κ = 7.77596191161693861459874e-4: all-rank donor flow and 52 final retimings

[eumemic]

κ = 7.77596191161693861459874e-4

A new bit source jointly optimizes donor reuse across all ranks and cube orientations, then rebuilds the complete downstream construction. The exact conditional assembled value is 388798095580846930729937/500000000000000000000000000, approximately 0.04219034% above frozen #332. Every previously published head remains unchanged.

The source adds an independent selector-port transposition and a joint all-rank donor-flow/orientation search to the explicitly modified #325 derivative. Optimization scores are discovery aids only: fresh producer regeneration, carrier matching, two concrete reuse/descent passes, and the strict source verifier establish the admitted word and its complete paid profile. Original producer hashes, selected maps/orientations, search provenance and all inherited notices are retained. Every outer replay regenerates all five complete source files and binds their exact payload bytes, permitting platform-dependent gzip representation while pinning the stored package bytes.

Fresh downstream selections apply 480 first retimings, 120 target groups, 1,244 entrance families of rank 1,248, 240 early restorations, 15 terminal sink removals, 125 reorderings and 52 final retimings. The last stage moves 14 single gates and 19 pairs through legal frames, removes 14 paid calls, and preserves every scalar instruction, COPY lifetime and endpoint map.

The final word has 324,351 ADDs (326,271 unit-expanded), 47,829 local paid calls, rank mass 177,852 and 8,085 independently dirty helpers. Across 300 replicas, the complete width-100 assembly uses 423,036 banks per stage and stock 3,267,180. It charges 1,918,670,037,000 selector calls and a counted primitive coefficient of 125,811,486,404,701,001, with a 93-bit signed payload bound. Stock and the full paid profile are recomputed together.

The complex supplier remains public #327 at 40ed0456ab1990beb3440e61bb883ccf95fdcea4, with full-fallback saving 779597612622781/10^18. Every full replay reruns the complete source and operational transfer, including signed scalar identities, arbitrary dirty restoration, both reflected splices, copied centres, dynamic scratch, precision and mutation controls. The bit root still binds.

Two independent complete immutable replays actually exited 0 on Python 3.11 and 3.12 (1,040.53 s and 836.05 s), executing all 22 ordered stages. Their mathematical certificates agree exactly after excluding only the top-level hashes of fresh timing-dependent receipts, and every consumed receipt hash was checked. Both runs freshly regenerated all five complete source payloads and passed all ten producer-binding mutation controls. The committed package is separately checked against all 404 manifest entries plus the manifest itself before publication.

Independent checks already reconstruct the complete F2 forward/inverse operators, dirty restoration, COPY immutability, both reflected ledgers and a distinct exact tiling from actual endpoint ranks. Omitting kernel restoration corrupts 959 formal rows. A separate modular determinant algorithm with exact Hadamard lifting checks all 27,808 nonzero basis/annihilator witnesses. Closed-form arithmetic independently verifies eight finite bootstrap levels, strict complex clipping, seven outer margins and the final rational grid. The full verifier retains both rational moment engines, every helper assignment, the complete invoice and all 47 assembly inequalities.

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

python -m pip install -r research/p10b-donor-flow52/requirements.txt
python -B research/p10b-donor-flow52/verify.py --output /tmp/p10b-donor-flow52-proof --cxx g++ --boost-include /usr/include

Credit includes DreamingOfClouds for the #325 bit construction and #327 complex supplier, Chafik Boukhalfa for transcript transforms and p10 adaptations, Rohan Arun for frame optimization and arithmetic refinements, and every contributor named in inherited notices. The new source optimization, composition, independent audits and packaging used substantial OpenAI Codex assistance; inherited Anthropic Claude and other AI disclosures remain intact.

The result remains conditional on 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 threshold q >= 2^127 - 1 retains the growing-prime regime. No unconditional theorem or new Lean-build claim is made. The repository-wide inherited joint-dual Makefile pin failure remains separate and is addressed by #318.

[Mister-Meeseeks]

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

Contribution: All-rank donor flow and final p10b retiming.

Review and limits: Full source-bound native replay includes producer and geometry checks. Earlier packages carried by this branch are reconciled by exact package identity.

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: 367f55f22e5f5e3aff47e6437bf0dfbf743bacec. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.