[utcorvusvolat-dotcom]

The supplied w3 word improves the exact conditional exponent to

κ = 94111687450666858500293 / 125000000000000000000000000
  = 0.000752893499605334868002344.

This is 0.18551765% above PR #309 at its checked head 19d148bd7aa199378816cf1fb9ff746eb4d815da, and 3.96366336% above #280. These are improvements in the conditional asymptotic exponent, not measured multiplication speed.

The cube-layer/twin/line-pair word is preserved exactly from the supplied archive. This package completes its source binding, bank allocation, rational frame and changed-projector charts, finite costs, and stronger complex-supplier admission:

• Freshly regenerate and fully replay PR249/source527 and PR256/PR233, retaining original source pins, licenses and notices.
• Prove 1,455 freed helpers absent from every record; independently check all original and compact physical F₂ columns, leaving 15,132 active helpers.
• Admit 3,473 new frames, 20,844 changed projector charts and 3,026,400 concrete role/replica/stage bank assignments. Exact width-120 packing gives normalized stock 162,123; retain conservative normalizer 787.
• Expand the PR233 supplier's coefficients through paid signed additions, with 40 exact recipe checks, and recompute scalar, scratch, splice, routing, precision and physical-row bounds.
• Check the complete finite invoice, exact fixed-prime fallback, two rational moment engines, eight positive-gap ordinary levels and all 47 strict assembly inequalities. The adjacent 10^-27 grid point is rejected.

Reproduce offline with Python 3.11+, C++17 and Boost:

python -m pip install -r research/w3-bitword/requirements.txt
python -B research/w3-bitword/verify.py --output /tmp/w3-proof

Every prerequisite and extension stage runs fresh; no saved PASS receipt substitutes for execution. The full local replay passed in 297 seconds. Package hashes are checked before and after execution. The full final committed package also passed a fresh Linux/Python 3.11/g++ replay in GitHub Actions, including its final manifest and both prerequisite source verifiers.

The claim remains conditional on the inherited all-size compiler, common weighted charts, restored rows, selectors, routing, prime supply, complex dirty lifting, precision/recovery and analytic transfer interfaces. This is not a new Lean certificate, an unconditional multiplication theorem or a practical speed benchmark. See README.md, PROOF.md, SOURCE.json and NOTICE.md for the exact boundary and provenance. Prepared with substantial OpenAI Codex assistance.

[Mister-Meeseeks]

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

Contribution: Design-T w3 bit word with native finite admission.

Review and limits: Source-bound emitted word and full finite checks; inherited compiler, routing, prime and analytic hypotheses remain conditional.

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: 484b85f1d1fada27fda2ddab3ec952c1314d84c7. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.