The target is the least input size beyond which the new construction costs less than Harvey–van der Hoeven, counting setup, recursive work, movement, precision and base cases on the same machine model.
A κ value alone cannot supply that number. This explorer distinguishes a complete runtime comparison, conditions for applying a proof, and calculations after explicit missing-cost assumptions.
The fully specified source uses d = 1729, n₀ = 2d¹² and C = max(B, 5000A). Its source does not report numerical A or B. This is the chosen theoretical baseline, not a normalized constant of one.
The audit lists the missing quantities. Numerical scenarios are displayed as conditional cost models, not as completed estimates of undocumented constants. A precision cutoff can be sufficient for one proof condition while giving neither a lower bound nor an upper bound on the true runtime crossover.
The operation-count tab fixes a nonuniform Boolean circuit model with AND cost 1 and XOR cost ρ. It includes input-dependent arithmetic, while circuit generation, length-only coefficients and fixed wiring are free. Its newly derived HvH envelope is a bound in that model, not a numerical value for the paper’s uniform Turing-machine constant. PR4470 now has a separate conditional whole-integer upper bound for the specified circuit instantiation. The raw-layer threshold remains a component result.
Here n is the number of bits in each operand. We write n = 22ᴴ and display H = log₂ log₂ n to retain values too large for ordinary scientific notation. No input of such a size is materialized.
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