "2026-10-18T21:27:22Z", "accepted_at": "2026-10-20T05:20:12Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "1.2299998E-7", "kappa_fraction": "6149999/50000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "individual-primary-interface-source/3804-manifest.json", "sha256": "d7459efedef50a65df6391acc931e6a6812604b19fd6f19be253d93ba02d2a3f" }, { "file": "remaining-record-audit/artifacts/3804/priority-manifest.json", "sha256": "6bd952d08846b8222cdfcc18fd0a30e5c8fd73bb5a17e24e10f13054538920a5" } ], "source_head": "d074ed59cd6c8f194d5cb6eb226607b0c2e254ff" } }, { "pr": 3734, "title": "Stage helper544 after a returning producer excursion; improve conditional kappa", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3734", "author": "dataisfire", "created_at": "2026-10-18T19:09:40Z", "accepted_at": "2026-10-20T05:20:13Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001730448360207635461739999999999999999999999900000000000", "kappa_fraction": "17304483602076354617399999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 225, "source_index": 377, "at": "2026-10-18T19:09:40Z", "until": "2026-10-18T21:20:21Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001730448360207635461740", "dashboard_float_text": "0.0017304483602076355", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3734", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 264, "source_index": null, "at": "2026-10-18T19:09:40Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001730448360207635461740", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3734", "evidence_excerpt": "The complete conditional endpoint is **kappa = 0.001730448360207635461740 - 10^-46 - 10^-70**, an increase of **0.000000029460441564297936** (about 0.0017%) over PR3682 on the same release grid. The claimed bound uses the actual integer packing, not the higher ideal packing ceiling. It includes 1,321,920 literal roles and 323,069 physical families.", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "selected_provider_controller", "cost_obligations": [ "Source-specific frozen V10 discovery snapshot: actual_own_source_selector_required; actual own source selector; expected 17304483602076354617399999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000; Read actual author-head CLAIM/verifier/SOURCES/MANIFEST and identify the selected complete kernel. A missing exact claim-kappa SPEC match is a discovery limitation, not mathematical rejection. Different quoted fixtures must not override a later actual final package. All listed SPEC candidates remain unselected until independently authenticated." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/3734/priority-manifest.json", "sha256": "074c40900e46911d7fd3f815aef9ba8bef4f82bda4c6c7c6c2204965f24dc57e" } ], "source_head": "fa041037a3374eaa08feeca0b26a5d6893194147" } }, { "pr": 3742, "title": "Locate the complex branch cutoff sequences in the frozen assembler (answers stock-margin-chain OQ2; no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3742", "author": "petalas", "created_at": "2026-10-18T19:21:10Z", "accepted_at": "2026-10-20T05:20:13Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "individual-primary-interface-source/3742-manifest.json", "sha256": "be866518450d26b59999bde5ffcd7d52c64a03a63b50d8c27c3355c3c6cd695d" }, { "file": "remaining-record-audit/artifacts/3742/priority-manifest.json", "sha256": "03d5dcadb45011f6693f402281f531e725bbb3f0ed4eddde9e585d2f103bf5c8" } ], "source_head": "89f6af270c550dd02bdb05d7a69987159aa110f2" } }, { "pr": 3945, "title": "Raise conditional staged544 \u03ba by filling idle owner slots", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3945", "author": "Dugongue", "created_at": "2026-10-19T05:48:00Z", "accepted_at": "2026-10-20T05:22:43Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001730663236534549309145999999999999999999999900000000000", "kappa_fraction": "17306632365345493091459999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 228, "source_index": 383, "at": "2026-10-19T05:48:00Z", "until": "2026-10-19T13:53:38Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001730663236534549309146", "dashboard_float_text": "0.0017306632365345492", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3945", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 269, "source_index": null, "at": "2026-10-19T05:48:00Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001730663236534549309146", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3945", "evidence_excerpt": "`0.001730663236534549309146 \u2212 10^-46 \u2212 10^-70`.", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "23/10000", "status": "Maintainer-reviewed conditional productive-helper construction; see integration receipt for publication state", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier4359.json", "path": "certificates/checkpoints/frontier4359.json", "commit": null, "at": null, "scope": "Productive-helper p3 construction under retained analytic decomposition, exact recovery, native ordered movement, fixed-tape execution, fine-prime padding and gauge-free outer estimates. Changed interfaces reviewed with AI assistance; no formal or independent human verification of the full theorem. Winning uniform templates are algorithm-defined, not materialized. Frozen claim publication booleans describe submission time. Unrelated H-branch research is not selected." }, { "stream": "all_selected_result_history", "record_kappa": "60403/20000000", "status": "Selected maintainer-reviewed conditional joint-helper construction; source-bound foundation reuse is explicit", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/4f19cedcd8d81e4a2359449309fa6e9f17dfd22e/certificates/selected-result.json", "path": null, "commit": "4f19cedcd8d81e4a2359449309fa6e9f17dfd22e", "at": "2026-10-22T12:16:48Z", "scope": "Maintainer-reviewed conditional PR4470 construction. Inherited native/all-column, owned-erasure, whole-job, compiler, precision/tape, analytic, prime and recovery hypotheses remain. Uniform words are not materialized." }, { "stream": "all_selected_result_history", "record_kappa": "23/10000", "status": "Maintainer-reviewed conditional productive-helper construction; see integration receipt for publication state", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/ae87507c0767c00f5a55ee9062c496191e978632/certificates/selected-result.json", "path": null, "commit": "ae87507c0767c00f5a55ee9062c496191e978632", "at": "2026-10-21T19:10:46Z", "scope": "Productive-helper p3 construction under retained analytic decomposition, exact recovery, native ordered movement, fixed-tape execution, fine-prime padding and gauge-free outer estimates. Changed interfaces reviewed with AI assistance; no formal or independent human verification of the full theorem. Winning uniform templates are algorithm-defined, not materialized. Frozen claim publication booleans describe submission time. Unrelated H-branch research is not selected." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 12, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/staged544-terminal-gap-fill/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/staged544-terminal-gap-fill/RESULT.json, research/staged544-terminal-gap-fill/SOURCES.json, research/staged544-terminal-gap-fill/admission/NATIVE-RECEIPT-CORRECTED.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/staged544-terminal-gap-fill/RESULT.json, research/staged544-terminal-gap-fill/SOURCES.json, research/staged544-terminal-gap-fill/admission/NATIVE-RECEIPT-CORRECTED.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/3945-manifest.json", "sha256": "a480ff1e38414f53d079b91b1036c41d3c97b4236188a3881ed67376f95325df" }, { "file": "remaining-record-audit/artifacts/3945/priority-manifest.json", "sha256": "13b1e951adf76334d7c999fc3beba03c510e3dfaac8d21e6f834f44e188f9714" } ], "source_head": "91f81d131252db704f945891da1ea54e29d46b8b" } }, { "pr": 3948, "title": "Negative result: +10% centre sharing at c* \u2248 0.0018433 needs 511 net complex rank-1 units (3.55/call, not 1.33); no admitted bit lever nets any of the 649 needed (no \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3948", "author": "thakrarsagar", "created_at": "2026-10-19T06:11:09Z", "accepted_at": "2026-10-20T05:22:43Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/3948-manifest.json", "sha256": "1fff8791442049f95467a2afd3a262e32cb5cdcab7f0a005b0b02a96d2bd2c7c" }, { "file": "remaining-record-audit/artifacts/3948/priority-manifest.json", "sha256": "b25f921c526210da8b0cc685eabd848391ec7f79b1ea33161a9573a5e219572f" } ], "source_head": "5505853988cfc05bc8ad9bfcf07879727932b0d5" } }, { "pr": 3968, "title": "Research: native P112 co-delivery block and cut contracts", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3968", "author": "Gonzalo-Mier", "created_at": "2026-10-19T07:20:44Z", "accepted_at": "2026-10-20T05:22:43Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.002", "kappa_fraction": "1/500", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain exact local evidence and stated restrictions with the named target. A whole-input crossover needs its own source-selected complete native/owner/recursive/precision/outer invoice and all-size realization." ], "source_manifest": [ { "file": "individual-primary-interface-source/3968-manifest.json", "sha256": "68ebfc754c9ba17bc3da6a9964773d395d082aaa3865ea68d3c4252f274de7e5" }, { "file": "remaining-record-audit/artifacts/3968/priority-manifest.json", "sha256": "7b7dad889b9373b3f385f97a5094f0f949e357991b5b6687ccf8d61b9c9496c2" } ], "source_head": "6b9850ded32b4606d75dfa215d56b739fa83adf3" } }, { "pr": 3974, "title": "Research: exact Toom-3 five-product profile screen", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3974", "author": "Gonzalo-Mier", "created_at": "2026-10-19T07:39:16Z", "accepted_at": "2026-10-20T05:22:43Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001730427469824", "kappa_fraction": "105616911/61035156250", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "individual-primary-interface-source/3974-manifest.json", "sha256": "b4a715ae7e31eeb79dc2919140110c58fd78097dceb935aeedc80b13c8b8da2e" }, { "file": "remaining-record-audit/artifacts/3974/priority-manifest.json", "sha256": "ea67c38905b6eed5620117e212b47d9866532d43ede0ef0f3c9da874fe498ef9" } ], "source_head": "23bb4de61d629e3f103a65baa7882b34042ab10f" } }, { "pr": 3857, "title": "Kernel-check the staged supplier moment and refine conditional \u03ba", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3857", "author": "Dugongue", "created_at": "2026-10-18T23:19:50Z", "accepted_at": "2026-10-20T05:22:44Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001730578437266246818740713218049857556556448073971562433", "kappa_fraction": "17305784372662468187407132180498575565564480739715624333119999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 267, "source_index": null, "at": "2026-10-18T23:19:50Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001730578437266246818740713218049857556556448073971562433312", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3857", "evidence_excerpt": "\u03ba = 0.001730578437266246818740713218049857556556448073971562433312", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/staged544-certified-endpoint/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/staged544-certified-endpoint/CLAIM.json, research/staged544-certified-endpoint/RESULT.json, research/staged544-certified-endpoint/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/staged544-certified-endpoint/RESULT.json#/outer/ledger and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/staged544-certified-endpoint/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3857-manifest.json", "sha256": "74a8bc0886b9b53fe831899b2d5c1d721a3c5e6406820f8006babbb548b10493" }, { "file": "remaining-record-audit/artifacts/3857/priority-manifest.json", "sha256": "8324a9673f4193f7680da424c796d2269e5396937adfc3883af0f030a0fdaabe" } ], "source_head": "ef4315b8caa605e47a2515004845eb2d2ed71a86" } }, { "pr": 3874, "title": "Certify the ideal combined-lever budget grid of the selected complex local word (screening; no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3874", "author": "petalas", "created_at": "2026-10-19T00:43:58Z", "accepted_at": "2026-10-20T05:22:44Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.01010101010101010101010101010101010101010101010101010101", "kappa_fraction": "1/99", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/3874-manifest.json", "sha256": "20289a56ae023443c30ec7fa11e466b4b8a4c6855ac8dfe5a5052f4790722f65" }, { "file": "remaining-record-audit/artifacts/3874/priority-manifest.json", "sha256": "ae804948428f30b99c0f4932d2b93736bdd9591c8ca2eda9de418b4cea78e2e0" } ], "source_head": "fb86b078a53042974d88b9758fe36622571349d0" } }, { "pr": 3875, "title": "Refine the certified staged544 conditional kappa endpoint to 80 digits", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3875", "author": "hexapode", "created_at": "2026-10-19T00:56:33Z", "accepted_at": "2026-10-20T05:22:44Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001730578437266246818740713218049857556556448073971562433", "kappa_fraction": "1730578437266246818740713218049857556556448073971562433312762590080026439756809999999999999999999998999999999999999999999999/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 268, "source_index": null, "at": "2026-10-19T00:56:33Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00173057843726624681874071321804985755655644807397156243331276259008002643975681", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3875", "evidence_excerpt": "kappa = 0.00173057843726624681874071321804985755655644807397156243331276259008002643975681", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/staged544-refined-endpoint/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/staged544-refined-endpoint/CLAIM.json, research/staged544-refined-endpoint/RESULT.json, research/staged544-refined-endpoint/PROOF.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/staged544-refined-endpoint/RESULT.json#/outer/ledger and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/staged544-refined-endpoint/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/3875-manifest.json", "sha256": "a119bac5e3e7491b9a612348d3607f901465c05e8425b052ec4745eed9c57b38" }, { "file": "remaining-record-audit/artifacts/3875/priority-manifest.json", "sha256": "a75a184ff668ee8981719c6fc2cb29c84e719d9aeaa39538b318e65097e50b7a" } ], "source_head": "a65afd67e0a43e02554b58b5593d253581207b04" } }, { "pr": 4076, "title": "Conditional \u03ba = 0.001730809033576552081734 (+1.458e-7 over #3945): three staged helper entries and an LP-exact T360 fill", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4076", "author": "rohanarun", "created_at": "2026-10-19T13:53:38Z", "accepted_at": "2026-10-20T05:24:24Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001730809033576552081733999999999999999999999900000000000", "kappa_fraction": "17308090335765520817339999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 229, "source_index": 384, "at": "2026-10-19T13:53:38Z", "until": "2026-10-19T16:04:31Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001730809033576552081734", "dashboard_float_text": "0.0017308090335765522", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4076", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 270, "source_index": null, "at": "2026-10-19T13:53:38Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001730809033576552081734", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4076", "evidence_excerpt": "Conditional \u03ba = 0.001730809033576552081734 (+1.458e-7 over #3945): three staged helper entries and an LP-exact T360 fill", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "23/10000", "status": "Maintainer-reviewed conditional productive-helper construction; see integration receipt for publication state", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier4359.json", "path": "certificates/checkpoints/frontier4359.json", "commit": null, "at": null, "scope": "Productive-helper p3 construction under retained analytic decomposition, exact recovery, native ordered movement, fixed-tape execution, fine-prime padding and gauge-free outer estimates. Changed interfaces reviewed with AI assistance; no formal or independent human verification of the full theorem. Winning uniform templates are algorithm-defined, not materialized. Frozen claim publication booleans describe submission time. Unrelated H-branch research is not selected." }, { "stream": "all_selected_result_history", "record_kappa": "60403/20000000", "status": "Selected maintainer-reviewed conditional joint-helper construction; source-bound foundation reuse is explicit", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/4f19cedcd8d81e4a2359449309fa6e9f17dfd22e/certificates/selected-result.json", "path": null, "commit": "4f19cedcd8d81e4a2359449309fa6e9f17dfd22e", "at": "2026-10-22T12:16:48Z", "scope": "Maintainer-reviewed conditional PR4470 construction. Inherited native/all-column, owned-erasure, whole-job, compiler, precision/tape, analytic, prime and recovery hypotheses remain. Uniform words are not materialized." }, { "stream": "all_selected_result_history", "record_kappa": "23/10000", "status": "Maintainer-reviewed conditional productive-helper construction; see integration receipt for publication state", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/ae87507c0767c00f5a55ee9062c496191e978632/certificates/selected-result.json", "path": null, "commit": "ae87507c0767c00f5a55ee9062c496191e978632", "at": "2026-10-21T19:10:46Z", "scope": "Productive-helper p3 construction under retained analytic decomposition, exact recovery, native ordered movement, fixed-tape execution, fine-prime padding and gauge-free outer estimates. Changed interfaces reviewed with AI assistance; no formal or independent human verification of the full theorem. Winning uniform templates are algorithm-defined, not materialized. Frozen claim publication booleans describe submission time. Unrelated H-branch research is not selected." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 12, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/staged544-triple-entry-fill/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/staged544-triple-entry-fill/RESULT.json, research/staged544-triple-entry-fill/SOURCES.json, research/staged544-triple-entry-fill/admission/pr3945/old-NATIVE-base.json.gz). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/staged544-triple-entry-fill/RESULT.json, research/staged544-triple-entry-fill/SOURCES.json, research/staged544-triple-entry-fill/admission/pr3945/old-NATIVE-base.json.gz) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/4076-manifest.json", "sha256": "f032cd540196317f0dd487f9179fb17804379678aa14c60a72d4e856a6efb43e" }, { "file": "remaining-record-audit/artifacts/4076/priority-manifest.json", "sha256": "eb94f66c94e7d8d3cfe88130afadc1f4fe71db01d04ebd945ddc39e88dca7da6" } ], "source_head": "9744f9df268590295a9872b1952c695a678192b9" } }, { "pr": 3988, "title": "Certify a complete tariff barrier for staged544 terminal-only extensions", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3988", "author": "Clear1nsight", "created_at": "2026-10-19T08:10:01Z", "accepted_at": "2026-10-20T05:24:25Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001730663236534549309146", "kappa_fraction": "865331618267274654573/500000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/3988-manifest.json", "sha256": "7f4a5d4b0b133f6aa4feebc0356f0869e843ddc578a1577f5ba7e3de19277eb8" }, { "file": "remaining-record-audit/artifacts/3988/priority-manifest.json", "sha256": "1d2f9c5a8a32cb312aab8ae645ae5f4c01391b1c828f66241e081aaf8757f8d7" } ], "source_head": "7d85649b64243022b3141df00c61027a083a533a" } }, { "pr": 3992, "title": "Bind one selected Toom candidate to its dirty-input interface", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3992", "author": "Clear1nsight", "created_at": "2026-10-19T08:16:07Z", "accepted_at": "2026-10-20T05:24:25Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/3992-manifest.json", "sha256": "4a2f1e344be8365aece006582c10280929eaecb0c4bad3951909128394f2dab5" }, { "file": "remaining-record-audit/artifacts/3992/priority-manifest.json", "sha256": "84f8afea7a4b35eb06f0b019dc080ae4b8286ead6d4d221df2369530662eacf8" } ], "source_head": "251aba3a98e6eae2e2dd26c954aa0d1b2069cd4c" } }, { "pr": 4012, "title": "Prove the 178-incidence P112 bound and rank-at-most-six strict-deficit corollary", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4012", "author": "Clear1nsight", "created_at": "2026-10-19T09:00:12Z", "accepted_at": "2026-10-20T05:24:25Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "individual-primary-interface-source/4012-manifest.json", "sha256": "79911882efc1d99b3f231aaab3cd0cbeee06be760eff9cc80ec4dab2662be078" }, { "file": "remaining-record-audit/artifacts/4012/priority-manifest.json", "sha256": "08d02440bd74e4248b68e214d7229df84c0878a6ea8f687dc485006fdb35e360" } ], "source_head": "678886290dbacd454f49965a1808b8b3072b1c98" } }, { "pr": 4164, "title": "Show a restored third bank does not add an unpaid coordinate.", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4164", "author": "unpaidmoon", "created_at": "2026-10-20T04:08:27Z", "accepted_at": "2026-10-20T05:28:20Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/4164-manifest.json", "sha256": "d8e348205effb222c0aa395d4f4ac55862cfb5aa309dbcba0833be718568ac8b" }, { "file": "remaining-record-audit/artifacts/4164/priority-manifest.json", "sha256": "900e1a92c2f781ad81204096195f0c55922f18527ca2628ee7bffdc03948f0f3" } ], "source_head": "799daee720cf968ff706a7c9bf5b5a6e8048f8f9" } }, { "pr": 4165, "title": "Record the idle cost blocking the mixed staged544 endpoint.", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4165", "author": "unpaidmoon", "created_at": "2026-10-20T04:41:05Z", "accepted_at": "2026-10-20T05:28:20Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001730979115670792472759999999999999999999999900000000000", "kappa_fraction": "17309791156707924727599999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "individual-primary-interface-source/4165-manifest.json", "sha256": "94a763e3cbd997c58c62c0774c8cfae3783e6d4301c7384a306ae7dd1838474b" }, { "file": "remaining-record-audit/artifacts/4165/priority-manifest.json", "sha256": "48b4ed5bf750ad220c0bfeec757ce62819ad1754170008b00f9d1944a5ac2b6c" } ], "source_head": "430072ee4130b58c1dd952cb37fd81759675a118" } }, { "pr": 4085, "title": "Conditional \u03ba = 0.001730970419199163702738 (+1.614e-7 over #4076): receiver sharing on the staged T360 supplier", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4085", "author": "zxv", "created_at": "2026-10-19T16:04:31Z", "accepted_at": "2026-10-20T05:28:21Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001730970419199163702737999999999999999999999900000000000", "kappa_fraction": "17309704191991637027379999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 230, "source_index": 385, "at": "2026-10-19T16:04:31Z", "until": "2026-10-19T17:39:08.711408Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001730970419199163702738", "dashboard_float_text": "0.0017309704191991637", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4085", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 271, "source_index": null, "at": "2026-10-19T16:04:31Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001730970419199163702738", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4085", "evidence_excerpt": "Conditional \u03ba = 0.001730970419199163702738 (+1.614e-7 over #4076): receiver sharing on the staged T360 supplier", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "23/10000", "status": "Maintainer-reviewed conditional productive-helper construction; see integration receipt for publication state", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier4359.json", "path": "certificates/checkpoints/frontier4359.json", "commit": null, "at": null, "scope": "Productive-helper p3 construction under retained analytic decomposition, exact recovery, native ordered movement, fixed-tape execution, fine-prime padding and gauge-free outer estimates. Changed interfaces reviewed with AI assistance; no formal or independent human verification of the full theorem. Winning uniform templates are algorithm-defined, not materialized. Frozen claim publication booleans describe submission time. Unrelated H-branch research is not selected." }, { "stream": "all_selected_result_history", "record_kappa": "60403/20000000", "status": "Selected maintainer-reviewed conditional joint-helper construction; source-bound foundation reuse is explicit", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/4f19cedcd8d81e4a2359449309fa6e9f17dfd22e/certificates/selected-result.json", "path": null, "commit": "4f19cedcd8d81e4a2359449309fa6e9f17dfd22e", "at": "2026-10-22T12:16:48Z", "scope": "Maintainer-reviewed conditional PR4470 construction. Inherited native/all-column, owned-erasure, whole-job, compiler, precision/tape, analytic, prime and recovery hypotheses remain. Uniform words are not materialized." }, { "stream": "all_selected_result_history", "record_kappa": "23/10000", "status": "Maintainer-reviewed conditional productive-helper construction; see integration receipt for publication state", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/ae87507c0767c00f5a55ee9062c496191e978632/certificates/selected-result.json", "path": null, "commit": "ae87507c0767c00f5a55ee9062c496191e978632", "at": "2026-10-21T19:10:46Z", "scope": "Productive-helper p3 construction under retained analytic decomposition, exact recovery, native ordered movement, fixed-tape execution, fine-prime padding and gauge-free outer estimates. Changed interfaces reviewed with AI assistance; no formal or independent human verification of the full theorem. Winning uniform templates are algorithm-defined, not materialized. Frozen claim publication booleans describe submission time. Unrelated H-branch research is not selected." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 12, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/kappa-next-regime/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/kappa-boundary-continuation/native-boundary/evidence/UNIFORM81-NATIVE.json.gz, research/kappa-global-continuation/helper-consumer/evidence/UNIPOTENT-PROGRAMS-base.json.gz, research/kappa-global-continuation/helper-consumer/evidence/UNIPOTENT-PROGRAMS-extra.json.gz). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/kappa-next-regime/CLAIM.json#/ and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/kappa-next-regime/CLAIM.