Κ = 0.003 for integer multiplication crossed

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Conditional κ = 0.00300105 (+4.105e-5 over #4440): combine query thinning and helper retiming - #4441

#4441

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1337isnot1337 wants to merge 7 commits intoCrocSwap:mainCrocSwap/integer-mult-bounds:mainfrom 1337isnot1337:research/fresh-helper-boundary-202610211337isnot1337/integer-mult-bounds:research/fresh-helper-boundary-20261021Copy head branch name to clipboard

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Conditional κ = 0.00300105 (+4.105e-5 over #4440): combine query thinning and helper retiming#4441

1337isnot1337 wants to merge 7 commits intoCrocSwap:mainCrocSwap/integer-mult-bounds:mainfrom 1337isnot1337:research/fresh-helper-boundary-202610211337isnot1337/integer-mult-bounds:research/fresh-helper-boundary-20261021Copy head branch name to clipboard

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1337isnot1337

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Oct 21, 2026

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Apply the verified fresh-helper retiming to all 19 full native calls of #4440's p17 query-thinned complex controller. All 16 paid query shears, whole idle calls, main operators and the stronger BIT supplier are retained. The resulting author-checked conditional bound is

This raises κ by 0.00004105 (+1.3868%) over #4440's 0.00296, 11.7098% over #4416's 0.00268647, and 30.4804% over the pinned selected 0.0023.

The new moment requires a repaired paid-tail limit: gamma < 97/100; #4440's 31/32 fails on this changed profile. At tested saving 0.003001052, power 1024, cutoff 20^1024 and target floor 21^1024 pay every original and completion tail. PR4433's generalized logarithmic majorant with power 1000 specifies sufficient uniform rank 2^165315500000000. The enormous word remains algorithmic rather than materialized.

The stronger BIT construction is unchanged: ordinary admission 0.0034 with atom power 0.004. All nine outer rows, 54 current predicates and four functional guards pass. Enlarged local scalar/route constants fit the complete raw nonrecursive budget.

Start at the combined package README, proof and audit of #4440.

The requested 20-minute frontier check found the stronger #4440 during the run. Its exact head 40e22a8 was audited and its registered replay passed before composition. That unchanged predecessor is included in actual publication ancestry. The helper unit is pinned to this PR's original ccdae89. Their source files are unchanged.

Normal combined CPython 3.12.15 registered replay passes, freshly executing both complete source verifiers before the new event-level invoice, two-engine moment check, ceiling, paid tails, compiler, scalar/route and full consumer checks. The native dependency checks both orientations and all 632 arbitrary input columns with two retained interpreters, plus 320 exact phase/boundary records and mutation controls. The published optional C++20 optimizer regenerates the helper patch exactly. Committed-byte/source-history preflight passes at 5f9d871.

The first hosted plan at ccdae89 stopped on four pre-existing selected-status navigation tests. This branch makes the minimal two-document navigation repair while retaining selected κ=0.0023; all six targeted navigation/locale tests pass. The combined 50-file Git-free export replay passes. Final-head hosted planning and the fresh-helper-thinned, fresh-helper-boundary and query-thinned-controllers scientific jobs all pass (workflow evidence). Overall CI remains red on three archived source-pin checks: historical-1042-link, test-suite-locale-reads and d8-mixed-target-seeda97c8e. Hash comparisons confirm that their expected sources already differed from upstream 2a13eb1; their frozen inputs have not been rewritten to force acceptance. The closing frontier check at 20:42 UTC found no stronger new kappa claim.

This is an author-checked conditional construction awaiting review. All-column/native, permitted physical movement and whole-job matching, owned-erasure, finite-template precision, analytic decomposition, fixed-tape, prime and recovery contracts remain premises. No selected-frontier change, unconditional theorem, practical runtime claim, global optimum or formal/independent-human acceptance is claimed.

Credit: #4440's query thinning, stronger BIT and owned-query construction; zxv's native/controller and higher-moment/logarithmic-compiler work; Jacob Alan Sussman's mixed flow; the #4416 paid-completion construction; and the retained native, Clifford, BIT, precision and outer contributors. New helper retiming and the combined construction were prepared for @1337isnot1337 with substantial OpenAI Codex assistance, Apache-2.0. All predecessor notices are retained. No subagents.

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