κ = 7.76523967665819025774905e-4: nested donor entrances on the p10b word

[eumemic]

κ = 7.76523967665819025774905e-4

Three additional rank-one entrance families improve frozen #330 to the exact conditional value 155304793533163805154981/200000000000000000000000000. They reuse donors along nested entrance chains: pivots 6949, 7055 and 7057 borrow from helpers 8464, 8479 and 8494, already used by the rank-four family at pivot 8509. The unchanged kernel materializer admits their ordered entrances and complete restoration; all existing families remain. The earlier discovery restriction requiring disjoint donors excluded these valid nested uses.

The new bit word has 1,340 entrance families and total entrance rank 1,450. Fresh reconstruction retains 480 original descent moves, 120 target groups, 240 early restorations, 10 terminal sinks, 130 reorder moves and 49 final constructed-frame retimings. It has 323,442 ADDs, 48,060 local paid calls, rank mass 177,750 and 8,090 independently dirty helpers. Exact width-100 tiling over 300 replicas uses 422,730 banks per stage and 3,265,650 scalar words. The complete finite invoice charges 1,919,845,947,000 selector calls and a primitive coefficient of 126,190,337,402,146,001, with a 96-bit signed payload bound.

The operational complex supplier remains #327 at 40ed0456ab1990beb3440e61bb883ccf95fdcea4, with full-fallback saving 779597612622781/10^18. Its complete public source replay and operational transfer check all scalar programs, dirty restoration, both reflected splices, copied centres, dynamic scratch, finite precision and mutation controls. No new Lean build is claimed. The bit moment root still determines the assembled bound.

Two complete fresh immutable replays passed under Python 3.11 and 3.12, with all 20 outer stages in each run. Their mathematical certificates match after excluding only top-level receipt hashes whose files contain execution timings. The final publication gate checked all 399 package files plus the manifest against the committed Git blobs at c0fa7e1be9e5f9f2316bb1f88e4c77298014492e. Full replay receipts and the matching mathematical certificate are saved outside the immutable package. A dedicated Linux/Python 3.12 workflow repeats the complete construction.

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 is not a claim of a clean repository-wide run.

Separate independent checks reconstruct the full F2 forward/inverse operators, arbitrary dirty restoration, COPY immutability, both reflected ledgers and a distinct exact tiling from actual endpoints. Omitting kernel restoration corrupts 1,130 formal rows. A different determinant algorithm with exact Hadamard lifting verifies all 27,834 basis and annihilator witnesses. Closed-form arithmetic independently checks eight finite bootstrap levels, the strict complex cap, seven outer margins and the final grid. The complete verifier retains both exact moment engines, full paid profiles 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-nested-donors-pr327/requirements.txt
python -B research/p10b-nested-donors-pr327/verify.py --output /tmp/p10b-nested-donors-proof --cxx g++ --boost-include /usr/include

The #325 source remains pinned at the originally verified c4f1b74bd580fc5a18fec6f12ab498dca01b5533. 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. This new nested-donor search, composition, audits and packaging used substantial OpenAI Codex assistance. Inherited Anthropic Claude and other AI disclosures are preserved. The separate #329 reorder ordering was inspected; after the 49 final retimings, its two gate moves were already present and the fresh second reorder screen found no further moves.

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 #330, remain frozen.

[Mister-Meeseeks]

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

Contribution: Nested donor entrances on p10b.

Review and limits: The common-entry and nesting obligations are checked on the emitted word, with full bank, prime and invoice charges retained.

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: c0fa7e1be9e5f9f2316bb1f88e4c77298014492e. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.