Conditional κ = 7.44714499649771e-4: eight completed bootstrap levels on #290

[M6LI]

Change and mathematical scope

Extending #290’s three completed ordinary bootstrap updates to eight increases its conditional κ from 186178624839407/250000000000000000 to 744714499649771/1000000000000000000, a strict gain of 292143/1000000000000000000 (2.92143e-13).

This is stacked on #290 at 739c3bb0ad0596f427e0a72a2ebeca23277217a3. The new contribution is the research/finite-eight-frontier/ supplement and its CI workflow. Its 136 original source files, kernel word, sixty-replica banks, source manifests, complex supplier, licences and contributor notices are preserved exactly. The proof supplies eight sequential finite cutoffs and small-width completions; it takes no infinite-depth limit.

Scope remains conditional on the inherited weighted compiler/native-front, fixed-tape ordinary primitives, selector/common-cover, ancestor-chart, restored-row, prime/recovery, complex scalar/Lean and analytic interfaces. No all-size theorem or new Lean certificate is claimed. Substantial OpenAI Codex assistance is disclosed; Chafik Boukhalfa, Rohan Arun, DreamingOfClouds, eumemic, Dugongue and other upstream contributors retain their credits and disclosures.

Newer submissions, including #296, report larger bounds. This PR records a verified improvement over its exact #290 parent and a reusable finite-depth refinement; it makes no current-record claim. Subsequent frontier adaptations can be added here without withholding this reviewed contribution.

Validation

• The unchanged original ten-stage verifier passed in 703.734 seconds, including all 19,406 formal columns in both directions, both integer decoders, all 4,765,800 bank assignments, kernel controls and original stage-omission controls.
• Both separately implemented rational moment engines derive the supplier bounds and exclude their adjacent grid points. All 47 strict assembly conditions and seven margins pass.
• The arithmetic ran normally and under -OO in 30.015 seconds total, with identical values and types and all 27 intended-reason negative controls in each mode. Actual certificates and concise source/resource evidence are included.
• Distinct AI source/proof and publication audits passed. The exact published combined public entry point passed locally in 751.875 seconds. Fork CI also passed its complete public replays on Python 3.11 and 3.13: https://github.com/M6LI/integer-mult-bounds/actions/runs/38043054255.
• The fork's shared repository workflow passed all 52 jobs at this exact head, including all 16 verification groups on Python 3.11/3.13/3.14, ranked-pair replay and three formal packages: https://github.com/M6LI/integer-mult-bounds/actions/runs/38043054206. This establishes the required groups through CI; the earlier local sequential attempt timed out and remains recorded as a failure. Fork CI is separate from upstream maintainer approval.

Reproduce from the repository root:

python -m pip install -r research/five-stage-gen5-collective-kernels/requirements.txt
python -X utf8 -B research/finite-eight-frontier/verify.py --output /tmp/finite-eight-fresh

The command reruns all ten original stages before the normal/optimized refinement. The workflow runs this same command and preserves its first result or failure.

[Mister-Meeseeks]

Thank you @M6LI. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Eight completed finite bootstrap levels on PR290.

Review and limits: Source-bound Linux run replays all ten original supplier stages, then the new arithmetic. Finite-depth refinement does not change the network or remove inherited 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: 7e7a6d796bf9dbc51d1d6d0855cc67bcf0668fbe. Publication: 50d768818f579d4e165b4c257c6ee25bca300802.