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/4085-manifest.json", "sha256": "cc62cd453294c5d1d57304771c2a87468bd2f90cfc524f026d22abbfecf22810" }, { "file": "remaining-record-audit/artifacts/4085/priority-manifest.json", "sha256": "80164cf51155841cda21c6e271103d03d7133f86dd5d068bb7fd25daa5261f25" } ], "source_head": "c5854c77620723aae6914c32122870519a6f820d" } }, { "pr": 4088, "title": "Improve conditional \u03ba with a mixed fourth staged entry (+8.696e-9)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4088", "author": "1337isnot1337", "created_at": "2026-10-19T16:52:08Z", "accepted_at": "2026-10-20T05:28:21Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001730979115670792472759999999999999999999999900000000000", "kappa_fraction": "17309791156707924727599999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 231, "source_index": 386, "at": "2026-10-19T17:39:08.711408Z", "until": "2026-10-19T20:17:28Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001730979115670792472760", "dashboard_float_text": "0.0017309791156707925", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4088", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 272, "source_index": null, "at": "2026-10-19T17:39:08.711408+00:00", "until": null, "date_basis": "observed_revision", "fraction": null, "value_decimal": "0.001730979115670792472760", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4088", "evidence_excerpt": "Under the retained transfer hypotheses and padding convention, the conditional endpoint is `\u03ba = 0.001730979115670792472760 \u2212 10^-46 \u2212 10^-70`. It exceeds #4085's certified upper endpoint by more than `8.696471628770020 \u00d7 10^-9`.", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "23/10000", "status": "Maintainer-reviewed conditional productive-helper construction; see integration receipt for publication state", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier4359.json", "path": "certificates/checkpoints/frontier4359.json", "commit": null, "at": null, "scope": "Productive-helper p3 construction under retained analytic decomposition, exact recovery, native ordered movement, fixed-tape execution, fine-prime padding and gauge-free outer estimates. Changed interfaces reviewed with AI assistance; no formal or independent human verification of the full theorem. Winning uniform templates are algorithm-defined, not materialized. Frozen claim publication booleans describe submission time. Unrelated H-branch research is not selected." }, { "stream": "all_selected_result_history", "record_kappa": "60403/20000000", "status": "Selected maintainer-reviewed conditional joint-helper construction; source-bound foundation reuse is explicit", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/4f19cedcd8d81e4a2359449309fa6e9f17dfd22e/certificates/selected-result.json", "path": null, "commit": "4f19cedcd8d81e4a2359449309fa6e9f17dfd22e", "at": "2026-10-22T12:16:48Z", "scope": "Maintainer-reviewed conditional PR4470 construction. Inherited native/all-column, owned-erasure, whole-job, compiler, precision/tape, analytic, prime and recovery hypotheses remain. Uniform words are not materialized." }, { "stream": "all_selected_result_history", "record_kappa": "23/10000", "status": "Maintainer-reviewed conditional productive-helper construction; see integration receipt for publication state", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/ae87507c0767c00f5a55ee9062c496191e978632/certificates/selected-result.json", "path": null, "commit": "ae87507c0767c00f5a55ee9062c496191e978632", "at": "2026-10-21T19:10:46Z", "scope": "Productive-helper p3 construction under retained analytic decomposition, exact recovery, native ordered movement, fixed-tape execution, fine-prime padding and gauge-free outer estimates. Changed interfaces reviewed with AI assistance; no formal or independent human verification of the full theorem. Winning uniform templates are algorithm-defined, not materialized. Frozen claim publication booleans describe submission time. Unrelated H-branch research is not selected." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/staged544-mixed-fourth-entry/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/staged544-mixed-fourth-entry/PROOF.md, research/staged544-mixed-fourth-entry/README.md, research/staged544-mixed-fourth-entry/RESULT.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/staged544-mixed-fourth-entry/PROOF.md, research/staged544-mixed-fourth-entry/README.md, research/staged544-mixed-fourth-entry/RESULT.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/4088-manifest.json", "sha256": "c18a9cd9ef99061b198ce241288de214bfba413795b3d0517ca82b0b576c8f16" }, { "file": "remaining-record-audit/artifacts/4088/priority-manifest.json", "sha256": "19206d97e8671109e41c94723d4fe2ebb0125aab1867c815355f7bf50472b27d" } ], "source_head": "72d7efc181edb21806a878f174847c96dd410ab0" } }, { "pr": 4094, "title": "Research: independent replay of the PR2972 stock margin table with tie-out and sensitivity facts (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4094", "author": "petalas", "created_at": "2026-10-19T18:13:16Z", "accepted_at": "2026-10-20T05:28:21Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001672660197076918", "kappa_fraction": "836330098538459/500000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "individual-primary-interface-source/4094-manifest.json", "sha256": "f9bc3f0c74ab411fecf0a7615c5a9102e2e3e079a0c24563f5680847d8452a95" }, { "file": "remaining-record-audit/artifacts/4094/priority-manifest.json", "sha256": "48dcbfdf132e11bcbfe5e763436682431b4422920a1f80ce9d1a58921c46f917" } ], "source_head": "fd58efb1646ea0d350f1f50057f9a05b4923c99c" } }, { "pr": 4100, "title": "Propose unconditional \u03ba = 0.00173097911567079247276057 via batched CRT", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4100", "author": "1337isnot1337", "created_at": "2026-10-19T20:17:28Z", "accepted_at": "2026-10-20T05:28:21Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00173097911567079247276057", "kappa_fraction": "173097911567079247276057/100000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "scope-flagged", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "current_chart_frontier", "stream_row": 273, "source_index": null, "at": "2026-10-19T20:17:28Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00173097911567079247276057", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4100", "evidence_excerpt": "Propose unconditional \u03ba = 0.00173097911567079247276057 via batched CRT", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Read the exact event-specific objection/model flags [{'pr': 4100, 'category': 'unreviewed_unconditional_claim', 'recommended_treatment': 'Label proposed unconditional theorem as author-submitted, archived and scientifically unreviewed; never describe it as an accepted unconditional record.', 'quarantine_from_screened_TM_record_series': False, 'event_rule': 'The documented claim/mechanism at the pinned head; later repaired constructions require their own source-bound evidence.', 'reason': 'The canonical ledger states archive-only merger, no independent scientific replay, and no admission of supplier, outer theorem or improved kappa. An unconditional title is not itself mathematical acceptance.', 'primary_url': 'https://github.com/CrocSwap/integer-mult-bounds/pull/4100', 'ledger_url': 'https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/docs/research/pr-ledger.json', 'ledger_evidence_pr': 4100, 'documented_question': 'Independent scientific review and source-bound replay remain open. Archival publication does not admit a supplier, outer theorem or improved kappa.', 'documented_scopes': [{'head': '337d04939571a637aeab54a0f58f54fde811663a', 'evidence': 'docs/research/pr-intake-decisions.json', 'scope': 'Exact Git inventory/modes, Python/JSON syntax and available declared source pins checked. Author scientific evidence not independently replayed.', 'kind': 'integration_or_partial_review'}]}] against this own head; neither positive title nor an unrelated repaired revision settles record validity.", "Adjudicate the actual own contribution/selected candidate from research/unconditional-batched-crt/PROOF.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/unconditional-batched-crt/BIT-PRIME-CERTIFICATE.json, research/unconditional-batched-crt/PROOF.md, research/unconditional-batched-crt/README.md). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/unconditional-batched-crt/BIT-PRIME-CERTIFICATE.json, research/unconditional-batched-crt/PROOF.md, research/unconditional-batched-crt/README.md) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/4100-manifest.json", "sha256": "986bbcc6b6569909d099cf10a2c371bdb47bbb41549b5901ccef55210415efc5" }, { "file": "remaining-record-audit/artifacts/4100/priority-manifest.json", "sha256": "c250ed6ace2c0144ab78d090de00426eedcecd80ecb8672e127e939f5d6a3804" } ], "source_head": "337d04939571a637aeab54a0f58f54fde811663a" } }, { "pr": 4181, "title": "Conditional \u03ba = 0.001730980255989036959962 (+1.140e-9 over #4088): one-third fourth-entry fill attaining #4091's pooled ceiling", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4181", "author": "rohanarun", "created_at": "2026-10-20T11:22:58Z", "accepted_at": "2026-10-21T19:10:56Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001730980255989036959961999999999999999999999900000000000", "kappa_fraction": "17309802559890369599619999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 232, "source_index": 388, "at": "2026-10-20T11:22:58Z", "until": "2026-10-21T10:29:12.471680Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.001730980255989036959962", "dashboard_float_text": "0.001730980255989037", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4181", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 274, "source_index": null, "at": "2026-10-20T11:22:58Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.001730980255989036959962", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4181", "evidence_excerpt": "Conditional \u03ba = 0.001730980255989036959962 (+1.140e-9 over #4088): one-third fourth-entry fill attaining #4091's pooled ceiling", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/staged544-pooled-ceiling-fill/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/staged544-pooled-ceiling-fill/README.md, research/staged544-pooled-ceiling-fill/RESULT.json, research/staged544-pooled-ceiling-fill/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/staged544-pooled-ceiling-fill/README.md, research/staged544-pooled-ceiling-fill/RESULT.json, research/staged544-pooled-ceiling-fill/SOURCES.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/4181-manifest.json", "sha256": "f2da758c921fdb006cba7ca426c5f5004ccdcf35faa0dd8baa85aa3493cba177" }, { "file": "remaining-record-audit/artifacts/4181/priority-manifest.json", "sha256": "a7c8d1df4bae319bc8b8e3b88b2b6f46af1620b8890d1ab1e26f574baf0fca1a" } ], "source_head": "4ed92bed95dd483f5662e98ef246b258c3cfe64f" } }, { "pr": 4359, "title": "Conditional \u03ba = 0.0023 (+5.690e-4, +32.87% over #4181): productive helper jobs compiled into a uniform supplier", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4359", "author": "zxv", "created_at": "2026-10-21T14:30:08Z", "accepted_at": "2026-10-21T19:10:56Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0023", "kappa_fraction": "23/10000", "kappa_status": "authenticated_earlier_conditional_source", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews. The crossover upper uses a weaker intermediate exponent before returning to the original record algorithm in its certified tail.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^276540184358-2^69)", "plot_triple_log": { "log2_of_integer": "276540184358", "negligible_negative_correction": true }, "source": "data/operation-audit/literal-feasibility-refinement-v5.json", "scope": "Unreduced PR4359 own p3 dense-complex-core realization when active; identical fixed optimized GMP reference when inactive. A whole field of at least2^N coefficients and at leastone retained p3 native unit are required.", "statistic": "Earliest input length at which some correct member of this family strictly beats the reference", "exact_individual_crossing": false, "all_PR4470_implementations": false, "full_upper_transferred": false }, "conditional_upper": { "input_bits": "2^(2^27664107384514198908)", "log2log2_input_bits": "27664107384514198908", "plot_triple_log": { "exact_log2log2_integer": "27664107384514198908" }, "source": "data/operation-audit/pr4359-crossover-retuned-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": "A separately counted realization of this own-source supplier under retained native/analytic contracts. A sufficient upper, not an actual crossing." }, "cost_status": "conditional_literal_family_range", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "historical_selected_or_reviewed_conditional_checkpoint_source", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 233, "source_index": 390, "at": "2026-10-21T14:30:08Z", "until": "2026-10-21T16:47:54Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.0023", "dashboard_float_text": "0.0023", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4359", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 275, "source_index": null, "at": "2026-10-21T14:30:08Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.0023", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4359", "evidence_excerpt": "Conditional \u03ba = 0.0023 (+5.690e-4, +32.87% over #4181): productive helper jobs compiled into a uniform supplier", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 549, "source_index": null, "at": "2026-10-21T14:30:08Z", "until": null, "date_basis": "body-version", "fraction": "23/10000", "value_decimal": "0.0023", "dashboard_float_text": null, "expression": "0.0023", "historical_title": "Conditional \u03ba = 0.0023 (+5.690e-4, +32.87% over #4181): productive helper jobs compiled into a uniform supplier", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4359", "evidence_excerpt": "existence result, not a\npractical algorithm.\n\n## Result\n\n\nT(n)=O\\left(n(\\log n)^(1-\u03ba)\\right),\\qquad \u03ba=0.0023.\n\n\n| Reference point | \u03ba | Gain from this PR |\n|---|---:|---:|\n| [#1094](https://github.com/CrocSwap/integer-mult-bounds/pull/1094), selected frontier (maintainer-reviewed) | 0.00", "automated_comparable": true, "body_sha256": "5853caae93d18bd12583c35ac12a4c642ffdc56f06849b4bbfb68ad9aca533a9" } ], "reviewed_checkpoint_associations": [ { "stream": "all_current_checkpoint_json", "record_kappa": "23/10000", "status": "Maintainer-reviewed conditional productive-helper construction; see integration receipt for publication state", "role": "first_listed_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/7c472563474e60185e6ca101a17622133d047e56/certificates/checkpoints/frontier4359.json", "path": "certificates/checkpoints/frontier4359.json", "commit": null, "at": null, "scope": "Productive-helper p3 construction under retained analytic decomposition, exact recovery, native ordered movement, fixed-tape execution, fine-prime padding and gauge-free outer estimates. Changed interfaces reviewed with AI assistance; no formal or independent human verification of the full theorem. Winning uniform templates are algorithm-defined, not materialized. Frozen claim publication booleans describe submission time. Unrelated H-branch research is not selected." }, { "stream": "all_selected_result_history", "record_kappa": "60403/20000000", "status": "Selected maintainer-reviewed conditional joint-helper construction; source-bound foundation reuse is explicit", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/4f19cedcd8d81e4a2359449309fa6e9f17dfd22e/certificates/selected-result.json", "path": null, "commit": "4f19cedcd8d81e4a2359449309fa6e9f17dfd22e", "at": "2026-10-22T12:16:48Z", "scope": "Maintainer-reviewed conditional PR4470 construction. Inherited native/all-column, owned-erasure, whole-job, compiler, precision/tape, analytic, prime and recovery hypotheses remain. Uniform words are not materialized." }, { "stream": "all_selected_result_history", "record_kappa": "23/10000", "status": "Maintainer-reviewed conditional productive-helper construction; see integration receipt for publication state", "role": "first_listed_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/ae87507c0767c00f5a55ee9062c496191e978632/certificates/selected-result.json", "path": null, "commit": "ae87507c0767c00f5a55ee9062c496191e978632", "at": "2026-10-21T19:10:46Z", "scope": "Productive-helper p3 construction under retained analytic decomposition, exact recovery, native ordered movement, fixed-tape execution, fine-prime padding and gauge-free outer estimates. Changed interfaces reviewed with AI assistance; no formal or independent human verification of the full theorem. Winning uniform templates are algorithm-defined, not materialized. Frozen claim publication booleans describe submission time. Unrelated H-branch research is not selected." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "uniform_rank_H": "276540184361", "tensor_power": 1, "fresh_arithmetic_replay_status": "PASS_SOURCE_CENSUS_ONLY", "replay_receipt": "data/operation-audit/pr4359-literal-work-lower.json", "early_effective_kappa": "1/500", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 0, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [], "source_head": "da637c87c89482bc4c86be36bd0071b3d400dbed" } }, { "pr": 4171, "title": "Independent numerical cross-check of PR4100's exact-root and paid-power ledger (finite layer; no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4171", "author": "petalas", "created_at": "2026-10-20T08:05:51Z", "accepted_at": "2026-10-21T19:22:10Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00173097911567079247276057", "kappa_fraction": "173097911567079247276057/100000000000000000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "individual-primary-interface-source/4171-manifest.json", "sha256": "6a2995408322631cd06d7a4988d58e97bb591b629e00f5c81e67cbcb80f122a2" }, { "file": "remaining-record-audit/artifacts/4171/priority-manifest.json", "sha256": "d50e5de5c26eb2322ef8291b5f85723f6f3bb20887abe20b575fd2fc00985e6c" } ], "source_head": "a3be6becf547c5c7657446843b59fdb50e655eac" } }, { "pr": 4332, "title": "Independently check #4270's conservative \u03ba = 1/580 exponent chain: every link holds (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4332", "author": "pinterbanget", "created_at": "2026-10-21T10:08:08Z", "accepted_at": "2026-10-21T19:24:10Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001724137931034482758620689655172413793103448275862068966", "kappa_fraction": "1/580", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No independent whole-multiplier cutoff is defined by this supplied contribution. Price the explicitly referenced complete algorithm only after binding its actual native/operator, ownership, recursive invoice, precision and outer parameters. Relevant local constants, guards and negative hypotheses remain attached to that target; they are not discarded." ], "source_manifest": [ { "file": "individual-primary-interface-source/4332-manifest.json", "sha256": "972c4dd4634b5f2ac75e69fdedf2a93fcc782303a4441f10ce0e3d3a889eb071" }, { "file": "remaining-record-audit/artifacts/4332/priority-manifest.json", "sha256": "4d7debdea96da981fc7c1f9c79421a41d42c3a712e0c68f5a868d7e34bcd9d6a" } ], "source_head": "07e6aada1f07d191d9d467c5aee46ffdc74dd51c" } }, { "pr": 4270, "title": "Complete pooled complex admission and conditional \u03ba = 1/580 transfer", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4270", "author": "RossRichardson", "created_at": "2026-10-20T22:54:44Z", "accepted_at": "2026-10-21T19:24:12Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.001724137931034482758620689655172413793103448275862068966", "kappa_fraction": "1/580", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/pooled-native-hosting-admission/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/complex-pooled-full-admission/evidence/RESULT.json, research/complex-pooled-full-admission/frozen/pr4181/RESULT.json, research/pooled-native-hosting-admission/NATIVE-PINS.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/complex-pooled-full-admission/evidence/RESULT.json, research/complex-pooled-full-admission/frozen/pr4181/RESULT.json, research/pooled-native-hosting-admission/NATIVE-PINS.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/complex-pooled-full-admission/evidence/ASSEMBLY.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/4270-manifest.json", "sha256": "0bb340827028a8efa3edca4899abba116343b8274b5d5094d426db3d9842e52f" }, { "file": "remaining-record-audit/artifacts/4270/priority-manifest.json", "sha256": "f42335204013d3e47468a62f847f416433b0fdfeca429a93117c82fb0ba8a828" } ], "source_head": "5913291c421e851fb5cfb90bc61760a4e58a28ba" } }, { "pr": 4411, "title": "Reduce conditional \u03ba = 0.0023 template ranks to 2^465000 and 2^7100", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4411", "author": "zxv", "created_at": "2026-10-21T17:06:56Z", "accepted_at": "2026-10-21T19:27:51Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0023", "kappa_fraction": "23/10000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^464997-2^69)", "plot_triple_log": { "log2_of_integer": "464997", "negligible_negative_correction": true }, "scope": "Own complete unreduced p3 native/controller boundary on full fields/spectators at positive column multiplicity when active, width at least two; identical optimized GMP when inactive.", "statistic": "Earliest possible strict win in the declared literal enhancement family", "exact_individual_crossing": false, "all_PR_implementations": false, "source": "data/operation-audit/pr4411-p3-refined-literal-lower.json" }, "conditional_upper": { "input_bits": "2^(2^1838703753540147)", "log2log2_input_bits": "1838703753540147", "plot_triple_log": { "exact_log2log2_integer": "1838703753540147" }, "source": "data/operation-audit/pr4411-p3-refined-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own exported p3 raw native arbitrary-input required-boundary/all-column/absolute-phase/Clifford identities and clean-owned/full-spectator semantics; type/census component bound, not a fresh native operator proof.", "Own new uniform-rank theorem and complete chronological integer compiler with ready barriers, separate role arrays and actual child/complement endpoints.", "Concrete normalized Gaussian/finite-LDU/narrow-gap/cyclic-border/fine-prime/exact-recovery interfaces and fixed repaired reference correctness/finite-kernel halting." ] }, "cost_status": "conditional_own_source_range", "own_source_cost_extension": true, "early_effective_kappa": "1/500", "own_source_scope": [ "Own exported p3 raw native arbitrary-input required-boundary/all-column/absolute-phase/Clifford identities and clean-owned/full-spectator semantics; type/census component bound, not a fresh native operator proof.", "Own new uniform-rank theorem and complete chronological integer compiler with ready barriers, separate role arrays and actual child/complement endpoints.", "Concrete normalized Gaussian/finite-LDU/narrow-gap/cyclic-border/fine-prime/exact-recovery interfaces and fixed repaired reference correctness/finite-kernel halting." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr4411-p3-refined-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/4411/priority-manifest.json", "sha256": "f13a53de025de938845ac6d1d8109e04851c1ea41d51d1efcd1e726562767971" } ], "source_head": "ec2c9505d863c7f5f2a5f08628e8ee6fb740c0a7" } }, { "pr": 4420, "title": "Independently check #4416's moment and paid-tail inequalities at \u03ba = 0.00268647: all hold; the tested saving sits 9.05e-9 below this invoice's limit (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4420", "author": "pinterbanget", "created_at": "2026-10-21T17:44:08Z", "accepted_at": "2026-10-21T19:27:51Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00268647", "kappa_fraction": "268647/100000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No independent whole-multiplier cutoff is defined by this supplied contribution. Price the explicitly referenced complete algorithm only after binding its actual native/operator, ownership, recursive invoice, precision and outer parameters. Relevant local constants, guards and negative hypotheses remain attached to that target; they are not discarded." ], "source_manifest": [ { "file": "individual-primary-interface-source/4420-manifest.json", "sha256": "f533a4d5d853515b88d101b252419a7767f47c3f18ee890f2fde48f991d88c89" }, { "file": "remaining-record-audit/artifacts/4420/priority-manifest.json", "sha256": "164b387e8f5601de75a225136c48153f5ef7c922e50efa6997b16312322b54c9" } ], "source_head": "64b4f5457613ada7f0e3f2f4d26f9978d19cdfa7" } }, { "pr": 4422, "title": "Independently check #4412's and #4414's strictification inequalities: all hold; each tested saving sits within 1e-8 of its invoice's limit (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4422", "author": "pinterbanget", "created_at": "2026-10-21T17:51:41Z", "accepted_at": "2026-10-21T19:27:51Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00247755", "kappa_fraction": "49551/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No independent whole-multiplier cutoff is defined by this supplied contribution. Price the explicitly referenced complete algorithm only after binding its actual native/operator, ownership, recursive invoice, precision and outer parameters. Relevant local constants, guards and negative hypotheses remain attached to that target; they are not discarded." ], "source_manifest": [ { "file": "individual-primary-interface-source/4422-manifest.json", "sha256": "2cdff214f0301780580ddc99ee4e01295d0b35f67369a2f2eef9bd152272346f" }, { "file": "remaining-record-audit/artifacts/4422/priority-manifest.json", "sha256": "2c9a3e82920c05d95a474e08106771b23b2bbe3f36987584ef7817cae7d6c9f5" } ], "source_head": "6977b9f52c8632d066b0d649f2a6280c5a96185e" } }, { "pr": 4425, "title": "Independently review #4411's logarithmic majorant: proof holds, arithmetic certified, least ranks slightly below stated, exact L(N) <= F(N) to N = 6000 (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4425", "author": "pinterbanget", "created_at": "2026-10-21T18:03:26Z", "accepted_at": "2026-10-21T19:27:51Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0023", "kappa_fraction": "23/10000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "individual-primary-interface-source/4425-manifest.json", "sha256": "6b7d51e41654dd1a746095da1e033b4ddf89250da9f93180f125d3b04d09de57" }, { "file": "remaining-record-audit/artifacts/4425/priority-manifest.json", "sha256": "649e6639ef6e2c96a07bee6c2ea94e31a82b6e52eebe78565aa27c9c11210a9e" } ], "source_head": "76613f8d29b664e386f29f30153f74087f462953" } }, { "pr": 4428, "title": "Independently check #4416's paid-completion tensor bound at kappa 0.00268647: proof steps and arithmetic hold; gamma margin 8e-6; least v 5745 (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4428", "author": "pinterbanget", "created_at": "2026-10-21T18:07:37Z", "accepted_at": "2026-10-21T19:27:51Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00268647", "kappa_fraction": "268647/100000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/4428-manifest.json", "sha256": "73a5f93ff357d08823ce6359e72dfac90d426631aae5c3a605664607d910d139" }, { "file": "remaining-record-audit/artifacts/4428/priority-manifest.json", "sha256": "a664bcb057fcd8a06141becebd7895d7a4871fa9715ae97db08188013cf6ec0a" } ], "source_head": "ba0efeaac4e62d1757d7a9be6fd8aaf8f9bd35dc" } }, { "pr": 4429, "title": "Independently check the #4412 and #4414 tensor endpoints: alpha/gamma bounds and ranks hold; least tensor powers 10,714 and 60,701 (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4429", "author": "pinterbanget", "created_at": "2026-10-21T18:10:38Z", "accepted_at": "2026-10-21T19:27:51Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00247755", "kappa_fraction": "49551/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "individual-primary-interface-source/4429-manifest.json", "sha256": "9912a60bc8a92b0ab466be56a89394cfbc066bf44172d02b660443566d07298f" }, { "file": "remaining-record-audit/artifacts/4429/priority-manifest.json", "sha256": "b66a60ec0f87e51989b0306ecb1078831d2c971fff8c4f07f547a5403a541bf8" } ], "source_head": "40f675338b7102ec38d858355a1db6cc051778e7" } }, { "pr": 