Eight-cold / width-seven composition and cold replay: conditional κ = 0.001600535778621932

[chafreaky]

Conditional κ = 0.001600535778621932, 0.02926651% above #569 and 0.27581821% above #568. The complex supplier binds at b = 0.001603101600089641927176. The cited unchanged #543 bit supplier remains nonbinding, with its bad-residue surcharge retained.

Concurrent #571 (b7bdc5a8de18fcf418cfb9c7d83a2b1097a5e4a3) admits a higher κ of 0.001600682403612293 using a new joint prefix. I independently replayed its 18 new-composition stages (127.8 s) against the previously verified #564/#569 dependencies. That prefix is not incorporated here. This submission preserves an independently constructed owner assignment, fully cold replay and generated-artifact portability evidence; it does not claim the current highest verified κ.

This composes #568's eight cold helpers with #569's 32 width-seven entrance promotions, then checks a new literal whole-owner assignment: 57 promoted calls and 15 plain calls. The 32 promotions change 96 frame annotations and no scalar operation, coefficient or order. The complete new word, phase recipes, owners and invoice are reconstructed; predecessor gains are not added.

H = {1:169728, 2:40529, 3:26169, 4:13824,
     5:4032, 6:4032, 7:5, 8:576, 48:1815}

Dimension 73, live stock 7168, physical stock 7682, rank mass 520704 and deficit 2560. The conservative complex model separately passes at κ = 0.001600535775835757.

The package is research/multicold-width7; it contains a standard-library cold verifier, frozen owners/plan, exact supplier endpoints, proof/dependency notes, source pins and retained notices. Discovery uses pattern-and-call flows with a bipartite-matching expansion, preventing repeated ownership within one invocation. Solver optimality is not used in admission.

python3 -B research/multicold-width7/verify.py --work /absolute/new/multicold-width7

Validation covers the complete pinned #568 replay; all 728 columns in both orientations; restoration of 504 dirty helpers; native frames, normalized wrappers, 3005 phase edges and 224 endpoints; all 36,288 helper roles and 16 controller mutations; a fresh full invoice; two exact rational moment engines; seven bootstrap levels and 47 strict outer inequalities per model; 93 malformed-assembly controls. Generated-artifact controls accept two actual recompressions and reject 18 consistently rebound proof mutations plus 18 stale-reference/invalid-timing mutations. Immutable sources stay byte-pinned; generated gzip identity uses the decompressed payload.

The final frozen source passed cold on macOS/Python 3.14.8 (399.9 s) and Linux aarch64/Python 3.12.3 (425.9 s). Result files are byte-identical; all seven provider content identities and all numerical/semantic invoice fields agree. Receipts and logs are in research/multicold-width7-validation. All 18 baseline make verify groups passed across an initial run and a resumed run: Apple clang initially rejected inherited -fopenmp; the failed and remaining groups passed using the installed OpenMP runtime, with no source/assertion changes. GitHub CI is monitored separately and is not claimed green.

Attribution: Jeremy Kothe (jeremykothe2, #568) supplies the eight-cold family; Dominik Scholz (DominikScholz, #569) supplies the width-seven recipes and frame propagation; Jonathan Capalbo (jon314159, #567) supplies portable generated identities and controls. The retained ancestry includes eumemic (#564/#561/#562/#558/#550 and cited #543), Rohan Arun (rohanarun, #559), Dugongue (#552 and whole-owner scheduling), icekylinx (#531/#535), DreamingOfClouds (#484 and successors), and earlier contributors credited in NOTICE.md and the original notices. All 229 vendored files match their original Git blobs. Substantial OpenAI Codex assistance was used for composition, search, implementation, review and verification.

This is conditional finite evidence. The all-size compiler, common-label/mutable-source realization, normalized recursive residuals, whole-call hosting, precision/tape and analytic-transfer premises remain; the bit supplier retains H1–H5. It is not an unconditional multiplication theorem, full Lean certification, practical speedup or κ = 1 result. No global packing optimum is claimed.

[Mister-Meeseeks]

Thank you @chafreaky. This contribution at 0c3a7d1b0d99dbc6a1cc5ec1675ddd74aa959586 is incorporated in the reviewed family through #588, published in 9594b61.

Thirty-two entrance promotions preserve every scalar operation, coefficient and order of the eight-cold word. New frame paths and owner schedule are fully charged. Exact integer width counts alone are insufficient; the actual per-call matching/owner map is the admission evidence.

Preserved implementation and research:

• research/multicold-width7
• research/multicold-width7-validation

The family review and individual disposition record the scope, evidence and attribution. Parallel and intermediate contributions remain credited even where a later composition has a stronger bound. The published multiplication bound remains conditional on the documented compiler, realization, hosting and analytic assumptions; these finite checks are not a full Lean multiplication proof.