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Thank you @eumemic. This contribution is now retained on main in the scoped 100-PR review and contributor credits. Contribution: Reordered stages with 471 twins and signed18. Review and limits: Complete native source-bound admission, including independent word/assembly checks. Different signed-lift candidates are not silently interchanged. 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: |
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κ = 8.03679711866261894738090e-4
Exact κ:
80367971186626189473809/100000000000000000000000000.This composes #353's reordered PLAIN12 producer with freshly selected #354 transcript stages, retains all 471 twins under the complete T=300 bank allocation, then adds eighteen signed helper-pair condensations. The reordered producer/stage composition is also presented in the concurrent draft #357; the extensions here retain the extra twin, add the eighteen signed pairs and supply complete native admission. The result improves #357's stated κ by approximately 0.00313% and #356 by approximately 0.06447%. This is a new branch and PR; all earlier published heads and claims remain frozen.
The new source is admitted explicitly. Its virtual circuit and physical frames, both signed defining-integer decoders, all 8,100 dirty helpers, and all 10,020 source F2 columns are checked. The source producer is regenerated and all five expanded physical files are compared exactly. The base export matches #353's shipped three-file snapshot. All four transcript-stage selections are rederived on this source: 480 descents, 120 target stages, 240 restorations and ten terminal sinks. Design T, completion and twin selection are rerun. Unlike the historical 60-replica route, the 300-replica native allocation admits all 471 twins, so the one-twin trim is unnecessary.
#353's recipe names PLAIN12 through an environment variable that its shipped producer does not read. The derived producer makes PLAIN=12 explicit and reproduces the shipped base exactly. Published upstream bytes and their provenance remain preserved. The old #325 replay supplies only explicitly retained arithmetic, prime and complex-interface references; it does not stand in for admission of the new source.
After ten sinks and removal of 480 no-event FULL/FULL helpers, the complete source/staged/compact role map retains the COPY slot. The signed extension is regenerated from the actual compacted source and its entire scalar operator is compared exactly over the integers, including arbitrary dirt and COPY/ERASE, with omission and sign controls. This comparison ignores MOVE operators; native geometry and both chronological reflected frame ledgers check those separately. The two additional signed pairs used on #356's base fail the proper-merge precondition here and are excluded.
The final word has 9,530 registers, 7,610 arbitrary dirty helpers, 406,961 events, 358,838 ADDs, 45,957 paid calls and rank mass 169,111. Native admission binds 13,908 frames, 993 new frame charts, 3,292 changed projectors, all-frame prime exclusions, 396,813 width-100 banks per stage, literal stock 3,136,065 and selector charge 1,806,129,192,000. The complete finite coefficient is 120,646,745,842,304,501. Eight finite bootstrap levels yield the displayed κ, with all 47 strict outer constraints positive and the adjacent grid point rejected.
Two complete immutable 24-stage replays passed under CPython 3.11 and 3.12 with actual observed exit 0 and matching mathematical certificates. A distinct literal-word, restoration, tiling, determinant and exact-assembly audit also exited 0. Every committed construction and audit blob was checked against the frozen manifests before publication. The dedicated Linux workflow repeats the full construction and independent audit.
The E8 supplier retains the corrected odd-dimensional finite invoice and full scalar, dirty, reflected-splice, paid-profile and two-moment replay. Its exact coarse saving is
876248285600677/10^18. All claims remain conditional on the inherited all-size compiler, selector/chart, restored-row, routing, growing-prime supply, precision/recovery, complex-symbolic and analytic interfaces. The bit word's global operator contract is F2; its signed defining-integer source decoder and the local signed extension have separate checks. E8 Lean data/configuration is regenerated byte for byte; no local Lean kernel build, module-to-gcert producer regeneration or unconditional multiplication theorem is claimed.Credits and AI disclosure: Rohan Arun supplied #353's reordered producer. Chafik Boukhalfa/Anthropic Claude supplied #329 and #354's transcript stages and Design T/twin reimplementation. Design T/twins originate with utcorvusvolat-dotcom's #310 and Louis Harrison/Anthropic Claude's h=20 port in #346. DreamingOfClouds/Anthropic Claude supplied #325. Jacob Sussman supplied the E8 unit and Lean data/checkers; DaysSky/Anthropic Claude supplied #352's E8 integration. The composition, explicit producer repair, signed pairs, complete native integration, independent audits and publication used substantial OpenAI Codex assistance. All original licenses, notices and contributor/checker lineages are retained.