4433, "title": "Reduce p7 tensor power and uniform-rank exponent (41.6\u00d7 and 46.38M\u00d7)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4433", "author": "zxv", "created_at": "2026-10-21T18:46:58Z", "accepted_at": "2026-10-21T19:27:51Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00268647", "kappa_fraction": "268647/100000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^349299999997-2^69)", "plot_triple_log": { "log2_of_integer": "349299999997", "negligible_negative_correction": true }, "scope": "Own complete unreduced p7 boundary/native word when active, width at least two, strict winning uniform supplier at its stated H; identical optimized GMP when inactive.", "statistic": "Earliest input width at which a correct member of this literal enhancement family strictly beats the reference", "source": "data/operation-audit/pr4433-literal-boundary-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "conditional_upper": null, "cost_status": "conditional_own_source_lower_only", "own_source_cost_extension": true, "early_effective_kappa": null, "own_source_scope": "Own complete unreduced p7 boundary/native word when active, width at least two, strict winning uniform supplier at its stated H; identical optimized GMP when inactive. This source has no newly derived sufficient upper. The exact first crossing remains unknown.", "own_source_record_tail_quantified": false, "own_source_certificate": "pr4433-literal-boundary-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 6, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/4433/priority-manifest.json", "sha256": "64ec219e9cac89bdb7d8ebe5f8322f24ca2fcf62bfafb10f5ed70bd3600299a8" } ], "source_head": "b84060c9cba91b1e76f84617a877d259621eb015" } }, { "pr": 4405, "title": "Refine PR4359: conditional \u03ba = 0.00230509 and smaller explicit template ranks", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4405", "author": "1337isnot1337", "created_at": "2026-10-21T16:47:54Z", "accepted_at": "2026-10-21T19:27:52Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00230509", "kappa_fraction": "230509/100000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^2099384703303215706-2^69)", "plot_triple_log": { "log2_of_integer": "2099384703303215706", "negligible_negative_correction": true }, "scope": "Own complete unreduced p3 native/controller boundary on full fields/spectators at positive column multiplicity when active, width at least two; identical optimized GMP when inactive.", "statistic": "Earliest possible strict win in the declared literal enhancement family", "exact_individual_crossing": false, "all_PR_implementations": false, "source": "data/operation-audit/pr4405-p3-refined-literal-lower.json" }, "conditional_upper": { "input_bits": "2^(2^210001456071982263781151649)", "log2log2_input_bits": "210001456071982263781151649", "plot_triple_log": { "exact_log2log2_integer": "210001456071982263781151649" }, "source": "data/operation-audit/pr4405-p3-refined-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own exported p3 raw native arbitrary-input required-boundary/all-column/absolute-phase/Clifford identities and clean-owned/full-spectator semantics; type/census component bound, not a fresh native operator proof.", "Own new uniform-rank theorem and complete chronological integer compiler with ready barriers, separate role arrays and actual child/complement endpoints.", "Concrete normalized Gaussian/finite-LDU/narrow-gap/cyclic-border/fine-prime/exact-recovery interfaces and fixed repaired reference correctness/finite-kernel halting." ] }, "cost_status": "conditional_own_source_range", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 234, "source_index": 391, "at": "2026-10-21T16:47:54Z", "until": "2026-10-21T17:07:37Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.00230509", "dashboard_float_text": "0.00230509", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4405", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 276, "source_index": null, "at": "2026-10-21T16:47:54Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00230509", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4405", "evidence_excerpt": "Refine PR4359: conditional \u03ba = 0.00230509 and smaller explicit template ranks", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 550, "source_index": null, "at": "2026-10-21T16:47:54Z", "until": null, "date_basis": "body-version", "fraction": "230509/100000000", "value_decimal": "0.00230509", "dashboard_float_text": null, "expression": "0.00230509", "historical_title": "Refine PR4359: conditional \u03ba = 0.00230509 and smaller explicit template ranks", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4405", "evidence_excerpt": " below the unchanged mixed root (the endpoint itself is not claimed). The concrete checked point is \u03ba = 0.00230509, versus #4359's 0.0023.\n- Replace the compiler's coarse eta > 1/4 / exit <= 1/8 estimate by its actual complement coefficient. At the original supplier savings, the specified comp", "automated_comparable": true, "body_sha256": "db70ddc5cd187e210125d51313f51b7b89f4256fcbfc0713c72b15f2ae01323b" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/500", "own_source_scope": [ "Own exported p3 raw native arbitrary-input required-boundary/all-column/absolute-phase/Clifford identities and clean-owned/full-spectator semantics; type/census component bound, not a fresh native operator proof.", "Own new uniform-rank theorem and complete chronological integer compiler with ready barriers, separate role arrays and actual child/complement endpoints.", "Concrete normalized Gaussian/finite-LDU/narrow-gap/cyclic-border/fine-prime/exact-recovery interfaces and fixed repaired reference correctness/finite-kernel halting." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr4405-p3-refined-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/4405/priority-manifest.json", "sha256": "d887aacfc3f79bb1261b7b0dd5f6a6b3d8869e127b67bd3bab3cb1c33675275a" } ], "source_head": "873d1b3c96a83b701a5c0bba8e37a861e6672fef" } }, { "pr": 4410, "title": "Independently check #4405's refined #4359 ranks and endpoint family: all reproduce; z0 and the exit constant are not levers, the uniform saving is (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4410", "author": "pinterbanget", "created_at": "2026-10-21T17:06:17Z", "accepted_at": "2026-10-21T19:27:52Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00230509", "kappa_fraction": "230509/100000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. 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This contribution pays to enlarge small productive transforms after tensor composition, raising the conditional multiplication saving to **\u03ba = 0.00268647**, from #4359's 0.0023.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 553, "source_index": null, "at": "2026-10-21T17:26:52Z", "until": null, "date_basis": "body-version", "fraction": "268647/100000000", "value_decimal": "0.00268647", "dashboard_float_text": null, "expression": "0.00268647", "historical_title": "Conditional \u03ba = 0.00268647 via paid target padding after native composition", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4416", "evidence_excerpt": "ll productive transforms after tensor composition, raising the conditional multiplication saving to \u03ba = 0.00268647, from #4359's 0.0023.\n\nThe exact p7/keep232127 controller is regenerated from authenticated source code, then physically audited on 121 axes. All 6,720 contacts and inverses, 1,56", "automated_comparable": true, "body_sha256": "769e25b152f87c499561f0f445d187e00be5e5634a9efd6e4ed6fb749706ac1f" } ], "reviewed_checkpoint_associations": [ { "stream": "all_selected_result_history", "record_kappa": "60403/20000000", "status": "Selected maintainer-reviewed conditional joint-helper construction; source-bound foundation reuse is explicit", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/4f19cedcd8d81e4a2359449309fa6e9f17dfd22e/certificates/selected-result.json", "path": null, "commit": "4f19cedcd8d81e4a2359449309fa6e9f17dfd22e", "at": "2026-10-22T12:16:48Z", "scope": "Maintainer-reviewed conditional PR4470 construction. Inherited native/all-column, owned-erasure, whole-job, compiler, precision/tape, analytic, prime and recovery hypotheses remain. Uniform words are not materialized." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "uniform_rank_H": "16201843136005340321", "tensor_power": 1, "early_effective_kappa": "1/500", "claim_type": "reviewed_checkpoint_conditional_source", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 0, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [], "source_head": "e9058860b5c850760fdf970e796a96aefcdb1d98" } }, { "pr": 4488, "title": "Bound one tensor axis by two section errors (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4488", "author": "jwr404", "created_at": "2026-10-22T01:22:35Z", "accepted_at": "2026-10-22T02:49:05Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0023", "kappa_fraction": "23/10000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain the exact stated lemma, finite-audit scope, correction or provenance with its actual selected target. A numerical runtime bound requires an actual source-selected full native/owner/recursive invoice/precision/outer realization and exact own commitments. No cutoff follows from unchanged kappa, a scalar lemma or an audit pass." ], "source_manifest": [ { "file": "individual-primary-interface-source/4488-manifest.json", "sha256": "6ff94383f7a35632c6ae69b13987aedd868128373df155352919bc34373906c1" }, { "file": "remaining-record-audit/artifacts/4488/priority-manifest.json", "sha256": "010edb440527ac909e3b7ff6a65279b3d5a2bd77113c5f03f33f12f5f55a1df3" } ], "source_head": "50264f24b5f94ebbcc92364e279c6e232d5978d9" } }, { "pr": 4501, "title": "Independently audit cross-cell rounding and inverse bounds (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4501", "author": "mihir-s-05", "created_at": "2026-10-22T02:28:21Z", "accepted_at": "2026-10-22T02:49:05Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0023", "kappa_fraction": "23/10000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "individual-primary-interface-source/4501-manifest.json", "sha256": "8b720259a382c78b9ad010c865a4aa34e0d6d38ba4e5c6951d5c6ad7d1a726fd" }, { "file": "remaining-record-audit/artifacts/4501/priority-manifest.json", "sha256": "5feb0deb635413b6e96e6840a4fe6dfa49ddc8334cac81709ef4b9823274fad8" } ], "source_head": "5fad1d2e9ae4e1ac269a812b024c9c53024603ec" } }, { "pr": 4440, "title": "Conditional \u03ba = 0.00296 via query-thinned productive controllers (+10.18%)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4440", "author": "1337isnot1337", "created_at": "2026-10-21T20:08:38Z", "accepted_at": "2026-10-22T02:49:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00296", "kappa_fraction": "37/12500", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews. The crossover upper uses a weaker intermediate exponent before returning to the original record algorithm in its certified tail.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^10418370291022214-2^69)", "plot_triple_log": { "log2_of_integer": "10418370291022214", "negligible_negative_correction": true }, "source": "data/operation-audit/literal-feasibility-refinement-v5.json", "scope": "Own unreduced p7/p17 source core when active; identical fixed optimizedGMP when inactive; complete fields and width>=2.", "statistic": "Earliest input length at which some correct member of this family strictly beats the reference", "exact_individual_crossing": false, "all_PR4470_implementations": false, "full_upper_transferred": false }, "conditional_upper": { "input_bits": "2^(2^1042149602839884152084659)", "log2log2_input_bits": "1042149602839884152084659", "plot_triple_log": { "exact_log2log2_integer": "1042149602839884152084659" }, "source": "data/operation-audit/p7-p17-record-crossover-bounds.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": "A separately counted realization of this own-source supplier under retained native/analytic contracts. A sufficient upper, not an actual crossing." }, "cost_status": "conditional_literal_family_range", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 238, "source_index": 395, "at": "2026-10-21T20:08:38Z", "until": "2026-10-21T20:26:57.968500Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.00296", "dashboard_float_text": "0.00296", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4440", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 280, "source_index": null, "at": "2026-10-21T20:08:38Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00296", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4440", "evidence_excerpt": "The all-native p7 controller pays full stage and idle transforms where a copied rank-one query shear suffices. Replacing those calls, charging the lost productive helpers, and removing the same multipliers from the complete physical word gives a new **author-checked conditional \u03ba = 37/12500 = 0.00296**. This is **10.18% above #4416/#4433's 0.00268647** and 28.70% above the selected 0.0023 checkpoint.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 554, "source_index": null, "at": "2026-10-21T20:08:38Z", "until": null, "date_basis": "body-version", "fraction": "37/12500", "value_decimal": "0.00296", "dashboard_float_text": null, "expression": "37/12500", "historical_title": "Conditional \u03ba = 0.00296 via query-thinned productive controllers (+10.18%)", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4440", "evidence_excerpt": "emoving the same multipliers from the complete physical word gives a new author-checked conditional \u03ba = 37/12500 = 0.00296. This is 10.18% above #4416/#4433's 0.00268647 and 28.70% above the selected 0.0023 checkpoint.\n\nThe complex word has 17 pairs, 19 full native calls and 16 query shears.", "automated_comparable": true, "body_sha256": "f8095dd5972df67b333d474993f5b71299f91b4b879b5aed8cb1b6ed604ff8b8" } ], "reviewed_checkpoint_associations": [ { "stream": "all_selected_result_history", "record_kappa": "60403/20000000", "status": "Selected maintainer-reviewed conditional joint-helper construction; source-bound foundation reuse is explicit", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/4f19cedcd8d81e4a2359449309fa6e9f17dfd22e/certificates/selected-result.json", "path": null, "commit": "4f19cedcd8d81e4a2359449309fa6e9f17dfd22e", "at": "2026-10-22T12:16:48Z", "scope": "Maintainer-reviewed conditional PR4470 construction. Inherited native/all-column, owned-erasure, whole-job, compiler, precision/tape, analytic, prime and recovery hypotheses remain. Uniform words are not materialized." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "uniform_rank_H": "10418370291022217", "tensor_power": 1, "early_effective_kappa": "1/500", "claim_type": "reviewed_checkpoint_conditional_source", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 0, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [], "source_head": "9123d75afea5096d25eb98b2b6080cbbe0d91c01" } }, { "pr": 4446, "title": "Independent retimed p17 certificate: conditional kappa = 0.003001053", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4446", "author": "1337isnot1337", "created_at": "2026-10-21T21:07:29Z", "accepted_at": "2026-10-22T02:49:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.003001053", "kappa_fraction": "3001053/1000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^15026650096742881962198-2^69)", "plot_triple_log": { "log2_of_integer": "15026650096742881962198", "negligible_negative_correction": true }, "scope": "Own selected hybrid supplier with complete unreduced boundary/native word when active, width at least two, whole-field/spectator rank N contract; identical optimized GMP when inactive.", "statistic": "Earliest possible strict win in the specified literal enhancement family", "source": "data/operation-audit/pr4446-hybrid-boundary-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "conditional_upper": null, "cost_status": "conditional_own_source_lower_only", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 240, "source_index": 397, "at": "2026-10-21T21:07:29Z", "until": "2026-10-21T21:14:57Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.003001053", "dashboard_float_text": "0.003001053", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4446", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 282, "source_index": null, "at": "2026-10-21T21:07:29Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.003001053", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4446", "evidence_excerpt": "Independent retimed p17 certificate: conditional kappa = 0.003001053", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 556, "source_index": null, "at": "2026-10-21T21:07:29Z", "until": null, "date_basis": "body-version", "fraction": "3001053/1000000000", "value_decimal": "0.003001053", "dashboard_float_text": null, "expression": "0.003001053", "historical_title": "Independent retimed p17 certificate: conditional kappa = 0.003001053", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4446", "evidence_excerpt": "ently replayed, source-bound conditional certificate for the retimed p17 native/direct controller:\n\n\u03ba = 0.003001053, with exact tested saving 0.003001054.\n\nThis is 11.7099% above #4416's 0.00268647 and 1.3869% above #4440's 0.00296. Updated #4441 independently contains the same complete combine", "automated_comparable": true, "body_sha256": "049d0618eb337d1688be4c9e376747fd0c392a4da39886a17fe4aeff3021a15c" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "3001053/1000000000", "own_source_scope": [ "Own full Laurent/direct/native arbitrary-input identity, required physical entry/output frames, absolute phase and complete all-column whole-job copied/owned/spectator semantics.", "Own strictifying physical native tensor/compiler realization, literal boundary retention, exact source interval enclosures and positive winning uniform supplier at the selected H.", "Fixed repaired optimized-GMP correctness/finite-kernel halting and prescribed unreduced XAG lowering." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr4446-hybrid-boundary-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/4446/priority-manifest.json", "sha256": "0200fe6cae60b08feb2b2ef7c158361390e61e5234e391a6855f1bafea838f99" } ], "source_head": "e2bde8f5b9bfa2e8d51f959656d84ebcc2af81b7" } }, { "pr": 4447, "title": "Conditional kappa = 0.00300123 via a missing three-dimensional contact span", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4447", "author": "1337isnot1337", "created_at": "2026-10-21T21:14:57Z", "accepted_at": "2026-10-22T02:49:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00300123", "kappa_fraction": "300123/100000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews. The crossover upper uses a weaker intermediate exponent before returning to the original record algorithm in its certified tail.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^64215199999997-2^69)", "plot_triple_log": { "log2_of_integer": "64215199999997", "negligible_negative_correction": true }, "source": "data/operation-audit/literal-feasibility-refinement-v5.json", "scope": "Own unreduced p7/p17 source core when active; identical fixed optimizedGMP when inactive; complete fields and width>=2.", "statistic": "Earliest input length at which some correct member of this family strictly beats the reference", "exact_individual_crossing": false, "all_PR4470_implementations": false, "full_upper_transferred": false }, "conditional_upper": { "input_bits": "2^(2^6423448376621603980270)", "log2log2_input_bits": "6423448376621603980270", "plot_triple_log": { "exact_log2log2_integer": "6423448376621603980270" }, "source": "data/operation-audit/p7-p17-record-crossover-bounds.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": "A separately counted realization of this own-source supplier under retained native/analytic contracts. A sufficient upper, not an actual crossing." }, "cost_status": "conditional_literal_family_range", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 241, "source_index": 398, "at": "2026-10-21T21:14:57Z", "until": "2026-10-21T21:38:35Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.00300123", "dashboard_float_text": "0.00300123", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4447", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 283, "source_index": null, "at": "2026-10-21T21:14:57Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00300123", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4447", "evidence_excerpt": "This adjoins one previously uncataloged contact span and carries the resulting native word through the complete conditional transfer to **kappa = 0.00300123**.", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 557, "source_index": null, "at": "2026-10-21T21:14:57Z", "until": null, "date_basis": "body-version", "fraction": "300123/100000000", "value_decimal": "0.00300123", "dashboard_float_text": null, "expression": "0.00300123", "historical_title": "Conditional kappa = 0.00300123 via a missing three-dimensional contact span", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4447", "evidence_excerpt": "ged contact span and carries the resulting native word through the complete conditional transfer to kappa = 0.00300123.\n\nThe increment over #4441 (0.00300105) and #4446 (0.003001053) is small. The new mathematical observation is that a missing three-dimensional span improves a four-dimensional sca", "automated_comparable": true, "body_sha256": "575611a33f938a0a27616aed2f6b4c56271a5035b513ddf0fb6fe10969ec0e0c" } ], "reviewed_checkpoint_associations": [ { "stream": "all_selected_result_history", "record_kappa": "60403/20000000", "status": "Selected maintainer-reviewed conditional joint-helper construction; source-bound foundation reuse is explicit", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/4f19cedcd8d81e4a2359449309fa6e9f17dfd22e/certificates/selected-result.json", "path": null, "commit": "4f19cedcd8d81e4a2359449309fa6e9f17dfd22e", "at": "2026-10-22T12:16:48Z", "scope": "Maintainer-reviewed conditional PR4470 construction. Inherited native/all-column, owned-erasure, whole-job, compiler, precision/tape, analytic, prime and recovery hypotheses remain. Uniform words are not materialized." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "uniform_rank_H": "64215200000000", "tensor_power": 1, "early_effective_kappa": "1/500", "claim_type": "reviewed_checkpoint_conditional_source", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 0, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [], "source_head": "02b51f341013c607dc480248c94c216b8260d8af" } }, { "pr": 4452, "title": "Lower the within-cell halo exponents to 11, 24, 26, 26 and 6 (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4452", "author": "jwr404", "created_at": "2026-10-21T21:36:09Z", "accepted_at": "2026-10-22T02:49:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0023", "kappa_fraction": "23/10000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain the exact stated lemma, finite-audit scope, correction or provenance with its actual selected target. A numerical runtime bound requires an actual source-selected full native/owner/recursive invoice/precision/outer realization and exact own commitments. No cutoff follows from unchanged kappa, a scalar lemma or an audit pass." ], "source_manifest": [ { "file": "individual-primary-interface-source/4452-manifest.json", "sha256": "c5b4ecbb3ee9021e02bf6d388f466fccea1577c37e65f725c7625bcc0a11beb5" }, { "file": "remaining-record-audit/artifacts/4452/priority-manifest.json", "sha256": "78ab8c288e1df4ab67e09a968d386d39e42b4a609d25a6da0b856956376282de" } ], "source_head": "af68f5973a572305af174b3c49c440592172134d" } }, { "pr": 4453, "title": "Conditional \u03ba = 0.00300120 (71.9\u00d7 smaller uniform-rank exponent)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4453", "author": "zxv", "created_at": "2026-10-21T21:38:35Z", "accepted_at": "2026-10-22T02:49:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0030012", "kappa_fraction": "7503/2500000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^2299849999997-2^69)", "plot_triple_log": { "log2_of_integer": "2299849999997", "negligible_negative_correction": true }, "scope": "Own complete unreduced p17 boundary/native word when active, width at least two, strict winning own uniform supplier; identical optimized GMP when inactive.", "statistic": "Earliest input width at which a correct member of this literal enhancement family strictly beats the reference", "source": "data/operation-audit/pr4453-separated-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "conditional_upper": { "input_bits": "2^(2^230055792290424752352)", "log2log2_input_bits": "230055792290424752352", "plot_triple_log": { "exact_log2log2_integer": "230055792290424752352" }, "source": "data/operation-audit/pr4453-separated-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own p17 native arbitrary-input/absolute-phase all-column endpoint and chronological owned return contracts", "Source separated-product/net-tax compiler realizes its strict winning uniform supplier at the stated own H with completed base cases paid", "Complete role fields and spectators, exact per-role Clifford endpoints, barriers and restored owned banks on fixed parent selected axes", "Own source raw nonrecursive allowance below1e9 and expanded whole-job normal-form/adapter interfaces", "Parameterized fine-prime/Gaussian/finite-section/boundary/recovery analytic branch and unchanged fixed XAG/repaired optimized-GMP semantics" ] }, "cost_status": "conditional_own_source_range", "own_source_cost_extension": true, "early_effective_kappa": "1/500", "own_source_scope": [ "Own p17 native arbitrary-input/absolute-phase all-column endpoint and chronological owned return contracts", "Source separated-product/net-tax compiler realizes its strict winning uniform supplier at the stated own H with completed base cases paid", "Complete role fields and spectators, exact per-role Clifford endpoints, barriers and restored owned banks on fixed parent selected axes", "Own source raw nonrecursive allowance below1e9 and expanded whole-job normal-form/adapter interfaces", "Parameterized fine-prime/Gaussian/finite-section/boundary/recovery analytic branch and unchanged fixed XAG/repaired optimized-GMP semantics" ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr4453-separated-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/4453/priority-manifest.json", "sha256": "c0cbc22988b42e79b15210a914767a7d95be2a4be950d0396d566373f7cfeaa4" } ], "source_head": "de6869e2e4d9c6f630bac5de4a919d99a2cb884b" } }, { "pr": 4455, "title": "Independently check the p17 chain #4440, #4441, #4446, #4447, #4453 (kappa 0.00296..0.0030012): invoices, strictification, roots and compiler ranks hold (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4455", "author": "pinterbanget", "created_at": "2026-10-21T22:24:21Z", "accepted_at": "2026-10-22T02:49:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00296", "kappa_fraction": "37/12500", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "individual-primary-interface-source/4455-manifest.json", "sha256": "ac27aca9c8f79afdb15df082188a9d259236e62f43fb008c4af6fbe1907b0c8b" }, { "file": "remaining-record-audit/artifacts/4455/priority-manifest.json", "sha256": "3a43bc3e62530d4be5d2cb6947fd8ebce8594667317df3d5257abb69d8cd91e8" } ], "source_head": "f848f014d4ca9dfc3beef0d4b615b572a7301605" } }, { "pr": 