κ = 7.72285110892838493685197e-4: source-bound p10b stages and retimed complex supplier

[eumemic]

κ = 7.72285110892838493685197e-4

This conditional finite construction combines the new p10 bit word from #325 with freshly derived descent, target-prefix, shared-donor kernel, restoration, sink and reorder stages, and a stronger complex supplier derived from #304/#315. The exact assembled value is 772285110892838493685197/10^27, about 0.338% above #325. The complex supplier now determines the assembled bound.

The bit stages are reconstructed on #325's actual register layout: 480 descent retimings, 120 target-prefix groups, 1,296 shared-donor kernel entrances, 240 early restorations, 10 terminal sinks and 130 reorders. The final literal word has 323,664 scalar ADDs, 47,923 local paid calls, rank mass 177,904 and 8,090 independently dirty helper registers. Exact width-100 tiling over 300 replicas uses 423,192 banks per stage and 3,267,960 literal scalar words. Both reflected required ledgers equal the complete actual paid histogram.

The complex scalar program remains unchanged while four frame-retiming stages improve its fallback-inclusive coarse saving to 30915279876953/40000000000000000. The combined verifier replays both suppliers, reconstructs complete profiles and finite invoices, retains the full bad-class fallback, uses two rational moment engines, and checks all 47 assembly constraints. Eight finite bootstrap levels and the arithmetic refinement from #321 use an eventual prime threshold q >= 2^127 - 1; the inherited growing-prime regime is retained.

Validation: two complete immutable replays passed, each running all 20 outer stages from fresh outputs with freshly compiled native checkers. Their mathematical certificates agree exactly; all 308 pinned files and the manifest match the committed Git blobs. The literal word SHA256 is 688d4706d9b083fc43951a47a9b95d31c51b1283d5b1e14a20671d2b652186ed.

Additional independent checks passed for the full F2 forward/inverse operators, arbitrary dirty restoration, COPY immutability, both reflected ledgers, exact bank tiling, all 27,802 determinant witnesses, complex clipping, eight finite recurrence levels and the final rational grid. Omitting kernel restoration corrupts 999 formal rows. Python 3.12 discovery reproducibility is pinned by an explicit ordered sum and frozen IEEE scoring values; every chosen move and the output word are still checked exactly. The new workflow repeats the complete verifier on Linux/Python 3.12. The broad current-main make verify run is still in progress and is not claimed as passed.

This new submission replaces withdrawn #326 only after the full replay and committed-byte gate passed. #326 stays closed and all prior PR heads remain unchanged. #327 now supplies a stronger public complex candidate; its full original offline replay has passed locally, but its separate operational integration is not part of this frozen construction.

Reproduce with Python 3.11+, SymPy 1.14.0, a C++17 compiler and Boost:

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

The package retains source notices and immutable predecessor snapshots. Credit includes DreamingOfClouds for #325 and #304/#315, Chafik Boukhalfa (chafreaky) for the transcript transforms, rohanarun for concave-descent and frame optimization, #321's arithmetic refinement, and all contributors named in the inherited notices. The new searches, composition, audits and packaging were prepared with substantial OpenAI Codex assistance; inherited Anthropic Claude and other AI disclosures remain intact.

This is a sufficient finite construction conditional on the inherited all-size compiler, dirty lifting, frame geometry, covering, weighted selector, routing, prime supply, precision/recovery, complex-symbolic and analytic-transfer interfaces. It is not a formal verification of the full multiplication theorem. All previously published PR heads and claims remain frozen.

[Mister-Meeseeks]

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

Contribution: p10b stages with a retimed complex supplier.

Review and limits: Both sides are admitted and priced together with actual bank/prime obligations. Independent-audit sources and discovery provenance are 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: 34af22b4f972f46870ba6b8c9dfaae1d0bb1b25d. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.