κ = 7.77268259042371640048112e-4: oriented p10b source and 42 constructed-frame retimings

[eumemic]

κ = 7.77268259042371640048112e-4

A new donor-guided cube orientation and pair-port relabeling improve the bit source, followed by fresh downstream stage selections. The exact conditional assembled value is 48579266190148227503007/62500000000000000000000000, approximately 0.0958491% above frozen #331. The source is an explicitly modified derivative of #325 at c4f1b74bd580fc5a18fec6f12ab498dca01b5533; the public #325 package is not presented as unchanged. The original hashes, selected orientation data, search provenance and all inherited notices are retained.

Every complete replay regenerates all five selected source files—graph, chronology, profile, scalar word and frames—from the pinned producers through two reuse/descent passes. All complete file bytes, including the compressed files, must match the vendored source before its nine-stage strict verification runs. This binds the changed construction to its actual producer.

Fresh downstream reconstruction applies 480 first-stage frame retimings, 120 target groups, 1,250 entrance families with total rank 1,254, 240 early restorations, 13 terminal sink removals, 127 reorderings and 42 final constructed-frame retimings. The latter move 21 pairs through genuine new frames, preserve scalar instructions and COPY lifetimes, and retain exact equality with the predecessor's endpoint map after early restoration.

The resulting word has 324,147 ADDs (326,067 unit-expanded), 47,832 local paid calls, rank mass 177,886 and 8,087 independently dirty helpers. Exact width-100 tiling across 300 replicas uses 423,138 banks per stage and stock 3,267,690. The complete finite invoice charges 1,919,143,767,000 selector calls, a primitive coefficient of 125,825,732,659,691,501 and a 94-bit signed payload bound. The complete profile and stock are recomputed together.

The complex supplier remains #327 at 40ed0456ab1990beb3440e61bb883ccf95fdcea4, with full-fallback saving 779597612622781/10^18. Every outer replay reruns its complete public source verifier and the operational transfer: signed scalar identities, arbitrary dirty restoration, both reflected splices, copied centres, dynamic scratch, finite precision and mutation controls. The bit root determines the final bound. This wrapper makes no new Lean-build claim; upstream Lean results retain their original scope.

Two complete fresh immutable replays passed under Python 3.11 and 3.12, each exiting successfully after all 21 outer stages. Both regenerated all five source files exactly, compiled five native checkers afresh, and replayed the complete bit and complex suppliers. Their mathematical certificates match after excluding only top-level receipt hashes whose files include execution timings. The final publication gate checked every one of the 401 package files plus the manifest against the committed Git blobs at f9136e76568100034aa37337251f93d684496c13. Completed replay receipts, the matching mathematical certificate and the source-regeneration gate are saved outside the immutable package. A dedicated Linux/Python 3.12 workflow repeats the complete construction.

Separate independent checks reconstruct the actual F2 forward/inverse operators, dirty restoration, COPY immutability, both reflected ledgers and an alternate exact tiling from actual endpoints. Omitting kernel restoration corrupts 966 formal rows. A separate modular determinant algorithm with exact Hadamard lifting verifies all 27,782 basis and annihilator witnesses. Closed-form arithmetic checks eight finite bootstrap levels, the strict complex cap, seven margins and the final rational grid. The full verifier retains both exact moment engines, the complete paid profile, every helper assignment and all 47 assembly inequalities.

The repository-wide make verify retains an inherited joint-dual Makefile pin failure, independently reproduced on unchanged upstream and addressed separately by #318. The remaining pair and isolated test targets passed. This PR does not claim a clean repository-wide run.

Reproduce with Python 3.11+, the pinned dependencies, a C++17 compiler and Boost:

python -m pip install -r research/p10b-oriented-constructed42/requirements.txt
python -B research/p10b-oriented-constructed42/verify.py --output /tmp/p10b-oriented42-proof --cxx g++ --boost-include /usr/include

Credit includes DreamingOfClouds for the #325 bit construction and #327 complex supplier, Chafik Boukhalfa for the transcript transforms and p10 adaptations, Rohan Arun for frame optimization, the #321 arithmetic refinement, and all contributors named in inherited notices. The new orientation and port search, producer binding, selections, composition, independent audits and packaging used substantial OpenAI Codex assistance. Inherited Anthropic Claude and other AI disclosures remain intact.

This is a sufficient finite construction under the inherited all-size compiler, dirty lifting, common-ancestor chart, restored-row, covering, weighted selector, routing, growing-prime supply, precision/recovery, complex-symbolic and analytic-transfer interfaces. The eventual prime threshold q >= 2^127 - 1 retains the growing-prime regime. All previously published heads and claims, including #331, remain frozen.

[Mister-Meeseeks]

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

Contribution: Source orientation and constructed-frame retiming on p10b.

Review and limits: Original Linux pipeline reaches the final overly strict gzip-container comparison. PR333 repairs complete-payload binding, not mathematical equality, and keeps all source/word checks.

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: f9136e76568100034aa37337251f93d684496c13. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.