Conditional κ = 0.00160073442456167: PR568 eight-cold provider at PR571's nine plain calls

[jeremykothe2]

Summary

Conditional κ = 0.00160073442456167, against PR571's 0.001600682403612293 (+5.2e-8). The conservative model gives 0.001600734421779035.

This is a small change to DominikScholz's PR571. Its 63 width-seven prefix-word calls and its dispatch stay exactly as they are. Only the nine plain four-cold calls change: they use PR568's eight-cold eight-pivot provider in place of PR569's plain provider, and a new literal owner map hosts the result.

Change

• Provider. PR568's eight-pivot multicold word (widths {4:8,5:48,8:164,9:284}, local profile {1:2332,2:436,3:448,4:192,5:56,6:56,8:8}) replaces the plain four-cold provider at PR571's nine plain call slots. The 63 width-seven calls use PR571's own combined-prefix-word unchanged.
• Owners.
  • The new owner map was found with a fixed-dispatch MILP over per-window patterns, warm-started from PR571's map.
  • Literal realization needed cross-time Hall cuts, added lazily: for each colour set C and each k, the flow into the top-k times is bounded by Σ p·min(count_C(p), k). Five iterations and 70 cuts reached a literal map at the unchanged MILP optimum.
  • Paid profile: {1:169164,2:40472,3:26398,4:13824,5:4032,6:4032,7:38,8:576,48:1810}.
• Code. code/ contains PR571's global-code. Only three files are adapted:
  • bind_providers_portable.py and audit_allcold.py: only the per-provider width inventory and profile for the plain slot change. DISPATCH and every mutation control are unchanged.
  • assemble.py: pins for the new provider and the new witness.
    emit_allcold.py, invoice_allcold.py, assembly_controls.py and phase_timing_controls.py are PR571's, unchanged.
• Package. research/complex-571-plain8/ has 13 files. PR568 (research/complex-multicold, 71c99ac) and PR571 (research/structural-gain, b7bdc5a) are pinned external sources. verify.py checks their manifests and the exact files it uses. Nothing is copied from them.

Verification

PR568 and PR571 are not merged, so first fetch their pinned commits:

git fetch origin pull/568/head:pr568 pull/571/head:pr571
git worktree add --detach ../pr568 71c99ac935a33bb7b59a1b4a7af8725a939b0b90
git worktree add --detach ../pr571 b7bdc5a8de18fcf418cfb9c7d83a2b1097a5e4a3
python3 -B research/complex-571-plain8/verify.py --work /tmp/571-plain8 \
  --multicold ../pr568/research/complex-multicold \
  --structural-gain ../pr571/research/structural-gain

verify.py uses only the standard library. It runs:

• the full PR558 replay;
• PR568's cold and multi-cut constructions with all omission controls, plus the static44 and rank-five audits;
• the native chain and exact phase edges for the eight-cold provider;
• a rebuild of the width-seven local from PR571's pinned word with PR571's pipeline, checked byte-for-byte against PR571's retained local;
• binding;
• the physical owner audit with 16 controller mutants;
• a fresh finite invoice;
• both exact moment engines and the 47 strict outer inequalities for each model;
• 93 assembly controls and the phase-timing controls.

Local result (Windows, CPython 3.11.11): PASS_PR571_PREFIX_WORD_WITH_PR568_EIGHT_COLD_PLAIN_CALLS_NATIVE_COMPLEX_AND_CITED_BIT, κ 0.00160073442456167, 24/24 stages exit 0, 298 s. The verified package tree is byte-identical to this commit, MANIFEST and the binary OWNERS file included.

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

Credits

• DominikScholz: PR571 (the 57-gate joint prefix, its composition and global code) and PR569 (the width-seven promotions and rank-sixteen packing). This PR changes only nine calls of that construction.
• eumemic: PR564, PR561, PR562, PR558, PR550, PR543, PR507.
• chafreaky: PR572, PR551.
• jon314159: PR567.
• rohanarun: PR559.
• Dugongue: PR552 and PR514.
• icekylinx: PR535 and PR531.
• DreamingOfClouds: PR484.
• higherbeing: the open allocator.
• lydakis: PR275.
• Douglas Colkitt / CrocSwap: maintenance.
• The original OpenAI Weighted dual-suffix carriers: conditional κ = 7.9961717358e-5 #109 framework.

AI disclosure and authorship: Claude Opus 5.5 (Anthropic), running in the omp coding harness, did the work for this PR: the owner solve, the package and this description. 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 is finite exact evidence. It is not an unconditional theorem, a complete Lean proof, or a practical speedup.

[Mister-Meeseeks]

Thank you @jeremykothe2. This contribution at f3e0af901f88f2fd3a213224ad3b59a16b5f4688 is incorporated in the reviewed family through #588, published in 9594b61.

Combines the existing #571 joint-prefix provider with #568 plain eight-cold calls under a new owner assignment. It adds no new local scalar identity. Retained #571 local proof must be reconstructed before use.

Preserved implementation and research:

• research/complex-571-plain8

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.