Conditional κ = 0.001636241501576388: h4a plus PR627's two factored jp8 cold ends

[jeremykothe2]

Summary

Conditional κ = 0.001636241501576388. This is +3.64e-7 (+0.022%) over PR632 (0.001635877117861902) and +4.73e-7 over our PR629. The conservative model gives 0.001636241498709272.

st2 = our PR629 (h4a) + PR627's two factored jp8 cold ends, credit jeremydiviney. Dispatch is jp8 ×71, ck ×1, with ck pinned at time 5 to satisfy PR604's parity rule. The owner map comes from exact-window RINS warm-started from PR627's map. The exact LP bound is 523257.7591528998. The MIP's status/gap line was not captured; cand.json records this.

Two data-only adaptations were needed to stack PR627's ends on h4a, and no code changed:

1. PR627's 18-gate rank-0 premix is re-derived exactly in h4a's basis: 12 dyadic rank-0 gates.
2. h4a's q95 release leaked into end 581's accumulator. One extra dead-port absorption cancels it exactly: q92 += ¼·S403 at anchor 1665, frame [265,137,96,6].

Against h4a, the profile changes per jp8 call by {1:+2, 2:+2, 5:−2}, PR627's full gain.

Code is byte-identical to PR629's independently reviewed set (all 24 files, with LF normalisation as in PR629). An independent review checked both the local stages and this strict run, and gave its verdict as SOUND. PROOF-NOTE.md has a new section covering the stack.

Declarative inputs ship in this first commit:

• data/WITNESS.json, data/EXPECTED.json and data/cand.json;
• data/search/, with PR627's map as the warm start, the LP patterns, the dispatch and the template plan;
• a definition-first README.

entering_helper_roles is corrected to the audited value, 16714. As in PR629, verify.sh's usage comment names an earlier package; use the command below.

Verification

research/complex-571-cold14-st2/verify.sh /tmp/complex-571-cold14-st2 ..   # SOURCE_ROOT holds worktrees pr568 pr569 pr571 pr575 pr583 at the pinned commits

Local result (Windows, CPython 3.11.11): the commit was preflighted from a fresh clone first (committed blobs equal the MANIFEST, every file LF, pin check passes, spec.py check OK, all 24 code files equal the reviewed set). The official run from that clean clone of a6895a69 then gave PASS_COLD14_NATIVE_COMPLEX_AND_CITED_BIT, κ 0.001636241501576388, 64/64 stages exit 0, 603 s, with no reused baseline or locals. The receipt records MANIFEST sha256 faa8559b…, equal to the committed MANIFEST.

GitHub CI has not run, and I make no claim about it.

Credits

• chafreaky: PR626, whose owner map warm-starts this one.
• jeremydiviney: PR627 (factored cold ends), PR624 and PR618.
• DreamingOfClouds: PR604 (the cold-ended construction, cold_end, verifier changes and package), PR599, PR509 and PR516 (Lean).
• jeremykothe2: PR629, PR625, PR623, PR622, PR617, PR615, PR614, PR609, PR607, PR601, PR600, PR596, PR593, PR592 and PR591 (the hyperplane-end base).
• The pinned PR568, PR569, PR571, PR575 and PR583 packages and all earlier contributors are listed in NOTICE.md.

AI disclosure and authorship: Claude Opus 5.5 (Anthropic), running in the omp coding harness, stacked PR627's ends on h4a (premix re-derivation and the q92 absorption), solved the owner map, ran the independent review, found the dispatch and owner map, built the declarative inputs and prepared the PR. Jeremy Kothe (jeremykothe2) directed and reviewed it and is submitting it.

Scope

The result is conditional on the inherited all-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape/exact recovery, analytic transfer and the bit H1–H5 assumptions. It builds on PR604, which is not merged. It is finite exact evidence, not an unconditional theorem, a complete Lean proof, or a practical speedup.

[Mister-Meeseeks]

Thank you @jeremykothe2. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Combination of h4a and two factored cold ends.

Review and limits: The interaction requires re-derived premixes and absorption repairs, not addition of separate savings. Full declarative reconstruction, dirty-state admission and ownership remain required.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: a6895a69f8ad98ab45777b03e9e6f48888c39f6f. Publication: 2ccf3fb7887d6ba103fb3abd5a62dce992713d9f.