Conditional κ = 0.001593667716067094: two compatible cold kernels in all 72 calls

[jon314159]

Raises the conditional bound from PR564's κ = 0.001593134158181640 to κ = 0.001593667716067094, an improvement of 0.03349108314035%. The native complex rate is b = 0.001596211546877366844000. The separately checked conservative complex model gives κ = 0.001593667713327391, also above PR564.

The change adds a compatible second cold kernel on helper 294 after reconstructing PR564's first kernel on helper 270. Its suffix relation is recomputed on the already modified word, and cleanup is rebuilt. All 72 calls use actual zero/four/eight-promotion providers with the existing 15/2/55 dispatch. A literal reassignment changes 798 of 36,288 owner records; live stock remains 7168 and physical stock 7682. The complete paid profile is:

{1:166640,2:31072,3:35604,4:13696,5:4032,6:4032,
 7:136,8:576,12:1,48:1675}

The verifier reconstructs all scalar words, dirty-helper restoration, reflected frame ledgers, exact phases and wrappers, then checks the owner schedule and a fresh finite invoice. It charges all 4,168 positive idle remainders, including the rank-12 child. Generated-artifact identities tolerate gzip serialization differences while retaining fresh raw-hash bindings and every mathematical field.

Validation: two independent clean reconstructions of the same source manifest passed all 47 stages each on Windows Python 3.14 and Linux Python 3.12. Both produce the exact native and conservative results above. This covers both reflected operators and dirty-helper restoration, all phase edges and endpoint adapters, 17 controller mutants, 57 malformed-admission controls, seven bootstrap levels and all 47 strict outer constraints. Both rational moment engines reject the adjacent supplier endpoint. Compression controls accept equivalent recompressions and reject altered proof contents or stale references.

All 18 required repository baseline groups also passed, including the Gen4 bank construction, after the documented SymPy-version, compiler-header and Git-worktree environment corrections. Initial failed attempts and their successful recoveries are preserved. Source-bound receipts, environment details and stage logs are in research/complex-doublecold-validation/. A Python 3.11/3.14 Linux CI workflow is included.

python3 -B research/complex-doublecold/verify.py --work /tmp/doublecold-replay

The result retains the inherited all-size compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic-transfer and bit H1–H5 assumptions. PR543 remains the cited bit supplier; its pinned profile is repriced. This is conditional finite evidence, with no unconditional theorem or practical-speed claim.

Credits: PR564 and its PR561/PR562/PR558 ancestry supply the retained construction; Rohan Arun's PR559 supplies the native exact-cover recurrence. Earlier author notices, licenses and AI disclosures are preserved in NOTICE.md and the vendored sources. The new construction, owner reassignment, review and packaging were prepared with OpenAI Codex assistance.

[Mister-Meeseeks]

Thank you @jon314159. This contribution at 7f452897d67282a76ada6df0162d34a751d5f3e6 is incorporated in the reviewed family through #588, published in 9594b61.

Second cold relation is recomputed after the first, and inverse cleanup rebuilt. Literal owner reassignment is necessary: merely enlarging old remainders can erase the gain. Portable identities retain decompressed proof bytes and validate references before normalizing timing metadata.

Preserved implementation and research:

• research/complex-doublecold
• research/complex-doublecold-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.