[utcorvusvolat-dotcom]

Change and mathematical scope

Conditional κ = 724189082265949363570532 / 10^27 = 0.000724189082265949363570532. This is +0.08533948% over PR279's 0.000723571590007464, the strongest public construction claim observed immediately before publication, and +0.18250242% over PR276. PR279 independently published the same 880 common-frame retimings during preparation; the additional gain here comes from composing them with 440 early helper restorations and 60 transported dirty entrances. No priority or global-optimality claim is made.

The additive package research/gen4-retiming-entrances/ includes its full immutable PR276 prerequisite (commit d428ab0462b9dfd3131ab4e89999f0adcd6173dd), frozen selections, exact emitters, proofs, native chart/column checkers, finite pricer, completed-bank admission and a network-free verifier. No existing construction is modified. Final word SHA256: 71dd08f325566160a01b1c3d8b38450eeb48f478c8f7588065e234d58bddef48.

The scalar changes are checked signed commuting shears: 440 helper restorations move to legal rank-23 endpoints, while 240 original dirty reads move beyond the last copied-center discard to support 60 larger entrances. The two helper sets are disjoint. Residual ranks tile all width-120 banks exactly at 60 replicas, reducing normalized stock to 255,841. The final chart bound raises the normalizer to 447, fully included in the finite invoice.

All-size compiler, common weighted chart, restored rows, selectors, routing, prime supply, precision/recovery, complex symbolic correctness and analytic reduction interfaces remain inherited assumptions. This is a conditional finite construction, not an unconditional multiplication theorem, new Lean proof or measured runtime improvement.

Validation

The published package was freshly replayed from its immutable inputs with Python/SymPy and clang C++17:

• Full unmodified PR276 nine-stage admission and source integrity, followed by actual source regeneration and each transformation.
• 4,400 exact retimed source-span inclusions; signed cleanup/entrance commutation checks; all 23,450 global formal columns, 120 fresh COPY episodes and six nonzero bridge controls.
• 3,784 exact changed projector charts, including every one of the 500 changed helper endpoints; max 208 chart factors, numerator 764 and denominator 351.
• 4,923,000 literal role/replica/stage bank assignments; 2,400 endpoint columns and 2,400 nonzero omission/repetition controls.
• Normalizer 447, selector charge 528,906,962,400, full finite primitive coefficient 92,488,203,535,344,001 and independently recomputed 91-bit signed payload bound.
• Exact q = 2^127 − 1 proof, retained full fallback, two rational moment engines, eight ordinary levels, all 47 strict outer inequalities and adjacent-grid rejection.
• Package input hashes unchanged before/after. Dedicated Linux/g++ workflow included.

sudo apt-get install -y g++ libboost-dev
python3 -m pip install -r research/gen4-retiming-entrances/requirements.txt
python3 -B research/gen4-retiming-entrances/verify.py --output /tmp/gen4-composed-replay

Use a fresh output outside the package. Python 3.11+ and SymPy 1.14.0 are required; no network is used by the verifier.

Credits

Prepared for utcorvusvolat-dotcom with substantial OpenAI Codex assistance. Full Apache-2.0 lineage and original prerequisite notices are retained. DreamingOfClouds/Anthropic Claude supply PR276's gen4 word; Henry Grant (hcg890)/Jacob Sussman the five-stage architecture; eumemic the scalar/physical/source527 and PR244 retiming lineage; Evan McKinney the PR197 banks and PR271 cleanup identity; Rohan Arun the PR237/263 work and concurrent PR279 retiming; PR270 supplies connected-block selection/binding. Chafik Boukhalfa, icekylinx, Avi Eisenberg and the remaining inherited contributors are credited in NOTICE.md and the untouched upstream notices.

[Mister-Meeseeks]

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

Contribution: Early helper restorations and entrance-aware gen4 banking.

Review and limits: Source-bound own Linux full replay. Endpoint obligations and actual dirty-helper restoration are checked, not presumed from scalar cleanliness.

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: f063aab8d6e514188e53db57218515df9cdd186e. Publication: 50d768818f579d4e165b4c257c6ee25bca300802.