4459, "title": "research: #4436 boundary exits \u2014 exact mirror identity, rigorous share bound 0.321, and a correction (leaf exits dominate)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4459", "author": "pinterbanget", "created_at": "2026-10-21T22:48:10Z", "accepted_at": "2026-10-22T02:49:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.99445", "kappa_fraction": "19889/20000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "individual-primary-interface-source/4459-manifest.json", "sha256": "aad44f310b2e31bcc8df79a7fb3e7a4f736137dfaae319bf6985bb1a482ef5d5" }, { "file": "remaining-record-audit/artifacts/4459/priority-manifest.json", "sha256": "8f1a4e7da3e269b022b1a17b0447acf07e39bbb0077f5a146eb7f6652b37382d" } ], "source_head": "488a75a9e95e14448b6301719249f876f3999931" } }, { "pr": 4465, "title": "research: refined-induction ceiling on #4436's direct flow grows with lockstep depth (log-gap g, no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4465", "author": "pinterbanget", "created_at": "2026-10-21T23:09:58Z", "accepted_at": "2026-10-22T02:49:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00003", "kappa_fraction": "3/100000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "individual-primary-interface-source/4465-manifest.json", "sha256": "d524a6e50ac8eefeab368a3eb1b3b6c3f59d0ce57e1e30c3e3b4e3dd6e257996" }, { "file": "remaining-record-audit/artifacts/4465/priority-manifest.json", "sha256": "680c3e410e9c6f02cbaaa343e8b6cd0cec2f4be8d5d5646fb27589ea82a8297d" } ], "source_head": "36d9c475d4bbc99e93952e0ad86a802e1bc581e8" } }, { "pr": 4470, "title": "Conditional kappa = 0.00302015 (+0.6304% over #4447): joint helper boundaries", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4470", "author": "1337isnot1337", "created_at": "2026-10-21T23:34:15Z", "accepted_at": "2026-10-22T02:49:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Selected maintainer-reviewed conditional TM result at pinned main; inherited physical, compiler, analytic and recovery premises remain. The crossover upper uses a weaker intermediate exponent before returning to the original record algorithm in its certified tail.", "source_status": "selected-reviewed-conditional", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^64215199999997-2^69+2045)", "plot_triple_log": { "log2_of_integer": "64215199999997", "negligible_negative_correction": true }, "source": "data/operation-audit/literal-feasibility-refinement-v5.json", "scope": "Exact optimized GMP when inactive; selected rank-N unreduced dense PR4470 supplier when active", "statistic": "Earliest input length at which some correct member of this family strictly beats the reference", "exact_individual_crossing": false, "all_PR4470_implementations": false, "full_upper_transferred": false }, "conditional_upper": { "input_bits": "2^(2^6423448376621591909063)", "log2log2_input_bits": "6423448376621591909063", "plot_triple_log": { "exact_log2log2_integer": "6423448376621591909063" }, "source": "data/operation-audit/pr4470-crossover-retuned-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": "A separately counted realization of this own-source supplier under retained native/analytic contracts. A sufficient upper, not an actual crossing." }, "cost_status": "conditional_literal_family_range", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "historical_selected_or_reviewed_conditional_checkpoint_source", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 242, "source_index": 400, "at": "2026-10-21T23:34:15Z", "until": "2026-10-22T04:18:44Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.00302015", "dashboard_float_text": "0.00302015", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4470", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 284, "source_index": null, "at": "2026-10-21T23:34:15Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00302015", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4470", "evidence_excerpt": "Conditional kappa = 0.00302015 (+0.6304% over #4447): joint helper boundaries", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 558, "source_index": null, "at": "2026-10-21T23:34:15Z", "until": null, "date_basis": "body-version", "fraction": "60403/20000000", "value_decimal": "0.00302015", "dashboard_float_text": null, "expression": "0.00302015", "historical_title": "Conditional kappa = 0.00302015 (+0.6304% over #4447): joint helper boundaries", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4470", "evidence_excerpt": "## Result\n\nThis contribution proposes conditional kappa = 0.00302015, up from #4447's 0.00300123: +0.00001892, or +0.630408%. It changes the complete native supplier and then uses an exactly replayed 16-pair query-thinned controller. This is an inc", "automated_comparable": true, "body_sha256": "4f91de55d3ee9ae7591622966fdfb56c0a7dc2d02a55cef93ffdf93354ac6ab2" } ], "reviewed_checkpoint_associations": [ { "stream": "all_selected_result_history", "record_kappa": "60403/20000000", "status": "Selected maintainer-reviewed conditional joint-helper construction; source-bound foundation reuse is explicit", "role": "first_listed_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/4f19cedcd8d81e4a2359449309fa6e9f17dfd22e/certificates/selected-result.json", "path": null, "commit": "4f19cedcd8d81e4a2359449309fa6e9f17dfd22e", "at": "2026-10-22T12:16:48Z", "scope": "Maintainer-reviewed conditional PR4470 construction. Inherited native/all-column, owned-erasure, whole-job, compiler, precision/tape, analytic, prime and recovery hypotheses remain. Uniform words are not materialized." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "uniform_rank_H": "64215200000000", "tensor_power": 1024, "early_effective_kappa": "1/500", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 0, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [], "source_head": "b9a13c1673e0e9697de410de16e8bbf3207a7363" } }, { "pr": 4474, "title": "Disposition receipt for the p17 \u03ba \u2248 0.003 PR chain (stacked content, pin-only differences, docs conflict with #4436)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4474", "author": "pinterbanget", "created_at": "2026-10-21T23:42:54Z", "accepted_at": "2026-10-22T02:49:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.003", "kappa_fraction": "3/1000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "individual-primary-interface-source/4474-manifest.json", "sha256": "60f984598c3fb6ffe99d3046f13a5af14832253a2221e001c8e8d892b12893f8" }, { "file": "remaining-record-audit/artifacts/4474/priority-manifest.json", "sha256": "373b1497453ecbc9eca027a05bb3e30de62efa90f4d0b828b9f180faac2c5cbd" } ], "source_head": "383f4f8825b1bf134206786e71d2a526de338982" } }, { "pr": 4478, "title": "Independently check #4470's arithmetic (\u03ba = 0.00302015): invoice, local change, root bracket, tails (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4478", "author": "pinterbanget", "created_at": "2026-10-22T00:05:20Z", "accepted_at": "2026-10-22T02:49:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "independent_validation_of_explicit_construction_targets", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Price the exact identified target word/controller, complete invoice, own compiler and precision/stock parameters; validation evidence may support that price but no cutoff is inherited from a title, unchanged kappa or matching histogram." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/4478/priority-manifest.json", "sha256": "ee6a3eb939a0cd4ab8cbfd02b33066bf909bd989976f27de2cc9c8902afb0113" } ], "source_head": "4e5072ad3bbdf76f2935f9488207db3969b38c90" } }, { "pr": 4479, "title": "Reduce #4470 local compiler rank 115\u00d7 at unchanged conditional \u03ba", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4479", "author": "Dugongue", "created_at": "2026-10-22T00:15:51Z", "accepted_at": "2026-10-22T02:49:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "authenticated_unchanged_kappa", "kappa_scope": "The source retains \u03ba=0.00302015. This is a compiler improvement with no new \u03ba claim. The crossover upper uses a weaker intermediate exponent before returning to the original record algorithm in its certified tail.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^558100005578-2^69+1362)", "plot_triple_log": { "log2_of_integer": "558100005578", "negligible_negative_correction": true }, "source": "data/operation-audit/literal-feasibility-refinement-v5.json", "scope": "Identical repaired optimized GMP when inactive; unreduced complete dense p16 native scalar word when active.", "statistic": "Earliest input length at which some correct member of this family strictly beats the reference", "exact_individual_crossing": false, "all_PR4470_implementations": false, "full_upper_transferred": false }, "conditional_upper": { "input_bits": "2^(2^55828536865193733668)", "log2log2_input_bits": "55828536865193733668", "plot_triple_log": { "exact_log2log2_integer": "55828536865193733668" }, "source": "data/operation-audit/pr-fixed-core-crossover-retuned-extensions.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": "A separately counted realization of this own-source supplier under retained native/analytic contracts. A sufficient upper, not an actual crossing." }, "cost_status": "conditional_literal_family_range", "fresh_arithmetic_replay_status": "PASS", "replay_receipt": "data/operation-audit/pr4470-descendant-replays/replay-results.json", "claim_type": "compiler_variant_same_kappa", "uniform_rank_H": "558100005581", "tensor_power": 682, "early_effective_kappa": "1/500", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 0, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [], "source_head": "035008ddc2cea4949829d309770e67479e696d9e" } }, { "pr": 4480, "title": "Reduce sufficient uniform-rank exponent 18.28\u00d7 with net taxes and log moments", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4480", "author": "zxv", "created_at": "2026-10-22T00:17:50Z", "accepted_at": "2026-10-22T02:49:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0030012", "kappa_fraction": "7503/2500000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^125789999997-2^69)", "plot_triple_log": { "log2_of_integer": "125789999997", "negligible_negative_correction": true }, "scope": "Own complete unreduced p17 boundary/native word when active, width at least two, strict winning own uniform supplier; identical optimized GMP when inactive.", "statistic": "Earliest input width at which a correct member of this literal enhancement family strictly beats the reference", "source": "data/operation-audit/pr4480-separated-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "conditional_upper": { "input_bits": "2^(2^12584566141734985381)", "log2log2_input_bits": "12584566141734985381", "plot_triple_log": { "exact_log2log2_integer": "12584566141734985381" }, "source": "data/operation-audit/pr4480-separated-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own p17 native arbitrary-input/absolute-phase all-column endpoint and chronological owned return contracts", "Source separated-product/net-tax compiler realizes its strict winning uniform supplier at the stated own H with completed base cases paid", "Complete role fields and spectators, exact per-role Clifford endpoints, barriers and restored owned banks on fixed parent selected axes", "Own source raw nonrecursive allowance below1e9 and expanded whole-job normal-form/adapter interfaces", "Parameterized fine-prime/Gaussian/finite-section/boundary/recovery analytic branch and unchanged fixed XAG/repaired optimized-GMP semantics" ] }, "cost_status": "conditional_own_source_range", "own_source_cost_extension": true, "early_effective_kappa": "1/500", "own_source_scope": [ "Own p17 native arbitrary-input/absolute-phase all-column endpoint and chronological owned return contracts", "Source separated-product/net-tax compiler realizes its strict winning uniform supplier at the stated own H with completed base cases paid", "Complete role fields and spectators, exact per-role Clifford endpoints, barriers and restored owned banks on fixed parent selected axes", "Own source raw nonrecursive allowance below1e9 and expanded whole-job normal-form/adapter interfaces", "Parameterized fine-prime/Gaussian/finite-section/boundary/recovery analytic branch and unchanged fixed XAG/repaired optimized-GMP semantics" ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr4480-separated-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 8, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/4480/priority-manifest.json", "sha256": "b9d6c165e5de125437d8128043b55f58bacb05bf8bec48893dd50ad6ec764c01" } ], "source_head": "4cf054a50c5718616594ec4ca2c9114278120a8b" } }, { "pr": 4481, "title": "Keep the 10 p^2 row margin through a Schur complement (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4481", "author": "jwr404", "created_at": "2026-10-22T00:42:54Z", "accepted_at": "2026-10-22T02:49:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0023", "kappa_fraction": "23/10000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain the exact stated lemma, finite-audit scope, correction or provenance with its actual selected target. A numerical runtime bound requires an actual source-selected full native/owner/recursive invoice/precision/outer realization and exact own commitments. 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A numerical runtime bound requires an actual source-selected full native/owner/recursive invoice/precision/outer realization and exact own commitments. No cutoff follows from unchanged kappa, a scalar lemma or an audit pass." ], "source_manifest": [ { "file": "individual-primary-interface-source/4482-manifest.json", "sha256": "b23906426cbfb196bac26d6f51f662a5c6d86cf53cc1d61b0bbb031c3b372b1a" }, { "file": "remaining-record-audit/artifacts/4482/priority-manifest.json", "sha256": "d58ef79a4505f114b81cccd4f28ae9c7fc1c525d4699aa1ac0dbd0459731f3f6" } ], "source_head": "c652a1eea829a5a4d826c254fdc0cfa77ed2bcfc" } }, { "pr": 4483, "title": "Remove tensor padding (199.32\u00d7 smaller uniform-rank exponent)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4483", "author": "zxv", "created_at": "2026-10-22T00:57:47Z", "accepted_at": "2026-10-22T02:49:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "authenticated_unchanged_kappa", "kappa_scope": "The source retains \u03ba=0.00302015. This is a compiler improvement with no new \u03ba claim. 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A numerical runtime bound requires an actual source-selected full native/owner/recursive invoice/precision/outer realization and exact own commitments. No cutoff follows from unchanged kappa, a scalar lemma or an audit pass." ], "source_manifest": [ { "file": "individual-primary-interface-source/4484-manifest.json", "sha256": "76855e36cc7fe5c583dee8b21acb1dfba601cc6e7ba2941fa68fd155a2b992a9" }, { "file": "remaining-record-audit/artifacts/4484/priority-manifest.json", "sha256": "ac666efb9ea6951171f69c41b724df7651ff4a220d047710d4f57b219900702c" } ], "source_head": "722f3a48119aa547784f307e6902d04069874880" } }, { "pr": 4485, "title": "Absorb the telescoping factor (10 p^2)^{g-1} p^6 (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4485", "author": "jwr404", "created_at": "2026-10-22T01:05:37Z", "accepted_at": "2026-10-22T02:49:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0023", "kappa_fraction": "23/10000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain the exact stated lemma, finite-audit scope, correction or provenance with its actual selected target. A numerical runtime bound requires an actual source-selected full native/owner/recursive invoice/precision/outer realization and exact own commitments. No cutoff follows from unchanged kappa, a scalar lemma or an audit pass." ], "source_manifest": [ { "file": "individual-primary-interface-source/4485-manifest.json", "sha256": "70f84de8cbb0dc46fed022ff82ef62ea14a45f3471ef7d66807d49956c6b3826" }, { "file": "remaining-record-audit/artifacts/4485/priority-manifest.json", "sha256": "f0ed76847d707ef1576cc79d1c67a5546e4a71bbfa923341a9b18b0a6d7d0721" } ], "source_head": "1dc102830b6e13238b0cd3b8f7dc2e3a102838a9" } }, { "pr": 4486, "title": "Absorb the approximant base 10 p^2 + p^6 exp(-p^2) (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4486", "author": "jwr404", "created_at": "2026-10-22T01:10:08Z", "accepted_at": "2026-10-22T02:49:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0023", "kappa_fraction": "23/10000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain the exact stated lemma, finite-audit scope, correction or provenance with its actual selected target. A numerical runtime bound requires an actual source-selected full native/owner/recursive invoice/precision/outer realization and exact own commitments. No cutoff follows from unchanged kappa, a scalar lemma or an audit pass." ], "source_manifest": [ { "file": "individual-primary-interface-source/4486-manifest.json", "sha256": "4ca29ae0272f775a82db7a996251d59f61329f67d24ea744806e0afe55da51db" }, { "file": "remaining-record-audit/artifacts/4486/priority-manifest.json", "sha256": "608ccf17256d3fdf9e709298248e6042e4d88daea8e143eb44ecf166f050e6f4" } ], "source_head": "dfc477842771516c48c4c144e42b5ef1309ca536" } }, { "pr": 4487, "title": "Absorb the face factor 2 on the approximant monomial (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4487", "author": "jwr404", "created_at": "2026-10-22T01:17:43Z", "accepted_at": "2026-10-22T02:49:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0023", "kappa_fraction": "23/10000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain the exact stated lemma, finite-audit scope, correction or provenance with its actual selected target. A numerical runtime bound requires an actual source-selected full native/owner/recursive invoice/precision/outer realization and exact own commitments. No cutoff follows from unchanged kappa, a scalar lemma or an audit pass." ], "source_manifest": [ { "file": "individual-primary-interface-source/4487-manifest.json", "sha256": "5088e8c68d5681083e89fcd2ee19c63dc829a16a365bf59a0cda39854c86761e" }, { "file": "remaining-record-audit/artifacts/4487/priority-manifest.json", "sha256": "5d232d49b1b0191676439f5bfaa0bc35a446094d9509b22b05bb159b20c16425" } ], "source_head": "a6794beea17c43ac66e7bc6af6d45488b9813761" } }, { "pr": 4489, "title": "Owned-query shear adapters and portable split-port search (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4489", "author": "Dugongue", "created_at": "2026-10-22T01:24:55Z", "accepted_at": "2026-10-22T02:49:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep the actual local construction, exact component count and stated exclusions with its named target. A whole runtime bound requires a complete source-selected caller/native/owner/recursive invoice/precision/outer realization; an autonomous target identity and a consistent complete cost meter cannot be replaced by a local moment screen." ], "source_manifest": [ { "file": "individual-primary-interface-source/4489-manifest.json", "sha256": "7ac29666402826d69857a60812ceaf9bcce45b750f1ce13cd1e568e15549451e" }, { "file": "remaining-record-audit/artifacts/4489/priority-manifest.json", "sha256": "6d45db7e5d78e9133a35f79b9b80ffcc3a7c549d0dfc38afbaaafcfd60ac59c5" } ], "source_head": "67d1ded63edc604b3d9e6506a4f5d3689bdc9f41" } }, { "pr": 4490, "title": "Split one axis through the section polynomial (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4490", "author": "jwr404", "created_at": "2026-10-22T01:26:39Z", "accepted_at": "2026-10-22T02:49:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0023", "kappa_fraction": "23/10000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain the exact stated lemma, finite-audit scope, correction or provenance with its actual selected target. A numerical runtime bound requires an actual source-selected full native/owner/recursive invoice/precision/outer realization and exact own commitments. No cutoff follows from unchanged kappa, a scalar lemma or an audit pass." ], "source_manifest": [ { "file": "individual-primary-interface-source/4490-manifest.json", "sha256": "ae2ef2f95f471d231530276ec2489cc967d7406d987131e3be4900d91e87b907" }, { "file": "remaining-record-audit/artifacts/4490/priority-manifest.json", "sha256": "ef8b79d174ae96325369893122744deae46ef8a8ec9131b7bb34c6fa23f2257a" } ], "source_head": "91b9fa3afcee9da37663c5a58905b25369f2a660" } }, { "pr": 4491, "title": "Place a core row past the agreement radius p^26 (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4491", "author": "jwr404", "created_at": "2026-10-22T01:33:09Z", "accepted_at": "2026-10-22T02:49:06Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0023", "kappa_fraction": "23/10000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Retain the exact stated lemma, finite-audit scope, correction or provenance with its actual selected target. A numerical runtime bound requires an actual source-selected full native/owner/recursive invoice/precision/outer realization and exact own commitments. No cutoff follows from unchanged kappa, a scalar lemma or an audit pass." ], "source_manifest": [ { "file": "individual-primary-interface-source/4491-manifest.json", "sha256": "fa1cd59de3393537d7320dfd49c8ece6fd1e89b5a9e1d209afe79f0abee95601" }, { "file": "remaining-record-audit/artifacts/4491/priority-manifest.json", "sha256": "5b61d1f78c0c566d2461de0e1681a03a4acf84ac6881f155908723727b42fa51" } ], "source_head": "2de9300c3026d124ba14dc279eaa321a02334cef" } }, { "pr": 4441, "title": "Conditional \u03ba = 0.00300105 (+4.105e-5 over #4440): combine query thinning and helper retiming", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4441", "author": "1337isnot1337", "created_at": "2026-10-21T20:11:02Z", "accepted_at": "2026-10-22T02:49:07Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00300105", "kappa_fraction": "60021/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews. 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A sufficient upper, not an actual crossing." }, "cost_status": "conditional_literal_family_range", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 239, "source_index": 396, "at": "2026-10-21T20:26:57.968500Z", "until": "2026-10-21T21:07:29Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.00300105", "dashboard_float_text": "0.00300105", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4441", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 281, "source_index": null, "at": "2026-10-21T20:26:57.968500+00:00", "until": null, "date_basis": "observed_revision", "fraction": null, "value_decimal": "0.00300105", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4441", "evidence_excerpt": "Conditional \u03ba = 0.00300105 (+4.105e-5 over #4440): combine query thinning and helper retiming", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 555, "source_index": null, "at": "2026-10-21T20:26:16Z", "until": null, "date_basis": "title-edit", "fraction": "60021/20000000", "value_decimal": "0.00300105", "dashboard_float_text": null, "expression": "0.00300105", "historical_title": "Conditional \u03ba = 0.00300105 (+4.105e-5 over #4440): combine query thinning and helper retiming", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4441", "evidence_excerpt": "Conditional \u03ba = 0.00300105 (+4.105e-5 over #4440): combine query thinning and helper retiming", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [ { "stream": "all_selected_result_history", "record_kappa": "60403/20000000", "status": "Selected maintainer-reviewed conditional joint-helper construction; source-bound foundation reuse is explicit", "role": "dependency_source", "role_basis": "Position in source_prs, not automatic proof of the dependency PR own headline.", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/blob/4f19cedcd8d81e4a2359449309fa6e9f17dfd22e/certificates/selected-result.json", "path": null, "commit": "4f19cedcd8d81e4a2359449309fa6e9f17dfd22e", "at": "2026-10-22T12:16:48Z", "scope": "Maintainer-reviewed conditional PR4470 construction. Inherited native/all-column, owned-erasure, whole-job, compiler, precision/tape, analytic, prime and recovery hypotheses remain. Uniform words are not materialized." } ], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "uniform_rank_H": "165315500000000", "tensor_power": 1, "early_effective_kappa": "1/500", "claim_type": "reviewed_checkpoint_conditional_source", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 0, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [], "source_head": "149af87f1101dc7a72f2fe57294f9bacf8d053ba" } }, { "pr": 4589, "title": "Independently check #4580's p3 H-branch budget (322/397) with own certified powers; note two rounded bracket endpoints (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4589", "author": "pinterbanget", "created_at": "2026-10-22T08:29:25Z", "accepted_at": "2026-10-22T19:19:22Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "supporting_endpoint_audit_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "fd9f28beff7d03464d5a07cbdb00c38f431a1613" } }, { "pr": 4604, "title": "Endpoint-frame audit of #4596: every main output chart changes under the span{511} quotient; replay checks only the word's own finals (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4604", "author": "pinterbanget", "created_at": "2026-10-22T09:27:15Z", "accepted_at": "2026-10-22T19:19:22Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0034", "kappa_fraction": "17/5000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "supporting_contract_audit_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "6d4d72885351e01d0a2ce2b20419c0d84cb4949c" } }, { "pr": 4610, "title": "Conditional \u03ba = 0.0030217758: joint helper interfaces and Lean compiler tightening", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4610", "author": "intqwq", "created_at": "2026-10-22T10:02:07Z", "accepted_at": "2026-10-22T19:19:22Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0030217758", "kappa_fraction": "15108879/5000000000", "kappa_status": "previous_reviewed_conditional_source", "kappa_scope": "Previously selected conditional PR4610 result, independently audited by PR5241. Its changed scalar program was freshly counted here. Its whole-integer upper is separately instantiated from its own source parameters and native class, under retained contracts.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^38569299999999997-2^69+2)", "plot_triple_log": { "log2_of_integer": "38569299999999997", "negligible_negative_correction": true }, "source": "data/operation-audit/literal-feasibility-refinement-v5.json", "scope": "Identical repaired optimized GMP when inactive; selected sufficient-rank unreduced complete dense native word when active, working word width>=2.", "statistic": "Earliest input length at which some correct member of this family strictly beats the reference", "exact_individual_crossing": false, "all_PR4470_implementations": false, "full_upper_transferred": false }, "conditional_upper": { "input_bits": "2^(2^3858087157930791192089081)", "log2log2_input_bits": "3858087157930791192089081", "plot_triple_log": { "exact_log2log2_integer": "3858087157930791192089081" }, "source": "data/operation-audit/pr-fixed-core-crossover-retuned-extensions.