κ = 7.51140529238897e-4: restart-packed kernels on weighted gen5b matching

[eumemic]

κ = 7.51140529238897e-4

Change and mathematical scope

Compose PR275's weighted gen5b matching at 10b40041d4ab8a6610083e95bc571aee3468bca2 with all 1,734 restart-packed kernels and 87 second-descent retimings from PR300 at aea3dc9ea40046bda035857dd613c041b977c837. The exact conditional bound is 751140529238897 / 10^18, about 0.00863% above the pinned PR275 value, κ ≈ 7.51075693834608 × 10⁻⁴.

This is a new additive package, research/gen5b-weighted-repacked/. Our earlier PRs remain untouched. Kernel pivots, donors and cut reads are translated through logical helper roles; second-descent gates additionally require a unique signed scalar/category occurrence and the same exact old-frame basis. Fresh endpoint screens admit 440 early restorations and eight terminal sinks. The result is priced from one emitted word; separate exponent gains are not added.

Quantity	Pinned PR275	This composition
Kernel entries	1,720	1,734
Kernel entrance rank	2,192	2,196
Second-descent gates	89	87
Terminal sinks	7	8
Independent dirty registers	15,425	15,424
Literal stock, 60 replicas	1,229,735	1,229,665
Weighted scalar ADDs	721,418	721,422

The sole inherited Python checker change is the global-lowering helper-count literal, 15,425 → 15,424, retaining the assertion against the emitted context. All other mathematical/checker code, the weighted virtual word and its producer remain byte-identical to PR275. Recomputed selections and pins remain mandatory checked inputs. The completed bank invoice includes 913 endpoint charts, normalizer bound 815 and 905,818,118,400 selector calls.

Retained predecessor proof files, including SECOND-DESCENT-PROOF.md, describe their original instances. The current PROOF.md, README, selections and pins specify the submitted 87-descent/1,734-kernel composition.

Final word SHA-256: 9c8dd18e7df17e3e98c4a7054334280e24967190af9c028365270ed51d21fdd3.

Validation

Two fresh immutable complete replays passed, including one directly from the release checkout (353.46 s) and a separate frozen-copy run (353.09 s). Both produced byte-identical certificates and retained all 163 input hashes. Package manifest: d0f4ae613751cb5d4c6c26cf370fabf6c42ee055cf1145d4c3ad98871cb753f8.

An additional independent audit reconstructed the logical-role mapping from inert source JSON, verified all 1,734 kernel and 87 descent bindings, replayed the final word in both F₂ directions on all 18,944 formal columns, and recounted 721,422 ADDs, 93,590 local paid calls and rank mass 404,394. Its receipt is certificates/gen5b-weighted-repacked-publication-audit.json.

The complete verifier checks signed source/dirty restoration, both reflected frame ledgers, nondegenerate bases and prime obligations, literal bank assignments, the complex supplier, two rational moment engines, all 47 strict outer constraints, adjacent-grid rejection, omitted-stage and mutation controls. The charged finite coefficient is 90,312,891,518,490,001; the signed payload bound is 98 bits. This is finite computational evidence under the inherited hypotheses.

python -m pip install -r research/gen5b-weighted-repacked/requirements.txt
python -B research/gen5b-weighted-repacked/verify.py --output /tmp/gen5b-weighted-repacked-verification

Python 3.11+, SymPy 1.14.0, a new output directory outside the package; no network after dependency installation. The dedicated workflow runs complete admission on Python 3.11 and 3.13 and separately regenerates the unchanged weighted virtual word.

The all-size compiler, common chart, restored rows, selectors, routing, prime supply, precision/recovery, complex correctness and analytic interfaces remain inherited assumptions. Binary kernel identities are over F₂; signed integer checks establish the retained defining decoder and coefficient bounds. This is a conditional finite construction, not an unconditional multiplication theorem, Lean proof or practical benchmark.

Credit George Lydakis/PR275 for weighted matching and integration; Rohan Arun/PR300 for restart packing and second descent; Chafik Boukhalfa/PR296/#299, DreamingOfClouds, Dugongue, utcorvusvolat-dotcom, eumemic, Henry Grant, Jacob Sussman, Evan McKinney and the full retained contributor lineage. Original notices, licenses and AI disclosures are preserved, with immutable input hashes in COMPOSITION-SOURCE.json. This composition and its additional audit were prepared with substantial OpenAI Codex assistance; independent AI-assisted checks are not human peer review.

[Mister-Meeseeks]

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

Contribution: Restart-packed kernels on the weighted gen5b word.

Review and limits: One composed word, with source-span, dirty restoration, reflected ledgers, bank and strict assembly checks; gains are not added across unrelated constructions.

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: a17c42903bbe8d9d26c4bc712d7216a7176237e9. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.