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Thank you @eumemic. This contribution is now retained on main in the scoped 100-PR review and contributor credits. Contribution: Shared-intersection expansion of transported entrances. Review and limits: Source-bound full Linux verifier on the changed word. Preserve simultaneous compatibility and endpoint accounting rather than adding independent gains. 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 = 7.10433687047883e-4
This extends PR249, which transported 21 dirty entrances at κ ≈ 7.10392186446856 × 10⁻⁴. The new shared intersections add 16 entrances and 224 entrance-rank units, giving 37 transported entrances with total rank 549.
Conditional κ ≈ 7.10433687047883 × 10⁻⁴, an improvement of 0.005842% over PR249.
Thirty-seven additional dirty entrances reduce the bank stock per replica by 22.875. Nine entrances have rank 18, nine rank 17, six rank 14, eleven rank 12 and two rank 9. Each selected helper is untouched up to the pinned cut after all 441 target-coordinate setup additions. Moving its original zero-frame compensation through that exact F₂ prefix changes its response to the corresponding transformed column. The 148 old reads become 150 reads at the new nondegenerate entrance frames. Every new entrance lies in the helper's first required frame and each affected target's next required frame. Several helpers share one entrance frame so the target paths can serve the whole cohort. Exact intersections of allowed frames and minimum-cut role selection find the additional cohorts; the verifier consumes their explicit rational bases and checks the resulting word independently.
The emitted word is checked on all 20,107 formal F₂ columns in both directions, including arbitrary dirty and source restoration. Both reflected frame ledgers are reconstructed from actual gate uses. The signed source527 producer keeps its original execution context; only the lowered word receives the separately cloned entrance context. The emitted signed prefix bounds remain 37,631 forward and 3,295,796 backward. This uses the retained F₂ payload contract and does not assert that the new integer lift has the old target decoder.
All five stages, bank assignments, exact charts, prime witnesses, routing, copied centers, cleanup and fallback remain charged. The charts require up to 548 elementary factors and normalizers up to 787 factors; the added bank selector bill is 376,079,448,960. This fixed bill is included in the finite accounting. The literal construction executes 24 replicas with stock 521,425, 11,792,280 paid calls, rank mass 62,465,400 and deficit 105,600. The exact moment uses that complete literal profile. The bit supplier binds.
The PR244 frame retimings and PR249 compensation-transport construction remain stable predecessors. This improvement is submitted as a separate branch and PR.
The immutable verification reconstructs all eight mandatory stages: source527 producer, actual five-stage bit word, scalar columns/restoration, exact prime witnesses, completed banks, complex supplier, rational moments/outer assembly, and full finite accounting. All 1,990,440 bank assignments and 245 exact charts are enumerated. Two moment engines, three completed ordinary-leaf levels, 47 strict assembly constraints and seven margins pass; the adjacent κ grid point fails. Two independent complete immutable replays pass and produce byte-identical final certificates.
Python 3.11+, SymPy 1.14.0 and a new output directory outside the package are required. Replay uses no network.
This conditional result retains the all-size compiler, common weighted chart, restored rows, selectors, tape routing, prime supply, precision/recovery, complex symbolic correctness and analytic reduction assumptions. The finite checks do not prove those interfaces from scratch and do not claim a practical multiplication benchmark or new Lean build.
Provenance: PR210's source527 helper and parity elision, plus PR244's common-frame retiming; hcg890's PR234 and Jacob Sussman's five-stage construction; Rohan Arun's earlier PR237 width-120 banking; Evan McKinney's PR197 completed banks; Chafik Boukhalfa's PR200 helper; Avi Eisenberg's PR193 complex supplier; and the retained PR207/211/216/230 improvements. Original source notices, licenses and AI disclosures are included. The new F₂ compensation transport, thirty-seven entrance gauges, exact bank charts and integration were prepared by eumemic with substantial OpenAI Codex assistance.