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": "A separately counted realization of this own-source supplier under retained native/analytic contracts. A sufficient upper, not an actual crossing." }, "cost_status": "conditional_literal_family_range", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "previous_selected_maintainer_reviewed_conditional_claim", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 247, "source_index": 407, "at": "2026-10-22T14:45:10.175982Z", "until": "2026-10-22T15:14:39Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.0030217758", "dashboard_float_text": "0.0030217758", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4610", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 289, "source_index": null, "at": "2026-10-22T14:45:10.175982+00:00", "until": null, "date_basis": "observed_revision", "fraction": null, "value_decimal": "0.0030217758", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4610", "evidence_excerpt": "Conditional \u03ba = 0.0030217758: joint helper interfaces and Lean compiler tightening", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 561, "source_index": null, "at": "2026-10-22T10:02:07Z", "until": null, "date_basis": "body-version", "fraction": "37769/12500000", "value_decimal": "0.0030217758", "dashboard_float_text": null, "expression": "37769/12500000", "historical_title": "Increase conditional kappa to 0.00302152 with changed warp maps and Lean certificates", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4610", "evidence_excerpt": "Jointly changing native warp maps and scalar-contact frames gives conditional\nkappa = 37769/12500000 = 0.00302152, improving PR4535's 0.003020165 by\n0.000001355. The selected repository frontier remains unchanged.\n\nThe frozen construction changes 34 native G maps and 422 scalar f", "automated_comparable": true, "body_sha256": "96bbbb03960d60b0f37480fc1b7e666d373c57151bfacabd6b3bbe7d7eb26345" }, { "stream": "recovered_literal_highwater", "stream_row": 564, "source_index": null, "at": "2026-10-22T11:58:56Z", "until": null, "date_basis": "title-edit", "fraction": "9443/3125000", "value_decimal": "0.0030217758", "dashboard_float_text": null, "expression": "0.00302176", "historical_title": "Conditional \u03ba = 0.00302176 (+0.00000024): joint helper interfaces and Lean certificates", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4610", "evidence_excerpt": "Conditional \u03ba = 0.00302176 (+0.00000024): joint helper interfaces and Lean certificates", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 566, "source_index": null, "at": "2026-10-22T14:42:26Z", "until": null, "date_basis": "title-edit", "fraction": "15108879/5000000000", "value_decimal": "0.0030217758", "dashboard_float_text": null, "expression": "0.0030217758", "historical_title": "Conditional \u03ba = 0.0030217758: joint helper interfaces and Lean compiler tightening", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4610", "evidence_excerpt": "Conditional \u03ba = 0.0030217758: joint helper interfaces and Lean compiler tightening", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "uniform_rank_H": "38569300000000000", "tensor_power": 1, "early_effective_kappa": "1/500", "fresh_arithmetic_replay_status": "PASS_SCALAR_CENSUS_ONLY", "replay_receipt": "data/operation-audit/pr4610-literal-work-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 0, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [], "source_head": "20bb93cd990d2ff683e4d0fc56b87a42cd5d3296" } }, { "pr": 4614, "title": "Scoped check of #4610: all 632 endpoint frames equal PR4470's, profile arithmetic exact, moment improvement proved on (0,1) (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4614", "author": "pinterbanget", "created_at": "2026-10-22T10:14:16Z", "accepted_at": "2026-10-22T19:19:22Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302152", "kappa_fraction": "37769/12500000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "b14d286c6e0276db052249929e1cbd2427975cfe" } }, { "pr": 4535, "title": "Improve conditional multiplication kappa to 0.003020165 via critical-root transfer", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4535", "author": "hexapode", "created_at": "2026-10-22T04:18:44Z", "accepted_at": "2026-10-22T19:19:23Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.003020165", "kappa_fraction": "604033/200000000", "kappa_status": "authenticated_source_kappa", "kappa_scope": "The source claims a higher \u03ba with the same raw p16 word. Its physical realization premises remain conditional. The crossover upper uses a weaker intermediate exponent before returning to the original record algorithm in its certified tail.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^999999999997-2^69+2)", "plot_triple_log": { "log2_of_integer": "999999999997", "negligible_negative_correction": true }, "source": "data/operation-audit/literal-feasibility-refinement-v5.json", "scope": "Identical repaired optimized GMP when inactive; unreduced complete dense raw p16 scalar word when active.", "statistic": "Earliest input length at which some correct member of this family strictly beats the reference", "exact_individual_crossing": false, "all_PR4470_implementations": false, "full_upper_transferred": false }, "conditional_upper": { "input_bits": "2^(2^100041795191117961669)", "log2log2_input_bits": "100041795191117961669", "plot_triple_log": { "exact_log2log2_integer": "100041795191117961669" }, "source": "data/operation-audit/pr-fixed-core-crossover-retuned-extensions.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": "A separately counted realization of this own-source supplier under retained native/analytic contracts. A sufficient upper, not an actual crossing." }, "cost_status": "conditional_literal_family_range", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 243, "source_index": 401, "at": "2026-10-22T04:18:44Z", "until": "2026-10-22T07:11:12Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.003020165", "dashboard_float_text": "0.003020165", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4535", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 285, "source_index": null, "at": "2026-10-22T04:18:44Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.003020165", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4535", "evidence_excerpt": "Improve conditional multiplication kappa to 0.003020165 via critical-root transfer", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 559, "source_index": null, "at": "2026-10-22T04:18:44Z", "until": null, "date_basis": "body-version", "fraction": "604033/200000000", "value_decimal": "0.003020165", "dashboard_float_text": null, "expression": "0.003020165", "historical_title": "Improve conditional multiplication kappa to 0.003020165 via critical-root transfer", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4535", "evidence_excerpt": "unchanged native supplier raises the conditional whole multiplication saving from \u03ba = 0.00302015 to \u03ba = 0.003020165 (+0.000000015).\n\nThe new contribution is research/critical-root-multiplication/: a finite-template argument, exact source-bound certificate and new complete outer parameter point.", "automated_comparable": true, "body_sha256": "292424c3eb9b82242d9351fa25cf5bbf2e87cce6603566c0770eec7c357e362b" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "fresh_arithmetic_replay_status": "NOT_RERUN", "replay_receipt": "data/operation-audit/pr4470-higher-kappa-bindings/bindings.json", "claim_type": "higher_kappa_source_claim", "uniform_rank_H": "1000000000000", "tensor_power": 1, "early_effective_kappa": "1/500", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 0, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [], "source_head": "a6d7237f697185e857090e174c23c1cb22c6563c" } }, { "pr": 4536, "title": "Independently check #4535's arithmetic (\u03ba = 0.003020165): critical root, gap 377e-12, mirror, absorption, binding outer row (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4536", "author": "pinterbanget", "created_at": "2026-10-22T04:40:36Z", "accepted_at": "2026-10-22T19:19:23Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.003020165", "kappa_fraction": "604033/200000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "independent_validation_of_explicit_construction_targets", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Price the exact identified target word/controller, complete invoice, own compiler and precision/stock parameters; validation evidence may support that price but no cutoff is inherited from a title, unchanged kappa or matching histogram." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/4536/priority-manifest.json", "sha256": "a6f5293e3da4dc880991cee594bb6084ff6c17456f72de3fc7644cc64094222c" } ], "source_head": "4617b96cb4020dd6f36ccff3f0832381b62ba512" } }, { "pr": 4537, "title": "Independently certify #4532's finite figures: abstract witness, counterexample, p7/p16 root applications (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4537", "author": "pinterbanget", "created_at": "2026-10-22T04:45:12Z", "accepted_at": "2026-10-22T19:19:23Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.003020165", "kappa_fraction": "604033/200000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "individual-primary-interface-source/4537-manifest.json", "sha256": "db870a9a39dad03a2f7a8303c1744a07bff927024cb3e1b512390812768d85bd" }, { "file": "remaining-record-audit/artifacts/4537/priority-manifest.json", "sha256": "a3613654e5e79979efb9a981365a3e2d05ffdbb9c344f5996416dcda67b7e69a" } ], "source_head": "530a5b6d2ae7ee0a1eccc88975a170cf39b60b94" } }, { "pr": 4563, "title": "Certify #4535 at a 13x smaller finite rank: N = 2^77,014,944,503 instead of 2^10^12 (same \u03ba = 0.003020165)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4563", "author": "pinterbanget", "created_at": "2026-10-22T06:54:11Z", "accepted_at": "2026-10-22T19:19:23Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.003020165", "kappa_fraction": "604033/200000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^77014944500-2^69+2)", "plot_triple_log": { "log2_of_integer": "77014944500", "negligible_negative_correction": true }, "scope": "Identical repaired optimized GMP when inactive; unreduced complete dense raw p16 scalar word when active, under own strict-winning supplier and all-column/spectator contracts.", "statistic": "Earliest input width at which some correct member of this literal enhancement family strictly beats the reference", "source": "data/operation-audit/pr4563-critical-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "conditional_upper": { "input_bits": "2^(2^7706367470242875174)", "log2log2_input_bits": "7706367470242875174", "plot_triple_log": { "exact_log2log2_integer": "7706367470242875174" }, "source": "data/operation-audit/pr4563-critical-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own finite rank/majorant numerical witness with unchanged raw p16 supplier; no strictified productivefloor21", "Upstream pinned PR4535 section4 arbitrary-input/all-column physical bridge applies to this own changed rank/outer schedule; upstream package is NOT present at this own head", "Exact chronological selected raw p16 native and absolute-phase endpoint identities", "Strict integer child descent, completed-call barriers and own class/width envelopes", "Separate whole-field roles, fixed parent selected axes, complete spectators and restored owned banks", "Exact per-role Clifford Gaussian-dyadic endpoints and no child rounding", "Parameterized fine-prime/Gaussian/finite-section/boundary/CRT-recovery analytic branch" ] }, "cost_status": "conditional_own_source_range", "own_source_cost_extension": true, "early_effective_kappa": "1/500", "own_source_scope": [ "Own finite rank/majorant numerical witness with unchanged raw p16 supplier; no strictified productivefloor21", "Upstream pinned PR4535 section4 arbitrary-input/all-column physical bridge applies to this own changed rank/outer schedule; upstream package is NOT present at this own head", "Exact chronological selected raw p16 native and absolute-phase endpoint identities", "Strict integer child descent, completed-call barriers and own class/width envelopes", "Separate whole-field roles, fixed parent selected axes, complete spectators and restored owned banks", "Exact per-role Clifford Gaussian-dyadic endpoints and no child rounding", "Parameterized fine-prime/Gaussian/finite-section/boundary/CRT-recovery analytic branch" ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr4563-critical-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 14, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/4563/manifest.json", "sha256": "ee5066bc3c5bfb3cf2670f0cd716e310b2e4574555c0f208f40251a74ce94fda" }, { "file": "remaining-record-audit/artifacts/4563/priority-manifest.json", "sha256": "0636463ceddaeb057c614c47bcb4dd6108192e29608100b17289cefc31b91868" } ], "source_head": "7db8ee8d97d456f120cb534d8cf356a1b8b02ca8" } }, { "pr": 4564, "title": "Certify #4535 at outer slack d=1e-12: all 54 predicates pass, frozen rank N = 2^29,328,002,299 (34x below 2^10^12, same \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4564", "author": "pinterbanget", "created_at": "2026-10-22T06:57:02Z", "accepted_at": "2026-10-22T19:19:23Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.003020165", "kappa_fraction": "604033/200000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^29328002296-2^69+2)", "plot_triple_log": { "log2_of_integer": "29328002296", "negligible_negative_correction": true }, "scope": "Identical repaired optimized GMP when inactive; unreduced complete dense raw p16 scalar word when active, under own strict-winning supplier and all-column/spectator contracts.", "statistic": "Earliest input width at which some correct member of this literal enhancement family strictly beats the reference", "source": "data/operation-audit/pr4564-critical-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "conditional_upper": { "input_bits": "2^(2^2935765629093878561)", "log2log2_input_bits": "2935765629093878561", "plot_triple_log": { "exact_log2log2_integer": "2935765629093878561" }, "source": "data/operation-audit/pr4564-critical-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own finite rank/majorant numerical witness with unchanged raw p16 supplier; no strictified productivefloor21", "Upstream pinned PR4535 section4 arbitrary-input/all-column physical bridge applies to this own changed rank/outer schedule; upstream package is NOT present at this own head", "Exact chronological selected raw p16 native and absolute-phase endpoint identities", "Strict integer child descent, completed-call barriers and own class/width envelopes", "Separate whole-field roles, fixed parent selected axes, complete spectators and restored owned banks", "Exact per-role Clifford Gaussian-dyadic endpoints and no child rounding", "Parameterized fine-prime/Gaussian/finite-section/boundary/CRT-recovery analytic branch" ] }, "cost_status": "conditional_own_source_range", "own_source_cost_extension": true, "early_effective_kappa": "1/500", "own_source_scope": [ "Own finite rank/majorant numerical witness with unchanged raw p16 supplier; no strictified productivefloor21", "Upstream pinned PR4535 section4 arbitrary-input/all-column physical bridge applies to this own changed rank/outer schedule; upstream package is NOT present at this own head", "Exact chronological selected raw p16 native and absolute-phase endpoint identities", "Strict integer child descent, completed-call barriers and own class/width envelopes", "Separate whole-field roles, fixed parent selected axes, complete spectators and restored owned banks", "Exact per-role Clifford Gaussian-dyadic endpoints and no child rounding", "Parameterized fine-prime/Gaussian/finite-section/boundary/CRT-recovery analytic branch" ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr4564-critical-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 14, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "remaining-record-audit/artifacts/4564/manifest.json", "sha256": "a5ed148d940529f2ddc1d56ab35198d217ec5be68d3a862a6bcc848b46eb0de9" }, { "file": "remaining-record-audit/artifacts/4564/priority-manifest.json", "sha256": "d17cf9aec45e8bff7e97c507660887effa2cfeb8735f0d2de26f9bfab52868c1" } ], "source_head": "fbcc9d63446cd4fc8eade8fc29b149fb60fa79ce" } }, { "pr": 4565, "title": "Retuned p16 critical-root majorant (M=2^24, ell0=64, p=3/10): #4535's frozen rank 2^11,825,387,808, 85x below 2^10^12 (same \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4565", "author": "pinterbanget", "created_at": "2026-10-22T07:02:48Z", "accepted_at": "2026-10-22T19:19:23Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.003020165", "kappa_fraction": "604033/200000000", "kappa_status": "authenticated_source_kappa", "kappa_scope": "The source retains \u03ba=0.003020165 while retuning the compiler. Its physical realization premises remain conditional.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^11825387805-2^69+2)", "plot_triple_log": { "log2_of_integer": "11825387805", "negligible_negative_correction": true }, "scope": "Identical repaired optimized GMP when inactive; unreduced complete dense raw p16 scalar word when active, under own strict-winning supplier and all-column/spectator contracts.", "statistic": "Earliest input width at which some correct member of this literal enhancement family strictly beats the reference", "source": "data/operation-audit/pr4565-critical-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "conditional_upper": { "input_bits": "2^(2^1184804022906385087)", "log2log2_input_bits": "1184804022906385087", "plot_triple_log": { "exact_log2log2_integer": "1184804022906385087" }, "source": "data/operation-audit/pr4565-critical-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own retuned critical-root compiler arbitrary-input/all-column physical realization, as explicitly retained by PR4565 README from PR4535 section4", "Exact chronological selected raw p16 native and absolute-phase endpoint identities", "Strict integer child descent, completed-call barriers and own class/width envelopes", "Separate whole-field roles, fixed parent selected axes, complete spectators and restored owned banks", "Exact per-role Clifford Gaussian-dyadic endpoints and no child rounding", "Parameterized fine-prime/Gaussian/finite-section/boundary/CRT-recovery analytic branch" ] }, "cost_status": "conditional_own_source_range", "fresh_arithmetic_replay_status": "PASS", "replay_receipt": "data/operation-audit/pr4470-higher-kappa-bindings/bindings.json", "claim_type": "compiler_variant_same_kappa", "uniform_rank_H": "11825387808", "tensor_power": 1, "own_source_cost_extension": true, "early_effective_kappa": "1/500", "own_source_scope": [ "Own retuned critical-root compiler arbitrary-input/all-column physical realization, as explicitly retained by PR4565 README from PR4535 section4", "Exact chronological selected raw p16 native and absolute-phase endpoint identities", "Strict integer child descent, completed-call barriers and own class/width envelopes", "Separate whole-field roles, fixed parent selected axes, complete spectators and restored owned banks", "Exact per-role Clifford Gaussian-dyadic endpoints and no child rounding", "Parameterized fine-prime/Gaussian/finite-section/boundary/CRT-recovery analytic branch" ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr4565-critical-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 0, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [], "source_head": "d6a9a75bf48b047927bc4103def6f821909bb835" } }, { "pr": 4568, "title": "Conditional \u03ba = 0.00302016597 (+9.7e-10 over #4535)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4568", "author": "hexapode", "created_at": "2026-10-22T07:11:12Z", "accepted_at": "2026-10-22T19:19:23Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302016597", "kappa_fraction": "302016597/100000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; 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the finite checker does not prove this bridge", "Own-head selected unchanged raw p16 native and exact absolute-phase endpoints; full native engine not replayed here", "Separate role fields and parent selected axes, completed child barriers, restored owned banks, exact per-role Clifford Gaussian-dyadic endpoints", "The source-parametric fine-prime/Gaussian/finite-section/boundary/whole-integer recovery analytic branch" ] }, "cost_status": "conditional_own_source_range", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 244, "source_index": 402, "at": "2026-10-22T07:11:12Z", "until": "2026-10-22T11:37:26.771874Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.00302016597", "dashboard_float_text": "0.00302016597", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4568", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 286, "source_index": null, "at": "2026-10-22T07:11:12Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.00302016597", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4568", "evidence_excerpt": "Conditional \u03ba = 0.00302016597 (+9.7e-10 over #4535)", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 560, "source_index": null, "at": "2026-10-22T07:11:12Z", "until": null, "date_basis": "opening-title", "fraction": "302016597/100000000000", "value_decimal": "0.00302016597", "dashboard_float_text": null, "expression": "0.00302016597", "historical_title": "Conditional \u03ba = 0.00302016597 (+9.7e-10 over #4535)", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4568", "evidence_excerpt": "Conditional \u03ba = 0.00302016597 (+9.7e-10 over #4535)", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/500", "own_source_scope": [ "Own source critical-root theorem/strict integer child descent and positive uniform supplier at this explicitly authenticated H", "Own source inherits arbitrary-input/all-column, owned/spectator and physical closure for its changed fixed word; the finite checker does not prove this bridge", "Own-head selected unchanged raw p16 native and exact absolute-phase endpoints; full native engine not replayed here", "Separate role fields and parent selected axes, completed child barriers, restored owned banks, exact per-role Clifford Gaussian-dyadic endpoints", "The source-parametric fine-prime/Gaussian/finite-section/boundary/whole-integer recovery analytic branch" ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr4568-critical-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 25, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "b269a729bc27ff3415e2b873ad00730ea6bc1a58" } }, { "pr": 4569, "title": "Independent proof check of #4532 \u00a71.1, \u00a72.2-2.3, \u00a73 (critical-root majorant under #4535's \u03ba): every step verified, no gap (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4569", "author": "pinterbanget", "created_at": "2026-10-22T07:25:25Z", "accepted_at": "2026-10-22T19:19:23Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.003020165", "kappa_fraction": "604033/200000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "supporting_proof_audit_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "c4607e578e09a7cc7fe60ee0b7685b941822135d" } }, { "pr": 4570, "title": "Independently check #4568's arithmetic (\u03ba = 0.00302016597): outer ledger, gap, absorption; frozen rank 6.9x smaller with #4565 (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4570", "author": "pinterbanget", "created_at": "2026-10-22T07:29:06Z", "accepted_at": "2026-10-22T19:19:23Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302016597", "kappa_fraction": "302016597/100000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^14562291820119-2^69+2)", "plot_triple_log": { "log2_of_integer": "14562291820119", "negligible_negative_correction": true }, "scope": "Identical repaired optimized GMP when inactive; unreduced complete dense raw p16 scalar word when active, under own strict-winning supplier and all-column/spectator contracts.", "statistic": "Earliest input width at which some correct member of this literal enhancement family strictly beats the reference", "source": "data/operation-audit/pr4570-critical-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "conditional_upper": { "input_bits": "2^(2^1456813509562998342039)", "log2log2_input_bits": "1456813509562998342039", "plot_triple_log": { "exact_log2log2_integer": "1456813509562998342039" }, "source": "data/operation-audit/pr4570-critical-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own source critical-root theorem/strict integer child descent and positive uniform supplier at this explicitly authenticated H", "Own source inherits arbitrary-input/all-column, owned/spectator and physical closure for its changed fixed word; the finite checker does not prove this bridge", "Own-head selected unchanged raw p16 native and exact absolute-phase endpoints; full native engine not replayed here", "Separate role fields and parent selected axes, completed child barriers, restored owned banks, exact per-role Clifford Gaussian-dyadic endpoints", "The source-parametric fine-prime/Gaussian/finite-section/boundary/whole-integer recovery analytic branch" ] }, "cost_status": "conditional_own_source_range", "own_source_cost_extension": true, "early_effective_kappa": "1/500", "own_source_scope": [ "Own source critical-root theorem/strict integer child descent and positive uniform supplier at this explicitly authenticated H", "Own source inherits arbitrary-input/all-column, owned/spectator and physical closure for its changed fixed word; the finite checker does not prove this bridge", "Own-head selected unchanged raw p16 native and exact absolute-phase endpoints; full native engine not replayed here", "Separate role fields and parent selected axes, completed child barriers, restored owned banks, exact per-role Clifford Gaussian-dyadic endpoints", "The source-parametric fine-prime/Gaussian/finite-section/boundary/whole-integer recovery analytic branch" ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr4570-critical-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 6, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "b5e119c1760203f10a2c2245bd8a50fa47b7013a" } }, { "pr": 4582, "title": "Independently certify all-length receiver-window floors with two exact algorithms", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4582", "author": "mihir-s-05", "created_at": "2026-10-22T08:09:28Z", "accepted_at": "2026-10-22T19:19:23Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0023", "kappa_fraction": "23/10000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "scoped_obstruction_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "23c515a3c071a6bfdd1fe80bc67cea55f6d43643" } }, { "pr": 4585, "title": "Prove receiver-window floors with mandatory contacts and bridges (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4585", "author": "mihir-s-05", "created_at": "2026-10-22T08:14:07Z", "accepted_at": "2026-10-22T19:19:23Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0023", "kappa_fraction": "23/10000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "scoped_obstruction_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "025f37fe346203cfe18d47367ce239e420961d36" } }, { "pr": 4516, "title": "Independently replay #4470's p16 controller: exact diagonal for all 32 monomials, invoice, controls (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4516", "author": "pinterbanget", "created_at": "2026-10-22T03:15:11Z", "accepted_at": "2026-10-22T19:19:24Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "individual-primary-interface-source/4516-manifest.json", "sha256": "3146018aaa654165d6ddca06586313e9514be8894169f2157d3e045f244b71a3" }, { "file": "remaining-record-audit/artifacts/4516/priority-manifest.json", "sha256": "8e69fce98eb22a22495857c54fab853ab42f5058db4e465c8ee0797647d993a7" } ], "source_head": "0a63873be8bb6a6e1ee682f46fb48be97447b2db" } }, { "pr": 4529, "title": "Independently certify #4483's finite gates (p16 2^2800000000, all four witnesses) and its arbitrary-height flow identities (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4529", "author": "pinterbanget", "created_at": "2026-10-22T03:48:50Z", "accepted_at": "2026-10-22T19:19:24Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "independent_validation_of_explicit_construction_targets", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 3, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Price the exact identified target word/controller, complete invoice, own compiler and precision/stock parameters; validation evidence may support that price but no cutoff is inherited from a title, unchanged kappa or matching histogram." ], "source_manifest": [ { "file": "remaining-record-audit/artifacts/4529/priority-manifest.json", "sha256": "78de0e33830bf43b6338fa09cecb847df0121d444825aaca74a3be1ed9def0a2" } ], "source_head": "a1b836c56b4cd40cdad8ca84691e0e59e5d19a45" } }, { "pr": 4533, "title": "Sharper #4483 witnesses: p16 2^1587000000, native4453 2^713000000, p7 2^2253000000, same \u03ba (compiler improvement, no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4533", "author": "pinterbanget", "created_at": "2026-10-22T04:10:54Z", "accepted_at": "2026-10-22T19:19:24Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "authenticated_unchanged_kappa", "kappa_scope": "The source retains \u03ba=0.00302015. This is a compiler improvement with no new \u03ba claim. The crossover upper uses a weaker intermediate exponent before returning to the original record algorithm in its certified tail.