κ = 7.7652200910342944936985e-4: cross-entrance retiming and operational PR327 supplier

[eumemic]

κ = 7.7652200910342944936985e-4

This conditional finite construction combines the bit source from #325 with the operationally checked p10 complex supplier from #327. The exact assembled value is 15530440182068588987397/20000000000000000000000000, approximately 0.5486% above frozen #328 and 0.0004327% above the κ claimed in #329. The bit moment root now determines the bound. This package was frozen before #329 and uses the separately pinned #325/#327 sources.

The new bit word has 1,337 entrance families with total entrance rank 1,447. It combines higher-rank families, two exchanges between entrance groups, and 49 additional frame retimings with the existing freshly reconstructed descent, target, restoration, sink and reorder stages. The last retimings preserve the exact predecessor endpoint map, including the 240 helpers already restored to proper frames. They preserve every scalar instruction and COPY lifetime, and reconstruct both reflected ledgers from actual gate requirements.

The literal word contains 323,444 ADDs, 48,057 local paid calls, rank mass 177,753 and 8,090 independently dirty helpers. Over 300 replicas, exact width-100 tiling uses 422,739 banks per stage and 3,265,695 scalar words. The finite invoice charges 1,919,846,082,000 selector calls and a full primitive coefficient of 126,185,730,445,433,501, with a 96-bit signed payload bound.

The complex transfer pins #327 at 40ed0456ab1990beb3440e61bb883ccf95fdcea4. It replays all four historical anchors and six public programs, then separately checks the strongest program's scalar identities, sign controls, both reflected full splices, dynamic scratch allocation and finite precision guard. Its full-fallback saving is 779597612622781/10^18; no Lean build is claimed by this wrapper. The original contributor's Lean results and disclosures are preserved in the pinned source.

Two complete fresh immutable replays passed, independently under Python 3.11 and 3.12, with all 20 outer stages in each run. Their mathematical certificates are identical after excluding only top-level receipt hashes whose files include execution timings. The final publication gate verified every one of the 399 package files and the manifest against the committed Git blobs at 6d1faafc1ac58adb885349b2b08813467a938563. Saved full-replay receipts and the matching mathematical certificate are included outside the immutable package. A dedicated Linux/Python 3.12 workflow replays the complete construction.

The repository-wide make verify still fails at the inherited joint-dual Makefile pin, independently reproduced on unchanged upstream; #318 addresses that separately. The remaining pair and isolated test targets passed. This PR does not claim a clean repository-wide run.

Separate independent checks reconstruct the complete F2 forward/inverse operators, dirty restoration, COPY immutability and both reflected ledgers. A distinct exact bank tiling is built from the actual endpoint ranks; omitting kernel restoration corrupts 1,130 formal rows. A modular determinant algorithm with exact Hadamard lifting verifies all 27,834 witnesses. Closed-form arithmetic independently verifies all eight finite bootstrap levels, the strict complex cap, seven outer margins and the final rational grid. The complete verifier retains both moment engines, the full paid profile and all 47 assembly inequalities.

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

python -m pip install -r research/p10b-cross49-pr327/requirements.txt
python -B research/p10b-cross49-pr327/verify.py --output /tmp/p10b-cross49-pr327-proof --cxx g++ --boost-include /usr/include

The package pins the original verified #325 source at c4f1b74bd580fc5a18fec6f12ab498dca01b5533 and preserves all source notices. Credit includes DreamingOfClouds for #325/#327, 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 searches, composition, 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, frame geometry, 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 PR heads and claims, including #328, remain frozen.

[Mister-Meeseeks]

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

Contribution: Cross-entrance retiming with the operational PR327 supplier.

Review and limits: Actual donor cuts, scalar restoration and complete finite supplier integration; source-bound historical full replay, not merely the declared price.

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: 6d1faafc1ac58adb885349b2b08813467a938563. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.