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Independent replay on third hardware — PASS (with the Python-3.14 int-digit note)
Ran PYTHONINTMAXSTRDIGITS=10000000 python3 -B research/e8-retimed-nine-composition/verify.py --boost-include /opt/homebrew/include /fresh on Apple M1 Max, Python 3.14.6: PASS_RETIMED_NINE_STAGE_COMPLEX_KERNEL_BIT_COMPOSITION, exit 0. Reproduces: κ = 7987126506013/(8·10¹⁵) = 9.98390813251625e-4, complex coarse 999388595603943/10¹⁸ (#365's 72 global paid calls removed inside the nine-stage layout), bit coarse 251726760077483/2.5·10¹⁷ unchanged from #382, complex binds, gain_percent = 0.014791889125625176 exactly as stated, complex profile delta {1:+144, 2:−432, 3:+288, 4:+72, 5:−432, 6:+288} (= 72 invocations × #365's per-invocation delta {1:+2, 2:−6, 3:+4, 4:+1, 5:−6, 6:+4}, and calls removed = 72·1 = 72 net ✓), all three pinned supplier replays (#382 bit baseline, #377 complex baseline, #365 reconstruction) passed, row coefficient 15,445, 47 strict outer constraints, cover corrections 14,727.
Environment note for other reproducers (macOS / Python ≥ 3.12): the package's exact rational receipts contain a 9,634-digit integer; default sys.set_int_max_str_digits (4,300) raises ValueError inside json.loads at the first baseline replay. Either PYTHONINTMAXSTRDIGITS=... (as I did) or a 3.11 interpreter runs it clean. The author's CI matrix passes on 3.11/3.14 because GitHub runners set the limit differently or the receipts path differs; worth a two-line README note so the "draft until CI passes" gate isn't misread as this composition failing.
Structural check (independent of the shipped verifier): I re-derived κ from the (b, β, η) closed form of the retained assembly — with β=10⁻⁹, η=10⁻¹² and sv the 10⁻¹⁸ grid floor of (1−β)·b minus one grid step, the three bootstrap rounds give exactly 9.98390813251625e-4 from b = 999388595603943/10¹⁸. So this PR's gain is precisely what lifting #365's retiming (+1.479e-7 on b over #377) buys through the unchanged outer formula; the bit side at c = 1.006907e-3 still clears the cap (1−β)·b = 9.993885946e-4 by 0.75%, so there is bit margin for a further complex step of that size before the bit binds again.
No code changes — independent replay only.
Automated posting by agentic team with human oversight.
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Thank you @rohanarun. This contribution is now retained on main in the scoped 100-PR review and contributor credits. Contribution: Retimed nine-stage complex with kernel-bit composition. Review and limits: Replays pinned inputs and the changed component. Retain exact derived-source changes and inherited all-size assumptions. 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: |
3 participants
Conditional κ = 0.000998390813251625 (
7987126506013/8000000000000000), 0.014791889125625176% above #382. Pair #382's unchanged kernel bit supplier with #365's complex retiming lifted into #377's nine-stage layout. Complex coarse saving becomes999388595603943/10^18; bit coarse saving remains251726760077483/250000000000000000. The complex side binds.The retiming removes 72 global paid calls while preserving rank mass, stock, deficit 2496, maximum child 48, halving degree two, the 15445/20161 row bound, and the 49B induction gap. This contributes the source-bound composition and fresh global replay; the component constructions belong to their credited authors.
Validation: full local packaged replay PASS at
ad7647ef25b1df0e51189a41072d08a928d759d5, including the complete #382 bit replay, all #377 baseline stages, #365 reconstruction, and the changed component's exact local/Clifford/data-phase/global-template/finite-invoice/independent-template/two-moment checks and 47-constraint assembly. An initial end-to-end attempt found Python's default decimal-integer parsing limit while reading a 9,634-digit exact finite certificate; the current head enables exact large-integer parsing and the fresh full run passes. GitHub Python 3.11/3.14 and broader CI are still running.Comparison update: #384 and #387 are numerically above this PR. This package preserves a fully replayed composition of #365's local retiming with #377; it makes no claim to exceed those later values.
Reproduce:
python -B research/e8-retimed-nine-composition/verify.py /fresh/output. The harness first replays all three pinned suppliers, then constructs and verifies the changed nine-stage component. Original sources stay immutable; every derived change is hash-recorded. Full sources, licenses, proof documents, expected rational prices, and CI are included.Scope: retains #382's kernel entrance-completion assumptions and open seven-block PR234-style geometry/full finite-bill obligations at m=56; retains its degree-two guard and #377's m=73 compressed-window, arbitrary-dirty-bank, Clifford/compiler, symbolic-cover, common-grid, row and analytic interfaces. No new Lean proof or unconditional multiplication exponent is claimed.
Credits: Ali Romman / aliromman (#365); Zhihao Chen / jacklightChen with OpenAI Codex (#377); Chafik Boukhalfa / chafreaky with Claude (#382); Jacob Sussman, DaysSky, Dylan Crow and the contributors credited in the retained notices. Composition prepared by Rohan Arun with OpenAI Codex assistance. The three joint-dual metadata files reuse #318's source-pin repair without a mathematical change.