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^1586999997-2^69+2)", "plot_triple_log": { "log2_of_integer": "1586999997", "negligible_negative_correction": true }, "source": "data/operation-audit/literal-feasibility-refinement-v5.json", "scope": "Identical repaired optimized GMP when inactive; unreduced complete dense p16 native scalar word when active.", "statistic": "Earliest input length at which some correct member of this family strictly beats the reference", "exact_individual_crossing": false, "all_PR4470_implementations": false, "full_upper_transferred": false }, "conditional_upper": { "input_bits": "2^(2^160555675878901663)", "log2log2_input_bits": "160555675878901663", "plot_triple_log": { "exact_log2log2_integer": "160555675878901663" }, "source": "data/operation-audit/adaptive-p16-crossover-bounds.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": "A separately counted realization of this own-source supplier under retained native/analytic contracts. A sufficient upper, not an actual crossing." }, "cost_status": "conditional_literal_family_range", "fresh_arithmetic_replay_status": "PASS", "replay_receipt": "data/operation-audit/adaptive-p16-witness-replay.json", "claim_type": "compiler_variant_same_kappa", "uniform_rank_H": "1587000000", "tensor_power": 1, "early_effective_kappa": "1/500", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 0, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [], "source_head": "e9e9f244108ab4c21f0293cbfca9cfc3206e772a" } }, { "pr": 4714, "title": "Construct affine centre access and prove literal Haar limits", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4714", "author": "aliromman", "created_at": "2026-10-22T17:41:50Z", "accepted_at": "2026-10-22T19:28:25Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 86, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No own full-integer runtime point follows. Retain this component/validation result with its named complete construction; an actual changed physical supplier and complete recursive/precision/outer invoice must be bound before new numerical costs." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "4c42b1925ca589ca5a773f3e791d90b28dd79dfa" } }, { "pr": 4728, "title": "Construct reciprocal native responses with sharp rank-two blocks and fewer child calls", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4728", "author": "aliromman", "created_at": "2026-10-22T18:12:31Z", "accepted_at": "2026-10-22T19:28:25Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 63, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep the actual local construction, exact component count and stated exclusions with its named target. A whole runtime bound requires a complete source-selected caller/native/owner/recursive invoice/precision/outer realization; an autonomous target identity and a consistent complete cost meter cannot be replaced by a local moment screen." ], "source_manifest": [ { "file": "individual-primary-interface-source/4728-manifest.json", "sha256": "3e2a6937396809f0389b4c6845c32462fe3d074a43aca4ac1fce38b3edb02d12" }, { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "4c903ff856e2cfbd6fc91d98b6b430e1b4955e72" } }, { "pr": 4671, "title": "Prove exact identity-pivot Schur dimension for every prescribed H (no \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4671", "author": "ssafwann", "created_at": "2026-10-22T15:07:46Z", "accepted_at": "2026-10-22T19:28:26Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "local_algebraic_result_no_integer_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "8d2e3bc76aa7d43e5c629daaf1e72d4dd5a81ed9" } }, { "pr": 4672, "title": "Coordinate contact/helper frames on the round-two supplier (conditional kappa 0.00302166; not frontier)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4672", "author": "1337isnot1337", "created_at": "2026-10-22T15:14:39Z", "accepted_at": "2026-10-22T19:28:26Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302166", "kappa_fraction": "151083/50000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^31385199999997-2^69)", "plot_triple_log": { "log2_of_integer": "31385199999997", "negligible_negative_correction": true }, "scope": "Own selected complete unreduced hyperplane-retimed raw controller/native word, full field/spectator ranges when active, stored width at least two; identical optimized GMP when inactive.", "statistic": "Earliest possible strict win in the declared literal enhancement family", "source": "data/operation-audit/pr4672-hyperplane-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "conditional_upper": null, "cost_status": "conditional_own_source_lower_only", "own_source_cost_extension": true, "early_effective_kappa": "151083/50000000", "own_source_scope": [ "Own source gauge/relative-helper arbitrary-input all-column required-entry/output-frame and absolute-phase identities, complete copied/owned/spectator interface; original full native engine is authenticated but not rerun here.", "Own physical mixed tensor/completion/splitting/compiler strict supplier at the selected H, literal complete raw occurrences retained.", "Same prescribed unreduced dense ADD lowering and fixed repaired-reference correctness/finite-kernel halting contracts." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr4672-hyperplane-literal-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 41, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "9da43a7d1ec73f4e6000a201d9d76818a8d4548f" } }, { "pr": 4678, "title": "Count complete headers with sharp identity-pivot Schur blocks (no \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4678", "author": "ssafwann", "created_at": "2026-10-22T15:34:57Z", "accepted_at": "2026-10-22T19:28:26Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "local_algebraic_result_no_integer_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "af9cf805c501e4e9e947c98c0b97b2281b6b6e97" } }, { "pr": 4707, "title": "Tighten conditional critical-root transfer to kappa = 0.0030201659769 (exact arithmetic)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4707", "author": "Chrisbryan17", "created_at": "2026-10-22T17:00:38Z", "accepted_at": "2026-10-22T19:28:26Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0030201659769", "kappa_fraction": "30201659769/10000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^999999999999997-2^69+2)", "plot_triple_log": { "log2_of_integer": "999999999999997", "negligible_negative_correction": true }, "scope": "Identical repaired optimized GMP when inactive; unreduced complete dense raw p16 scalar word when active, under own strict-winning supplier and all-column/spectator contracts.", "statistic": "Earliest input width at which some correct member of this literal enhancement family strictly beats the reference", "source": "data/operation-audit/pr4707-critical-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "conditional_upper": { "input_bits": "2^(2^100040004792191118061679)", "log2log2_input_bits": "100040004792191118061679", "plot_triple_log": { "exact_log2log2_integer": "100040004792191118061679" }, "source": "data/operation-audit/pr4707-critical-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "Own source critical-root theorem/strict integer child descent and positive uniform supplier at this explicitly authenticated H", "Own source inherits arbitrary-input/all-column, owned/spectator and physical closure for its changed fixed word; the finite checker does not prove this bridge", "Own-head selected unchanged raw p16 native and exact absolute-phase endpoints; full native engine not replayed here", "Separate role fields and parent selected axes, completed child barriers, restored owned banks, exact per-role Clifford Gaussian-dyadic endpoints", "The source-parametric fine-prime/Gaussian/finite-section/boundary/whole-integer recovery analytic branch" ] }, "cost_status": "conditional_own_source_range", "own_source_cost_extension": true, "early_effective_kappa": "1/500", "own_source_scope": [ "Own source critical-root theorem/strict integer child descent and positive uniform supplier at this explicitly authenticated H", "Own source inherits arbitrary-input/all-column, owned/spectator and physical closure for its changed fixed word; the finite checker does not prove this bridge", "Own-head selected unchanged raw p16 native and exact absolute-phase endpoints; full native engine not replayed here", "Separate role fields and parent selected axes, completed child barriers, restored owned banks, exact per-role Clifford Gaussian-dyadic endpoints", "The source-parametric fine-prime/Gaussian/finite-section/boundary/whole-integer recovery analytic branch" ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr4707-critical-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 3, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "ccc1517daba8fa7d4a571ce72cace1789bac1cf4" } }, { "pr": 4713, "title": "Conditional DIV-free Word RAM \u03ba = 0.0030217758 (+4e-10 over #4635)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4713", "author": "Dugongue", "created_at": "2026-10-22T17:38:28Z", "accepted_at": "2026-10-22T19:28:26Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0030217758", "kappa_fraction": "15108879/5000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^38569299999999997-2^69)", "plot_triple_log": { "log2_of_integer": "38569299999999997", "negligible_negative_correction": true }, "scope": "Derived bit-circuit enhancement family retaining own complete unreduced raw controller/native boundary on full fields/spectators, width at least two when active; identical optimizedGMP when inactive. Not all WordRAM or bit implementations.", "statistic": "Earliest possible strict win in this own-source literal bit enhancement family", "exact_individual_crossing": false, "all_PR_implementations": false, "source": "data/operation-audit/pr4713-derived-xag-literal-lower.json" }, "conditional_upper": { "input_bits": "2^(2^3858472889500089802740160)", "log2log2_input_bits": "3858472889500089802740160", "plot_triple_log": { "exact_log2log2_integer": "3858472889500089802740160" }, "source": "data/operation-audit/pr4713-derived-xag-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "NEW direct Gaussian/Fermat XAG bit realization of own explicitly selected algebraic native core, not original division-free Word RAM lookup/MUL instruction cost translation.", "Own actual selected arbitrary-input required Gaussian endpoint/absolute-phase/all-fiber/owned/spectator and bounded finite-Clifford monomial identities; same raw component recovered by exact source hashes, not a fresh universal native proof.", "Own chronological source/complement/exit complete integer compiler, ready barriers and nested widths with strict rank descent, and own freshly replayed critical majorant.", "Concrete normalized Gaussian/finite-LDU/narrow-gap/cyclic-border/fine-prime/exact-recovery and fixed repaired optimizedGMP correctness/finite-kernel halting." ] }, "cost_status": "conditional_own_source_range", "own_source_cost_extension": true, "early_effective_kappa": "1/500", "own_source_scope": [ "NEW direct Gaussian/Fermat XAG bit realization of own explicitly selected algebraic native core, not original division-free Word RAM lookup/MUL instruction cost translation.", "Own actual selected arbitrary-input required Gaussian endpoint/absolute-phase/all-fiber/owned/spectator and bounded finite-Clifford monomial identities; same raw component recovered by exact source hashes, not a fresh universal native proof.", "Own chronological source/complement/exit complete integer compiler, ready barriers and nested widths with strict rank descent, and own freshly replayed critical majorant.", "Concrete normalized Gaussian/finite-LDU/narrow-gap/cyclic-border/fine-prime/exact-recovery and fixed repaired optimizedGMP correctness/finite-kernel halting." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr4713-derived-xag-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 41, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "9bb3f3f72925e8825c8b4851dfdc8e92b72db949" } }, { "pr": 4717, "title": "Prove sharp centre encoding bounds and implement native metric services", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4717", "author": "aliromman", "created_at": "2026-10-22T17:48:12Z", "accepted_at": "2026-10-22T19:28:26Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 81, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep the actual local construction, exact component count and stated exclusions with its named target. A whole runtime bound requires a complete source-selected caller/native/owner/recursive invoice/precision/outer realization; an autonomous target identity and a consistent complete cost meter cannot be replaced by a local moment screen." ], "source_manifest": [ { "file": "individual-primary-interface-source/4717-manifest.json", "sha256": "cd06be89a327a0b2bdb8e03435df9ebac2a6e4cc0b1978a4f1c81c1b4afe0471" }, { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "6c6ff8b48ef238a7adebe2391c3c2912ae90f0c4" } }, { "pr": 4630, "title": "Conditional native Word RAM \u03ba = 0.0030201655: fused execution without TM simulation", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4630", "author": "Dugongue", "created_at": "2026-10-22T12:40:24Z", "accepted_at": "2026-10-22T19:28:27Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0030201655", "kappa_fraction": "6040331/2000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^999999999997-2^69)", "plot_triple_log": { "log2_of_integer": "999999999997", "negligible_negative_correction": true }, "scope": "Derived bit-circuit enhancement family retaining own complete unreduced raw controller/native boundary on full fields/spectators, width at least two when active; identical optimizedGMP when inactive. Not all WordRAM or bit implementations.", "statistic": "Earliest possible strict win in this own-source literal bit enhancement family", "exact_individual_crossing": false, "all_PR_implementations": false, "source": "data/operation-audit/pr4630-derived-xag-literal-lower.json" }, "conditional_upper": { "input_bits": "2^(2^100041795189802580144)", "log2log2_input_bits": "100041795189802580144", "plot_triple_log": { "exact_log2log2_integer": "100041795189802580144" }, "source": "data/operation-audit/pr4630-derived-xag-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "NEW direct Gaussian/Fermat XAG bit realization of the own explicitly selected algebraic native core, not original Word RAM lookup/MUL/DIV instruction cost translation.", "Own actual selected arbitrary-input required Gaussian endpoint/absolute-phase/all-fiber/owned/spectator and bounded finite-Clifford monomial identities; same raw component recovered by exact source hashes, not a fresh universal native proof.", "Own chronological source/complement/exit complete integer compiler, ready barriers and nested widths with strict rank descent, and own freshly replayed critical majorant.", "Concrete normalized Gaussian/finite-LDU/narrow-gap/cyclic-border/fine-prime/exact-recovery and fixed repaired optimizedGMP correctness/finite-kernel halting." ] }, "cost_status": "conditional_own_source_range", "own_source_cost_extension": true, "early_effective_kappa": "1/500", "own_source_scope": [ "NEW direct Gaussian/Fermat XAG bit realization of the own explicitly selected algebraic native core, not original Word RAM lookup/MUL/DIV instruction cost translation.", "Own actual selected arbitrary-input required Gaussian endpoint/absolute-phase/all-fiber/owned/spectator and bounded finite-Clifford monomial identities; same raw component recovered by exact source hashes, not a fresh universal native proof.", "Own chronological source/complement/exit complete integer compiler, ready barriers and nested widths with strict rank descent, and own freshly replayed critical majorant.", "Concrete normalized Gaussian/finite-LDU/narrow-gap/cyclic-border/fine-prime/exact-recovery and fixed repaired optimizedGMP correctness/finite-kernel halting." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr4630-derived-xag-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 57, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "f4b974db1f651250a252721cf127d0491a802699" } }, { "pr": 4635, "title": "Conditional Word RAM \u03ba = 0.0030217754 (+0.0000016099 over #4630)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4635", "author": "Dugongue", "created_at": "2026-10-22T13:24:59Z", "accepted_at": "2026-10-22T19:28:27Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0030217754", "kappa_fraction": "15108877/5000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Different computational model; separate from fixed-tape TM series.", "source_status": "scope-flagged", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^999999999997-2^69)", "plot_triple_log": { "log2_of_integer": "999999999997", "negligible_negative_correction": true }, "scope": "Derived bit-circuit enhancement family retaining own complete unreduced raw controller/native boundary on full fields/spectators, width at least two when active; identical optimizedGMP when inactive. Not all WordRAM or bit implementations.", "statistic": "Earliest possible strict win in this own-source literal bit enhancement family", "exact_individual_crossing": false, "all_PR_implementations": false, "source": "data/operation-audit/pr4635-derived-xag-literal-lower.json" }, "conditional_upper": { "input_bits": "2^(2^100041795189802580144)", "log2log2_input_bits": "100041795189802580144", "plot_triple_log": { "exact_log2log2_integer": "100041795189802580144" }, "source": "data/operation-audit/pr4635-derived-xag-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": [ "NEW direct Gaussian/Fermat XAG bit realization of the own explicitly selected algebraic native core, not original Word RAM lookup/MUL/DIV instruction cost translation.", "Own actual selected arbitrary-input required Gaussian endpoint/absolute-phase/all-fiber/owned/spectator and bounded finite-Clifford monomial identities; same raw component recovered by exact source hashes, not a fresh universal native proof.", "Own chronological source/complement/exit complete integer compiler, ready barriers and nested widths with strict rank descent, and own freshly replayed critical majorant.", "Concrete normalized Gaussian/finite-LDU/narrow-gap/cyclic-border/fine-prime/exact-recovery and fixed repaired optimizedGMP correctness/finite-kernel halting." ] }, "cost_status": "conditional_own_source_range", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "documented_event_specific_objection_or_different_model", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 246, "source_index": 405, "at": "2026-10-22T13:24:59Z", "until": "2026-10-22T14:33:27Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.0030217754", "dashboard_float_text": "0.0030217754", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4635", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 288, "source_index": null, "at": "2026-10-22T13:24:59Z", "until": null, "date_basis": "source_update_estimate", "fraction": null, "value_decimal": "0.0030217754", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4635", "evidence_excerpt": "Conditional Word RAM \u03ba = 0.0030217754 (+0.0000016099 over #4630)", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 565, "source_index": null, "at": "2026-10-22T13:24:59Z", "until": null, "date_basis": "body-version", "fraction": "15108877/5000000000", "value_decimal": "0.0030217754", "dashboard_float_text": null, "expression": "0.0030217754", "historical_title": "Conditional Word RAM \u03ba = 0.0030217754 (+0.0000016099 over #4630)", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4635", "evidence_excerpt": "\u03ba = 0.0030201655. This source-bound sufficient assembly lifts Cao Yifan's stronger #4610 profile to \u03ba = 0.0030217754, an exact increase of 0.0000016099, on w = \u0398(log n) Word RAM with bounded-word MUL/DIV. The construction uses neither a TM simulator nor a TM multiplier. It does not discover anot", "automated_comparable": true, "body_sha256": "1ccd7eece6c7be66faed4b9c1057e2a8fea460979ba43de08263c542477a3b3e" } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/500", "own_source_scope": [ "NEW direct Gaussian/Fermat XAG bit realization of the own explicitly selected algebraic native core, not original Word RAM lookup/MUL/DIV instruction cost translation.", "Own actual selected arbitrary-input required Gaussian endpoint/absolute-phase/all-fiber/owned/spectator and bounded finite-Clifford monomial identities; same raw component recovered by exact source hashes, not a fresh universal native proof.", "Own chronological source/complement/exit complete integer compiler, ready barriers and nested widths with strict rank descent, and own freshly replayed critical majorant.", "Concrete normalized Gaussian/finite-LDU/narrow-gap/cyclic-border/fine-prime/exact-recovery and fixed repaired optimizedGMP correctness/finite-kernel halting." ], "own_source_record_tail_quantified": true, "own_source_certificate": "pr4635-derived-xag-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 67, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "898b0c8e2ca23897c312230988515c2553154f30" } }, { "pr": 4636, "title": "Audit #4633: full replay, native contract failures and verifier false positives", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4636", "author": "1337isnot1337", "created_at": "2026-10-22T13:48:03Z", "accepted_at": "2026-10-22T19:28:27Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.25", "kappa_fraction": "1/4", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 71, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "b0a325a3e312b7c5ebceb420de4b8cb13181f43e" } }, { "pr": 4637, "title": "Join the CRT scanner-owned mask to conditional sparse repair (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4637", "author": "codyw912", "created_at": "2026-10-22T13:48:26Z", "accepted_at": "2026-10-22T19:28:27Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "60d0b09f13a9f9ebdd93d98d83d16ce6907d70b6" } }, { "pr": 4638, "title": "Sharpen chronological width to d+1 and extend batching to adaptive heights (no new kappa)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4638", "author": "codyw912", "created_at": "2026-10-22T13:48:28Z", "accepted_at": "2026-10-22T19:28:27Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 16, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/adaptive-chronological-batching/README.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "No explicit selected native semantic-program binding has been adjudicated from the current own primary set (research/adaptive-chronological-batching/README.md, research/adaptive-chronological-batching/RESULT.json, research/adaptive-chronological-batching/SOURCES.json). Recover the actual emitter/selected word and public input/output-frame contract; do not import a later equal-kappa native.", "Recompute the complete own productive/paid histogram from research/adaptive-chronological-batching/WIDTH-RESULT.json#/profile_applications/2 and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "385a4436a47ea8e80cc1503948fe7a36e1b1c5af" } }, { "pr": 4641, "title": "Independently check #4635's native \u03ba step: the +1.6099e-6 is #4610's paid profile, not the Word RAM transfer (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4641", "author": "lm1909", "created_at": "2026-10-22T14:00:26Z", "accepted_at": "2026-10-22T19:28:27Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0030201655", "kappa_fraction": "6040331/2000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "independent_validation_of_explicit_construction_targets", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Price the exact identified target word/controller, complete invoice, own compiler and precision/stock parameters; validation evidence may support that price but no cutoff is inherited from a title, unchanged kappa or matching histogram." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "99007ce1bb6a3d2889ddeb763bbc7546724e1f52" } }, { "pr": 4642, "title": "Independently check #4629's re-padding ledger and price: \u03ba 0.015637149091 reproduces; re-pad is +1\u00d7187/+5\u00d726, block-7 surplus \u2212256, ninth axis reached only by padding (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4642", "author": "lm1909", "created_at": "2026-10-22T14:01:14Z", "accepted_at": "2026-10-22T19:28:27Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.015637149090882", "kappa_fraction": "7818574545441/500000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No independent whole-multiplier cutoff is defined by this supplied contribution. Price the explicitly referenced complete algorithm only after binding its actual native/operator, ownership, recursive invoice, precision and outer parameters. Relevant local constants, guards and negative hypotheses remain attached to that target; they are not discarded." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "d8c59e36a8efb301f0298871218cfe00f4e043f7" } }, { "pr": 4647, "title": "Prove length-2 S3 words miss the transposition (0 2).", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4647", "author": "unpaidmoon", "created_at": "2026-10-22T14:06:10Z", "accepted_at": "2026-10-22T19:28:27Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "scoped_obstruction_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "734bb589d082ccd7c61b987d36a84b85c318e117" } }, { "pr": 4657, "title": "Prove identity-pivot Schur dimension bounds; attain 4d (no \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4657", "author": "ssafwann", "created_at": "2026-10-22T14:32:43Z", "accepted_at": "2026-10-22T19:28:27Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "local_algebraic_result_no_integer_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "b79f90bc8d839a4998a40b10bcb437e87baa8397" } }, { "pr": 4626, "title": "Improve conditional kappa to 0.003021569 with helper621 and a funded compiler gap", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4626", "author": "hexapode", "created_at": "2026-10-22T11:18:01Z", "accepted_at": "2026-10-22T19:28:28Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.003021569", "kappa_fraction": "3021569/1000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^337847999999997-2^69)", "plot_triple_log": { "log2_of_integer": "337847999999997", "negligible_negative_correction": true }, "scope": "Own complete unreduced changed-helper621 boundary/native word when active, width at least two, strict winning own uniform supplier; identical optimized GMP when inactive.", "statistic": "Earliest input width at which a correct member of this literal enhancement family strictly beats the reference", "source": "data/operation-audit/pr4626-helper621-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "conditional_upper": { "input_bits": "2^(2^33794937907887191919064)", "log2log2_input_bits": "33794937907887191919064", "plot_triple_log": { "exact_log2log2_integer": "33794937907887191919064" }, "source": "data/operation-audit/pr4626-helper621-early-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": "Own changed-helper621 unreduced separated-product instantiation with complete source profile, required physical frames and owned/spectator contracts. Both early and original-record tails are priced. Native finite engine passed; all-width compiler and analytic contracts remain premises." }, "cost_status": "conditional_own_source_range", "historical_streams": [ "current_chart_frontier", "reconstructed_highwater", "recovered_literal_highwater" ], "historical_status": "literal_author_claim_not_newly_adjudicated_as_record", "historical_events": [ { "stream": "reconstructed_highwater", "stream_row": 245, "source_index": 403, "at": "2026-10-22T11:37:26.771874Z", "until": "2026-10-22T12:40:24Z", "date_basis": "reconstructed_dashboard_segment", "fraction": null, "value_decimal": "0.003021569", "dashboard_float_text": "0.003021569", "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4626", "evidence_excerpt": "", "automated_comparable": null, "body_sha256": null }, { "stream": "current_chart_frontier", "stream_row": 287, "source_index": null, "at": "2026-10-22T11:37:26.771874+00:00", "until": null, "date_basis": "observed_revision", "fraction": null, "value_decimal": "0.003021569", "dashboard_float_text": null, "expression": null, "historical_title": null, "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4626", "evidence_excerpt": "Improve conditional kappa to 0.003021569 with helper621 and a funded compiler gap", "automated_comparable": true, "body_sha256": null }, { "stream": "recovered_literal_highwater", "stream_row": 562, "source_index": null, "at": "2026-10-22T11:18:01Z", "until": null, "date_basis": "body-version", "fraction": "75539/25000000", "value_decimal": "0.003021569", "dashboard_float_text": null, "expression": "0.00302156", "historical_title": "Improve conditional kappa to 0.00302156 by combining helper621 and warp interfaces", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4626", "evidence_excerpt": "for helper621 improves the supported conditional whole multiplication saving from \u03ba = 0.00302152 to \u03ba = 0.00302156 (+0.00000004).\n\nHelper621 starts in span [30,429], and its first scalar contact uses that same chart. Regenerated climbs change the paid profile to {1:2202,2:414,3:505,4:134,5:36,", "automated_comparable": true, "body_sha256": "ad5248aca1f810ed6b98e66fafb628badda94edac9f79b588b112f40cd0a492c" }, { "stream": "recovered_literal_highwater", "stream_row": 563, "source_index": null, "at": "2026-10-22T11:36:46Z", "until": null, "date_basis": "title-edit", "fraction": "3021569/1000000000", "value_decimal": "0.003021569", "dashboard_float_text": null, "expression": "0.003021569", "historical_title": "Improve conditional kappa to 0.003021569 with helper621 and a funded compiler gap", "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4626", "evidence_excerpt": "Improve conditional kappa to 0.003021569 with helper621 and a funded compiler gap", "automated_comparable": true, "body_sha256": null } ], "reviewed_checkpoint_associations": [], "historical_source": "data/operation-audit/record-cost-coverage/reconciled-record-candidates.json", "own_source_cost_extension": true, "early_effective_kappa": "1/500", "own_source_scope": "Own changed-helper621 unreduced separated-product instantiation with complete source profile, required physical frames and owned/spectator contracts. Both early and original-record tails are priced. Native finite engine passed; all-width compiler and analytic contracts remain premises.", "own_source_record_tail_quantified": true, "own_source_certificate": "pr4626-helper621-early-upper.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 15, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "e4413c43eeaacdd20be123fdd7d7add53427f028" } }, { "pr": 4720, "title": "Prove information and snapshot cut bounds for the historical routed queries", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4720", "author": "aliromman", "created_at": "2026-10-22T17:52:26Z", "accepted_at": "2026-10-22T19:31:50Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "scoped_information_bound_no_independent_algorithm", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 96, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "cb102a57254748651ce16aa4454bb611f6380e53" } }, { "pr": 4729, "title": "Construct selected response units and reduce two normalization costs", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4729", "author": "aliromman", "created_at": "2026-10-22T18:14:49Z", "accepted_at": "2026-10-22T19:31:50Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 83, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/publication-reviews/raw-selected-centre-units/REVIEW.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 1 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Recompute the complete own productive/paid histogram from research/publication-reviews/raw-selected-centre-units/final-annex-review/cold-replay/signed-words/normal/REVIEW.json#/providers/extra/oblique_backward and actual call/owner windows, including every idle/spectator/owned field; the discovered JSON is a profile candidate, not a complete invoice proof.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Supply a complete own outer precision/analytic/recovery schedule and operation constants, or explicitly bind a source-correct inherited schedule, before a numerical integer cutoff can be derived." ], "source_manifest": [ { "file": "individual-primary-interface-source/4729-manifest.json", "sha256": "d72da96136e9e1fbc100846498c0002748ab70ad59c9ba46a8271a45925b6ca6" }, { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "0c4a16bfbcb18eb483bbe617f5ed340b1171356e" } }, { "pr": 4733, "title": "Add exact centre-entry, rational-code, and retained-reader services", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4733", "author": "aliromman", "created_at": "2026-10-22T18:18:47Z", "accepted_at": "2026-10-22T19:31:50Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "own_source_fetched_cost_obligations_open", "audit_completed": false, "numeric_bound_completed": false, "verified_artifact_count": 90, "source_family": "source_interface_requires_individual_analysis", "cost_obligations": [ "Adjudicate the actual own contribution/selected candidate from research/centre-code-services/NOTICE.md; the literal scope excerpts in this report are unadjudicated, not a semantic exclusion.", "Resolve complete selected-provider dispatch and actual program/canonical/orientation identity. 0 exact primary/archive pin matches and 0 derived-object pin matches were recovered; byte equality alone does not establish which provider executes or its operator/phase semantics.", "Bind a complete physical and recursive invoice for the selected changes. Current primary candidates (research/centre-code-services/CHECKS.json, research/centre-code-services/NOTICE.md, research/centre-code-services/PACKAGE-MANIFEST.json) have not yielded an adjudicated whole paid/idle/owner profile; local operation savings or baseline quotes cannot be promoted to a full multiplier cost.", "No complete own work/height/precision/stock interface has been cost-bound by this inventory. Locate its exact inherited dependency bytes or derive it from the actual selected operations; the current source files are not automatically closed by an exponent claim.", "Re-evaluate all whole integer cost rows with the exact own outer/saving candidate at research/centre-code-services/annexes/pivot-code-invoice/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json#/ after native/invoice selection. No numerical cutoff follows from these fields alone." ], "source_manifest": [ { "file": "individual-primary-interface-source/4733-manifest.json", "sha256": "0e7b03ecc476e59bff8d336d3b47d9ca1777773a4d471aca16c772bcfa3cb311" }, { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "dd6948e95eb002d903ce36dd21e0c075e00790ed" } }, { "pr": 4734, "title": "Certify conditional R437 original-root STEP and capsule handoff (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4734", "author": "codyw912", "created_at": "2026-10-22T18:20:01Z", "accepted_at": "2026-10-22T19:31:50Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "4c1a746590ec97fa84537da43dc662775a5b72e7" } }, { "pr": 4736, "title": "Completed-bit codes, outer-transform composition, and conditional terminal factors", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4736", "author": "aliromman", "created_at": "2026-10-22T18:32:40Z", "accepted_at": "2026-10-22T19:31:50Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 92, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No own full-integer runtime point follows. Retain this component/validation result with its named complete construction; an actual changed physical supplier and complete recursive/precision/outer invoice must be bound before new numerical costs." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "5e3c47e9e60e47971bafe9d09aa8bb1ffb3e8927" } }, { "pr": 4777, "title": "Prove the binary pair-versus-singleton full-guard inequality (no \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4777", "author": "petalas", "created_at": "2026-10-22T19:51:31Z", "accepted_at": "2026-10-23T01:45:57Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No independent whole-multiplier cutoff is defined by this supplied contribution. Price the explicitly referenced complete algorithm only after binding its actual native/operator, ownership, recursive invoice, precision and outer parameters. Relevant local constants, guards and negative hypotheses remain attached to that target; they are not discarded." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "d161261eaf899e0d15036a312aac0022aa1a4ab6" } }, { "pr": 4906, "title": "Fix current task startup guidance while preserving frozen inputs", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4906", "author": "mihir-s-05", "created_at": "2026-10-22T23:35:07Z", "accepted_at": "2026-10-23T01:48:15Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 2, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "A numerical whole-multiplier comparison must separately identify an actual complete selected native/caller/owner/recursive work-height-stock interface and precision/analytic/outer realization. This source-scope disposition neither supplies nor transfers that bound, and does not extend a restricted negative result beyond its stated family." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "6b179376a3fe18a6efc57951c2df48bef9fed117" } }, { "pr": 4916, "title": "Prove exact dirty-fanout tariffs over unital rings (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4916", "author": "petalas", "created_at": "2026-10-22T23:45:12Z", "accepted_at": "2026-10-23T01:48:15Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep the actual named multiplier/changedprogram as a distinct costing target. This contribution is validation, a restricted theorem or an unimplementedtarget; it defines no new fullruntime point. Its target-specific scope/negative controls/constant qualifications must be checked when a complete supplier is priced." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "459a1d9984e8c5bf09257a409863e63282c282e6" } }, { "pr": 4951, "title": "Independently join the selected #4470 p16 invoice to its moment bill: exact agreement, surplus below one rank-one job (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4951", "author": "JoyboyBrian", "created_at": "2026-10-23T03:54:55Z", "accepted_at": "2026-10-23T04:00:25Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "4b72f7553211b7ee46ecb530daa6b5a4b172df0a" } }, { "pr": 4933, "title": "Emit a phase-correct coded p16 caller removing 144 center calls (no \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4933", "author": "dillona", "created_at": "2026-10-23T02:23:40Z", "accepted_at": "2026-10-23T04:00:26Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 23, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep the actual local construction, exact component count and stated exclusions with its named target. A whole runtime bound requires a complete source-selected caller/native/owner/recursive invoice/precision/outer realization; an autonomous target identity and a consistent complete cost meter cannot be replaced by a local moment screen." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "d969c458c24278e0fd37e5b4c0ff8a53a496b430" } }, { "pr": 4954, "title": "Bound the selected #4470 BIT-stage stock on both sides: every single-cover-level width overdraws, fit from log2 e = 52182660963735 (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4954", "author": "JoyboyBrian", "created_at": "2026-10-23T04:00:20Z", "accepted_at": "2026-10-23T04:01:17Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No own full-integer runtime point follows. Retain this component/validation result with its named complete construction; an actual changed physical supplier and complete recursive/precision/outer invoice must be bound before new numerical costs." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "cc1bfc06883ba5a274b09fdd509975b24f04ed06" } }, { "pr": 4972, "title": "The complex row coefficient of the selected outer reserve is one (log2 C \u221264 bits, no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4972", "author": "jwr404", "created_at": "2026-10-23T04:43:44Z", "accepted_at": "2026-10-23T05:35:46Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0015", "kappa_fraction": "3/2000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "0622d9a6648ca33b9b7595cdff0cb27f57896155" } }, { "pr": 4973, "title": "Keep an inherited PYTHONPATH from hollowing out registered and selected replays", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4973", "author": "jwr404", "created_at": "2026-10-23T04:58:01Z", "accepted_at": "2026-10-23T05:35:46Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "incorporated", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 2, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "A numerical whole-multiplier comparison must separately identify an actual complete selected native/caller/owner/recursive work-height-stock interface and precision/analytic/outer realization. This source-scope disposition neither supplies nor transfers that bound, and does not extend a restricted negative result beyond its stated family." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "58d738af630092d9a56de349f795bd2a7c6a353f" } }, { "pr": 4974, "title": "Prove a single three-cycle costs six with arbitrary address spectators", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4974", "author": "JoyboyBrian", "created_at": "2026-10-23T05:03:11Z", "accepted_at": "2026-10-23T05:35:46Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 9, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "538ccab19e01012ecd67a79d5a0a6341a9ebe933" } }, { "pr": 4990, "title": "Pay the two-target CRT stencil producer and join its repair mask", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4990", "author": "kumagi", "created_at": "2026-10-23T05:40:39Z", "accepted_at": "2026-10-23T06:06:28Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep the actual local construction, exact component count and stated exclusions with its named target. A whole runtime bound requires a complete source-selected caller/native/owner/recursive invoice/precision/outer realization; an autonomous target identity and a consistent complete cost meter cannot be replaced by a local moment screen." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "ea2b6fa4d6479813c36ca0c0396c8d06437fb486" } }, { "pr": 5025, "title": "Complete the admitted R437 fibre Count with one radix validation", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5025", "author": "JoyboyBrian", "created_at": "2026-10-23T06:43:46Z", "accepted_at": "2026-10-23T07:14:44Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 11, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep the actual local construction, exact component count and stated exclusions with its named target. A whole runtime bound requires a complete source-selected caller/native/owner/recursive invoice/precision/outer realization; an autonomous target identity and a consistent complete cost meter cannot be replaced by a local moment screen." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "764b06d86b1ec48b74e5ae2d29c7e521cf69301a" } }, { "pr": 5023, "title": "Prove exact unequal query capacity for every odd cycle", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5023", "author": "JoyboyBrian", "created_at": "2026-10-23T06:35:26Z", "accepted_at": "2026-10-23T07:14:45Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 9, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep the actual local construction, exact component count and stated exclusions with its named target. A whole runtime bound requires a complete source-selected caller/native/owner/recursive invoice/precision/outer realization; an autonomous target identity and a consistent complete cost meter cannot be replaced by a local moment screen." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "1b069fc3d6bb463ab212f3ebc644abe838efa550" } }, { "pr": 5037, "title": "Construct a bounded-lane border core without an exact boundary provider", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5037", "author": "Lyy-iiis", "created_at": "2026-10-23T07:11:27Z", "accepted_at": "2026-10-23T07:15:17Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 24, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep the actual local construction, exact component count and stated exclusions with its named target. A whole runtime bound requires a complete source-selected caller/native/owner/recursive invoice/precision/outer realization; an autonomous target identity and a consistent complete cost meter cannot be replaced by a local moment screen." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "e30cfa384f7e48581f9e5a5cb036b1ee7a3b46a9" } }, { "pr": 5136, "title": "Prove rank-eight owned high contacts after removing all native constraints", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5136", "author": "1337isnot1337", "created_at": "2026-10-23T10:36:27Z", "accepted_at": "2026-10-23T10:40:44Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "2172943239af745ce43ede68afafb8d8783d7011" } }, { "pr": 5137, "title": "Prove exact two-call capacity for homogeneous query chains (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5137", "author": "1337isnot1337", "created_at": "2026-10-23T10:38:58Z", "accepted_at": "2026-10-23T10:41:23Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep the actual named multiplier/changedprogram as a distinct costing target. This contribution is validation, a restricted theorem or an unimplementedtarget; it defines no new fullruntime point. Its target-specific scope/negative controls/constant qualifications must be checked when a complete supplier is priced." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "f2d83999edccdad625ea686ff3f0d03b7d208965" } }, { "pr": 5170, "title": "Prove bounded native corrective ADD chains cannot improve paid profiles", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5170", "author": "1337isnot1337", "created_at": "2026-10-23T11:41:30Z", "accepted_at": "2026-10-23T11:56:46Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "5f3e088621e0a510f5b07ece590409e94ae45897" } }, { "pr": 5140, "title": "Extend owned-wire floor to free native/helper boundaries and nonnested C moves", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5140", "author": "1337isnot1337", "created_at": "2026-10-23T10:47:53Z", "accepted_at": "2026-10-23T11:56:47Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "1d1b593168a36ee524300752a5e33f6cd7a08314" } }, { "pr": 5147, "title": "Price native helper reuse: even a free third H17 loses (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5147", "author": "1337isnot1337", "created_at": "2026-10-23T11:01:42Z", "accepted_at": "2026-10-23T11:56:47Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 7, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No independent whole-multiplier cutoff is defined by this supplied contribution. Price the explicitly referenced complete algorithm only after binding its actual native/operator, ownership, recursive invoice, precision and outer parameters. Relevant local constants, guards and negative hypotheses remain attached to that target; they are not discarded." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "8d1a267b708bd30bdd84a3ab47d5a67de7aeb745" } }, { "pr": 5212, "title": "Screen coupled five-chart nonmonotone owned contacts (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5212", "author": "1337isnot1337", "created_at": "2026-10-23T12:42:27Z", "accepted_at": "2026-10-23T13:09:35Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 8, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep the actual local construction, exact component count and stated exclusions with its named target. A whole runtime bound requires a complete source-selected caller/native/owner/recursive invoice/precision/outer realization; an autonomous target identity and a consistent complete cost meter cannot be replaced by a local moment screen." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "7930e5a4597e3bd5b2a73740cbecad26e7a69940" } }, { "pr": 5220, "title": "Research: active p2 feedback and exact output coupling (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5220", "author": "1337isnot1337", "created_at": "2026-10-23T12:51:43Z", "accepted_at": "2026-10-23T13:09:35Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep the actual local construction, exact component count and stated exclusions with its named target. A whole runtime bound requires a complete source-selected caller/native/owner/recursive invoice/precision/outer realization; an autonomous target identity and a consistent complete cost meter cannot be replaced by a local moment screen." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "73b5f0d8c0a6410c3ab4bf45643c54f8802b84e3" } }, { "pr": 5224, "title": "Price heterogeneous native stages with all changed main and idle ranks (no new \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5224", "author": "1337isnot1337", "created_at": "2026-10-23T12:57:28Z", "accepted_at": "2026-10-23T13:09:35Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 10, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "This contribution supplies a restricted theorem, audit, tool or favorable screen rather than a new fully supplied multiplier. Preserve its relevant constants/qualification with the named target; bind an actual source-selected complete physical/native/owner/invoice/precision/outer implementation, whether changed or exact-source-identical with its own commitments, before a distinct cutoff is defined." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "351fba667cfe8c5b07622f2eac6bba5839da24a5" } }, { "pr": 5226, "title": "Fragmentation-loss ceiling: exact \u039b ship threshold for the #4610 family, with Lean (no \u03ba change)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5226", "author": "DreamingOfClouds", "created_at": "2026-10-23T13:01:36Z", "accepted_at": "2026-10-23T13:09:35Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0030233", "kappa_fraction": "30233/10000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "dc5764630fdf34f72bbe76efd4b79d3b2bc3dd40" } }, { "pr": 5339, "title": "Prove finite separation and fund dyadic detection of orthogonal witnesses", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5339", "author": "aliromman", "created_at": "2026-10-23T17:40:23Z", "accepted_at": "2026-10-23T18:37:52Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 22, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No independent whole-multiplier cutoff is defined by this supplied contribution. Price the explicitly referenced complete algorithm only after binding its actual native/operator, ownership, recursive invoice, precision and outer parameters. Relevant local constants, guards and negative hypotheses remain attached to that target; they are not discarded." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "26fe40cbca6972a0e392e9248a9cb8a84368530b" } }, { "pr": 5256, "title": "Prove block Schur central action and the exact sharp restriction (no \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5256", "author": "ssafwann", "created_at": "2026-10-23T14:24:11Z", "accepted_at": "2026-10-23T18:37:53Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "c72d6ff431cf5c979f5010018d8eba0c15577bce" } }, { "pr": 5267, "title": "Prove nilpotent Schur residual normal form and fixed-H weights (no \u03ba)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5267", "author": "ssafwann", "created_at": "2026-10-23T14:56:37Z", "accepted_at": "2026-10-23T18:37:53Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "No new global kappa claimed in current title; quoted numbers may be benchmarks or scoped quantities.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": false, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 5, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "8ab280c8a3ef0544f13ff23a1c69df4757cd4900" } }, { "pr": 5275, "title": "Prove the printed #4100 ledger boundary row uses tau_eff", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5275", "author": "unpaidmoon", "created_at": "2026-10-23T15:16:07Z", "accepted_at": "2026-10-23T18:37:53Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302015", "kappa_fraction": "60403/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Author-stated conditional/numerical claim; acceptance must be read from source-bound reviews.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 6, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "Keep all relevant proven/reported constants, guards, corrections and negative scopes with the actual selected target. A runtime cutoff requires an actual source-selected fullnative/owner/recursiveinvoice/precision/outer realization with exact own commitments; neither unchangedkappa nor an auditpass transfers a cutoff." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "2a9f81f687fd7b584a8fabbf6b3b0d0e426e55d8" } }, { "pr": 5243, "title": "Verify a one-native-fusion conditional compiler construction target", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5243", "author": "Clear1nsight", "created_at": "2026-10-23T13:47:35Z", "accepted_at": "2026-10-23T18:37:54Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.003022", "kappa_fraction": "1511/500000", "kappa_status": "positive_source_quote", "kappa_scope": "Research/audit/formalization title; a literal kappa mention is not automatically its own global improvement.", "source_status": "partially_reviewed", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": null, "conditional_upper": null, "cost_status": "not_costed", "source_audit": { "status": "source_scope_completed_supporting_or_restricted_result", "audit_completed": true, "numeric_bound_completed": false, "verified_artifact_count": 35, "source_family": "supporting_evidence_or_tooling", "cost_obligations": [ "No own full-integer runtime point follows. Retain this component/validation result with its named complete construction; an actual changed physical supplier and complete recursive/precision/outer invoice must be bound before new numerical costs." ], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "cc8cb58ab4083c1cfd58e0e2eb17c0b2a88070a9" } }, { "pr": 5413, "title": "Complete coupled-output caller: conditional \u03ba = 0.003027288235 (+5e-12 over #5400)", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5413", "author": "Clear1nsight", "created_at": "2026-10-24T02:07:02Z", "accepted_at": "2026-10-24T02:54:32Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.003027288235", "kappa_fraction": "605457647/200000000000", "kappa_status": "latest_reviewed_conditional_source", "kappa_scope": "Selected conditional PR5413 completion, with PR5407 provider and PR5414 companion audits. Its own changed caller and source parameters were counted. Native and analytic contracts remain assumptions.", "source_status": "unreviewed_current_metadata_claim", "historical_leader_candidate": true, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^38569299999999997-2^69+1)", "plot_triple_log": { "log2_of_integer": "38569299999999997", "negligible_negative_correction": true }, "source": "data/operation-audit/literal-feasibility-refinement-v5.json", "scope": "Own unreduced normalized PR5413 dense core when active, identical fixed optimizedGMP reference when inactive; width>=2, all-column complete spectators retained.", "statistic": "Earliest input length at which some correct member of this family strictly beats the reference", "exact_individual_crossing": false, "all_PR4470_implementations": false, "full_upper_transferred": false }, "conditional_upper": { "input_bits": "2^(2^3858087157930831818791345)", "log2log2_input_bits": "3858087157930831818791345", "plot_triple_log": { "exact_log2log2_integer": "3858087157930831818791345" }, "source": "data/operation-audit/pr5413-crossover-retuned-upper.json", "model": "xag-straightline-v1", "baseline": "gmp-630-native-skylake-unbounded-exact-constants-v2", "all_positive_xor_tariffs": true, "scope": "A separately counted realization of this own-source supplier under retained native/analytic contracts. A sufficient upper, not an actual crossing." }, "cost_status": "conditional_literal_family_range", "claim_snapshot_at": "2026-10-24T10:37:55.183347+00:00", "claim_type": "post_snapshot_current_title_claim", "historical_source": "data/operation-audit/post-snapshot-metadata-20261024/metadata-delta.json", "uniform_rank_H": "38569300000000000", "tensor_power": 1, "early_effective_kappa": "1/500", "historical_status": "latest_selected_maintainer_reviewed_conditional_claim", "fresh_arithmetic_replay_status": "PASS_SOURCE_CENSUS_ONLY", "replay_receipt": "data/operation-audit/pr5413-literal-work-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 0, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [], "source_head": "0c1fa2f47fb5ea17b93a4b67063d08e49cc38e51" } }, { "pr": 5377, "title": "Conditional \u03ba = 0.00302235 (+5.742e-7 over #4610): one owned helper relation", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5377", "author": "aliromman", "created_at": "2026-10-23T20:26:27Z", "accepted_at": "2026-10-24T02:54:33Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302235", "kappa_fraction": "60447/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Current literal title claim fetched 2026-10-24. This is not proof that the same kappa was accepted at merge, nor a verified record.", "source_status": "unreviewed_current_metadata_claim", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^31385199999997-2^69)", "plot_triple_log": { "log2_of_integer": "31385199999997", "negligible_negative_correction": true }, "scope": "Own complete unreduced raw controller/native word, complete field and spectators when active, stored width at least two; identical repaired optimized GMP when inactive.", "statistic": "Earliest input width at which a correct member of the declared own-source literal enhancement family strictly beats the reference", "source": "data/operation-audit/pr5377-changed-native-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "conditional_upper": null, "cost_status": "conditional_own_source_lower_only", "claim_snapshot_at": "2026-10-24T10:37:55.183347+00:00", "claim_type": "post_snapshot_current_title_claim", "historical_source": "data/operation-audit/post-snapshot-metadata-20261024/metadata-delta.json", "own_source_cost_extension": true, "early_effective_kappa": null, "own_source_scope": "Own complete unreduced raw controller/native word, complete field and spectators when active, stored width at least two; identical repaired optimized GMP when inactive. Own native engine receipts are authenticated but not freshly replayed here. No sufficient upper has been derived.", "own_source_record_tail_quantified": false, "own_source_certificate": "pr5377-changed-native-literal-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 9, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "c448d13c71908647f968b06cddb795ce7d288139" } }, { "pr": 5383, "title": "Conditional \u03ba = 0.00302666 (+4.31e-6 over #5377): eight joint helper relations", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5383", "author": "aliromman", "created_at": "2026-10-23T20:52:12Z", "accepted_at": "2026-10-24T02:54:33Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302666", "kappa_fraction": "151333/50000000", "kappa_status": "positive_source_quote", "kappa_scope": "Current literal title claim fetched 2026-10-24. This is not proof that the same kappa was accepted at merge, nor a verified record.", "source_status": "unreviewed_current_metadata_claim", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^31385199999997-2^69)", "plot_triple_log": { "log2_of_integer": "31385199999997", "negligible_negative_correction": true }, "scope": "Own complete unreduced raw controller/native word, complete field and spectators when active, stored width at least two; identical repaired optimized GMP when inactive.", "statistic": "Earliest input width at which a correct member of the declared own-source literal enhancement family strictly beats the reference", "source": "data/operation-audit/pr5383-changed-native-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "conditional_upper": null, "cost_status": "conditional_own_source_lower_only", "claim_snapshot_at": "2026-10-24T10:37:55.183347+00:00", "claim_type": "post_snapshot_current_title_claim", "historical_source": "data/operation-audit/post-snapshot-metadata-20261024/metadata-delta.json", "own_source_cost_extension": true, "early_effective_kappa": null, "own_source_scope": "Own complete unreduced raw controller/native word, complete field and spectators when active, stored width at least two; identical repaired optimized GMP when inactive. Own native engine receipts are authenticated but not freshly replayed here. No sufficient upper has been derived.", "own_source_record_tail_quantified": false, "own_source_certificate": "pr5383-changed-native-literal-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 10, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "4bd6efa51a495a7c7b7754915cf0244e7e60969e" } }, { "pr": 5384, "title": "Independently validate \u03ba = 0.00302235 and the owned-relation price ceiling", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5384", "author": "Clear1nsight", "created_at": "2026-10-23T20:52:34Z", "accepted_at": "2026-10-24T02:54:33Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302235", "kappa_fraction": "60447/20000000", "kappa_status": "positive_source_quote", "kappa_scope": "Current literal title claim fetched 2026-10-24. This is not proof that the same kappa was accepted at merge, nor a verified record.", "source_status": "unreviewed_current_metadata_claim", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^31385199999997-2^69)", "plot_triple_log": { "log2_of_integer": "31385199999997", "negligible_negative_correction": true }, "scope": "Own selected complete unreduced raw controller/native word with full field/spectator ranges when active, stored width at least two; identical optimized GMP when inactive.", "statistic": "Earliest possible strict win in the specified own-source literal enhancement family", "source": "data/operation-audit/pr5384-reviewed-selected-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "conditional_upper": null, "cost_status": "conditional_own_source_lower_only", "claim_snapshot_at": "2026-10-24T10:37:55.183347+00:00", "claim_type": "post_snapshot_current_title_claim", "historical_source": "data/operation-audit/post-snapshot-metadata-20261024/metadata-delta.json", "own_source_cost_extension": true, "early_effective_kappa": "60447/20000000", "own_source_scope": [ "Own source native arbitrary-input required entry/output frames, absolute phase, all-column whole-job/owned/spectator and actual changed caller semantics. Stored validation evidence is authenticated, not a freshly rerun original native or validation engine here.", "Own physically realized strict winning uniform compiler at the selected H, literal raw occurrences/boundary instructions retained, no materialized enormous uniform-word claim.", "Prescribed unreduced dense ADD macros and the same fixed reference correctness/finite-kernel halting contracts." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr5384-reviewed-selected-literal-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 87, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "411648821f0208d60099be8ca42957ca3a1c4316" } }, { "pr": 5390, "title": "Certify \u03ba = 0.0030266747680744 and a smaller matched compiler using direct tails", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5390", "author": "Dugongue", "created_at": "2026-10-23T21:23:08Z", "accepted_at": "2026-10-24T02:54:33Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.0030266747680744", "kappa_fraction": "3783343460093/1250000000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Current literal title claim fetched 2026-10-24. This is not proof that the same kappa was accepted at merge, nor a verified record.", "source_status": "unreviewed_current_metadata_claim", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^3634889999999999999997-2^69)", "plot_triple_log": { "log2_of_integer": "3634889999999999999997", "negligible_negative_correction": true }, "scope": "Own complete unreduced raw controller/native word, complete field and spectators when active, stored width at least two; identical repaired optimized GMP when inactive.", "statistic": "Earliest input width at which a correct member of the declared own-source literal enhancement family strictly beats the reference", "source": "data/operation-audit/pr5390-changed-native-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "conditional_upper": null, "cost_status": "conditional_own_source_lower_only", "claim_snapshot_at": "2026-10-24T10:37:55.183347+00:00", "claim_type": "post_snapshot_current_title_claim", "historical_source": "data/operation-audit/post-snapshot-metadata-20261024/metadata-delta.json", "own_source_cost_extension": true, "early_effective_kappa": null, "own_source_scope": "Own complete unreduced raw controller/native word, complete field and spectators when active, stored width at least two; identical repaired optimized GMP when inactive. Own native engine receipts are authenticated but not freshly replayed here. No sufficient upper has been derived.", "own_source_record_tail_quantified": false, "own_source_certificate": "pr5390-changed-native-literal-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 15, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "654ab79238e957eb20eced5197c3c38d5738183f" } }, { "pr": 5392, "title": "Conditional \u03ba = 0.00302725 (+5.75235e-7 over #5387): owned circuit transposition", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5392", "author": "aliromman", "created_at": "2026-10-23T21:28:41Z", "accepted_at": "2026-10-24T02:54:33Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302725", "kappa_fraction": "12109/4000000", "kappa_status": "positive_source_quote", "kappa_scope": "Current literal title claim fetched 2026-10-24. This is not proof that the same kappa was accepted at merge, nor a verified record.", "source_status": "unreviewed_current_metadata_claim", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^31385199999997-2^69)", "plot_triple_log": { "log2_of_integer": "31385199999997", "negligible_negative_correction": true }, "scope": "Own complete unreduced raw controller/native word, complete field and spectators when active, stored width at least two; identical repaired optimized GMP when inactive.", "statistic": "Earliest input width at which a correct member of the declared own-source literal enhancement family strictly beats the reference", "source": "data/operation-audit/pr5392-changed-native-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "conditional_upper": null, "cost_status": "conditional_own_source_lower_only", "claim_snapshot_at": "2026-10-24T10:37:55.183347+00:00", "claim_type": "post_snapshot_current_title_claim", "historical_source": "data/operation-audit/post-snapshot-metadata-20261024/metadata-delta.json", "own_source_cost_extension": true, "early_effective_kappa": null, "own_source_scope": "Own complete unreduced raw controller/native word, complete field and spectators when active, stored width at least two; identical repaired optimized GMP when inactive. Own native engine receipts are authenticated but not freshly replayed here. No sufficient upper has been derived.", "own_source_record_tail_quantified": false, "own_source_certificate": "pr5392-changed-native-literal-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 23, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "329b2ff35d2994b11abbb59f770d12da75c494ac" } }, { "pr": 5395, "title": "Independently validate \u03ba = 0.003026674765 and the eight-relation price plane", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5395", "author": "Clear1nsight", "created_at": "2026-10-23T21:34:07Z", "accepted_at": "2026-10-24T02:54:33Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.003026674765", "kappa_fraction": "605334953/200000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Current literal title claim fetched 2026-10-24. This is not proof that the same kappa was accepted at merge, nor a verified record.", "source_status": "unreviewed_current_metadata_claim", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^409548999999999997-2^69)", "plot_triple_log": { "log2_of_integer": "409548999999999997", "negligible_negative_correction": true }, "scope": "Own source-selected unreduced full-field/native/complete controller enhancement family at positive multiplicity and width>=2 when active; identical repaired optimizedGMP when inactive.", "statistic": "Earliest possible strict win in this declared source-selected literal enhancement family", "exact_individual_crossing": false, "all_PR_implementations": false, "source": "data/operation-audit/pr5395-source-committed-literal-lower.json" }, "conditional_upper": null, "cost_status": "conditional_own_source_lower_only", "claim_snapshot_at": "2026-10-24T10:37:55.183347+00:00", "claim_type": "post_snapshot_current_title_claim", "historical_source": "data/operation-audit/post-snapshot-metadata-20261024/metadata-delta.json", "own_source_cost_extension": true, "early_effective_kappa": "605334953/200000000000", "own_source_scope": [ "Own complete required physical entry/output-frame/absolute-phase/all-column/owned/spectator native endpoint and literal complete controller, not established by source scalar statistics or formal nonzero-cut diagnostics.", "Own source physically realized strict winning uniform supplier, chronological integer compiler/fullfields and source complete-template applicability. Exact own stored evidence is authenticated, not freshly rerun original native/phase/validation engines here.", "Same prescribed unreduced dense arithmetic macros and repaired optimizedGMP correctness/finite-kernel halting." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr5395-source-committed-literal-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 89, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "275dc377246f91ef30dc9e05241b0f637aa807fb" } }, { "pr": 5396, "title": "Independently validate joint relations and conditional \u03ba = 0.003026674765", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5396", "author": "Clear1nsight", "created_at": "2026-10-23T21:35:22Z", "accepted_at": "2026-10-24T02:54:33Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.003026674765", "kappa_fraction": "605334953/200000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Current literal title claim fetched 2026-10-24. This is not proof that the same kappa was accepted at merge, nor a verified record.", "source_status": "unreviewed_current_metadata_claim", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^409548999999999997-2^69)", "plot_triple_log": { "log2_of_integer": "409548999999999997", "negligible_negative_correction": true }, "scope": "Own selected complete unreduced raw controller/native word with full field/spectator ranges when active, stored width at least two; identical optimized GMP when inactive.", "statistic": "Earliest possible strict win in the specified own-source literal enhancement family", "source": "data/operation-audit/pr5396-reviewed-selected-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "conditional_upper": null, "cost_status": "conditional_own_source_lower_only", "claim_snapshot_at": "2026-10-24T10:37:55.183347+00:00", "claim_type": "post_snapshot_current_title_claim", "historical_source": "data/operation-audit/post-snapshot-metadata-20261024/metadata-delta.json", "own_source_cost_extension": true, "early_effective_kappa": "605334953/200000000000", "own_source_scope": [ "Own source native arbitrary-input required entry/output frames, absolute phase, all-column whole-job/owned/spectator and actual changed caller semantics. Stored validation evidence is authenticated, not a freshly rerun original native or validation engine here.", "Own physically realized strict winning uniform compiler at the selected H, literal raw occurrences/boundary instructions retained, no materialized enormous uniform-word claim.", "Prescribed unreduced dense ADD macros and the same fixed reference correctness/finite-kernel halting contracts." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr5396-reviewed-selected-literal-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 70, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "787efce72a908f92b8a8b4ebb677a6fdb7729e33" } }, { "pr": 5398, "title": "Conditional \u03ba = 0.00302728823 (+3.823e-8 over #5392): direct backward caller", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5398", "author": "aliromman", "created_at": "2026-10-23T21:52:26Z", "accepted_at": "2026-10-24T02:54:33Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302728823", "kappa_fraction": "302728823/100000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Current literal title claim fetched 2026-10-24. This is not proof that the same kappa was accepted at merge, nor a verified record.", "source_status": "unreviewed_current_metadata_claim", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^38569299999999997-2^69)", "plot_triple_log": { "log2_of_integer": "38569299999999997", "negligible_negative_correction": true }, "scope": "Own complete unreduced raw controller/native word, complete field and spectators when active, stored width at least two; identical repaired optimized GMP when inactive.", "statistic": "Earliest input width at which a correct member of the declared own-source literal enhancement family strictly beats the reference", "source": "data/operation-audit/pr5398-changed-native-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "conditional_upper": null, "cost_status": "conditional_own_source_lower_only", "claim_snapshot_at": "2026-10-24T10:37:55.183347+00:00", "claim_type": "post_snapshot_current_title_claim", "historical_source": "data/operation-audit/post-snapshot-metadata-20261024/metadata-delta.json", "own_source_cost_extension": true, "early_effective_kappa": null, "own_source_scope": "Own complete unreduced raw controller/native word, complete field and spectators when active, stored width at least two; identical repaired optimized GMP when inactive. Own native engine receipts are authenticated but not freshly replayed here. No sufficient upper has been derived.", "own_source_record_tail_quantified": false, "own_source_certificate": "pr5398-changed-native-literal-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 11, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "174fb211493b43a42210434083e9702b4fb7a2ce" } }, { "pr": 5399, "title": "Independently validate \u03ba = 0.00302725 and the owned-transpose phase/cost proof", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5399", "author": "Clear1nsight", "created_at": "2026-10-23T22:12:18Z", "accepted_at": "2026-10-24T02:54:33Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302725", "kappa_fraction": "12109/4000000", "kappa_status": "positive_source_quote", "kappa_scope": "Current literal title claim fetched 2026-10-24. This is not proof that the same kappa was accepted at merge, nor a verified record.", "source_status": "unreviewed_current_metadata_claim", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^31385199999997-2^69)", "plot_triple_log": { "log2_of_integer": "31385199999997", "negligible_negative_correction": true }, "scope": "Own source-selected unreduced full-field/native/complete controller enhancement family at positive multiplicity and width>=2 when active; identical repaired optimizedGMP when inactive.", "statistic": "Earliest possible strict win in this declared source-selected literal enhancement family", "exact_individual_crossing": false, "all_PR_implementations": false, "source": "data/operation-audit/pr5399-source-committed-literal-lower.json" }, "conditional_upper": null, "cost_status": "conditional_own_source_lower_only", "claim_snapshot_at": "2026-10-24T10:37:55.183347+00:00", "claim_type": "post_snapshot_current_title_claim", "historical_source": "data/operation-audit/post-snapshot-metadata-20261024/metadata-delta.json", "own_source_cost_extension": true, "early_effective_kappa": "12109/4000000", "own_source_scope": [ "Own complete required physical entry/output-frame/absolute-phase/all-column/owned/spectator native endpoint and literal complete controller, not established by source scalar statistics or formal nonzero-cut diagnostics.", "Own source physically realized strict winning uniform supplier, chronological integer compiler/fullfields and source complete-template applicability. Exact own stored evidence is authenticated, not freshly rerun original native/phase/validation engines here.", "Same prescribed unreduced dense arithmetic macros and repaired optimizedGMP correctness/finite-kernel halting." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr5399-source-committed-literal-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 83, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "702fde7d0a7cde17bc51a9a0bd3a3f740fefc199" } }, { "pr": 5400, "title": "Independently validate \u03ba = 0.00302728823 for the direct backward caller", "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5400", "author": "Clear1nsight", "created_at": "2026-10-23T22:16:57Z", "accepted_at": "2026-10-24T02:54:33Z", "acceptance_basis": "github_merged_at", "kappa_decimal": "0.00302728823", "kappa_fraction": "302728823/100000000000", "kappa_status": "positive_source_quote", "kappa_scope": "Current literal title claim fetched 2026-10-24. This is not proof that the same kappa was accepted at merge, nor a verified record.", "source_status": "unreviewed_current_metadata_claim", "historical_leader_candidate": false, "unflagged_kappa_entry": true, "actual_crossover": null, "meaningful_lower_bound": { "input_bits": "2^(2^38569299999999997-2^69)", "plot_triple_log": { "log2_of_integer": "38569299999999997", "negligible_negative_correction": true }, "scope": "Own selected complete unreduced raw controller/native word with full field/spectator ranges when active, stored width at least two; identical optimized GMP when inactive.", "statistic": "Earliest possible strict win in the specified own-source literal enhancement family", "source": "data/operation-audit/pr5400-reviewed-selected-literal-lower.json", "exact_individual_crossing": false, "all_PR_implementations": false }, "conditional_upper": null, "cost_status": "conditional_own_source_lower_only", "claim_snapshot_at": "2026-10-24T10:37:55.183347+00:00", "claim_type": "post_snapshot_current_title_claim", "historical_source": "data/operation-audit/post-snapshot-metadata-20261024/metadata-delta.json", "own_source_cost_extension": true, "early_effective_kappa": "302728823/100000000000", "own_source_scope": [ "Own source native arbitrary-input required entry/output frames, absolute phase, all-column whole-job/owned/spectator and actual changed caller semantics. Stored validation evidence is authenticated, not a freshly rerun original native or validation engine here.", "Own physically realized strict winning uniform compiler at the selected H, literal raw occurrences/boundary instructions retained, no materialized enormous uniform-word claim.", "Prescribed unreduced dense ADD macros and the same fixed reference correctness/finite-kernel halting contracts." ], "own_source_record_tail_quantified": false, "own_source_certificate": "pr5400-reviewed-selected-literal-lower.json", "source_audit": { "status": "closed_conditional_numeric_bound", "audit_completed": true, "numeric_bound_completed": true, "verified_artifact_count": 80, "source_family": "source_bound_construction", "cost_obligations": [], "source_manifest": [ { "file": "late-uniform-source-extraction/source-manifest.json", "sha256": "2568014b4044e15a207aaffcfda6c0952b7dbf67937de4fd85cb7681ac8610ae" } ], "source_head": "7ea72fb692cbfd64fea556de84327bbf88555986" } } ] }