[rohanarun]

Conditional κ = 160987957846297 / 200000000000000000 = 8.04939789231485e-4, improving frozen PR364's 8.04879370798932e-4 by 0.007506520200%.

The final Design T/min-cost-carrier word admits 123 coupled ADD-frame changes in 35 beneficial components: 71 dimension-13 frames become dimension 12, and 52 dimension-15 frames become dimension 14. Every signed scalar instruction and its order, register, COPY window, entrance and endpoint is preserved. The local paid-call count decreases by 17, with unchanged rank mass and helper stock. The E8 complex supplier is unchanged; the bit side still binds.

The package vendors PR364 at immutable commit f8c6a47abfec24b87cb1eb0a138dd73dfce2abe4, preserving its full manifests and notices. A source-bound selection, reconstruction, exact price, proof and dedicated Python 3.11/3.12 workflow are included. Candidate discovery used the prior campaign's free-form annealer and a bounded CP-SAT solve, followed by exact component reduction and compatibility checking; floating-point search scores are not certificate inputs.

Validation: the complete immutable PR364 replay and fresh final standalone replay passed locally. All 58 GitHub checks passed at head d3d84202e528d6e147a8ea62463ae5c0125997cf, including the dedicated full certificate replays on Python 3.11 and 3.12 (run). Checks cover exact signed-instruction identity, frame/source-span and dirty-helper restoration, nondegeneracy of all 53 new frames, native five-stage formal columns and negative controls, historical reconstruction, bank tiling, both rational pricing engines and all 47 strict outer inequalities. The adjacent κ tick is rejected.

python -m pip install -r research/w3-design-t-mc-coupled-retiming/requirements.txt
python -B research/w3-design-t-mc-coupled-retiming/verify.py /fresh/output

The compiler, common-chart, restored-row, selector/routing, prime-supply, precision/recovery and analytic-transfer interfaces remain inherited assumptions. This is a conditional finite-word improvement, not an unconditional integer-multiplication theorem, a global optimum, or a new Lean certificate.

Credit includes DreamingOfClouds, Chafik Boukhalfa, Jacob Sussman, the prior Rohan Arun research campaign and all contributors named in the retained notices. New selection, exact component reduction, integration and verification were prepared with substantial OpenAI Codex assistance. New contributions are Apache-2.0.

The three-file source-pin repair from PR318 (a45747d2559141a594916475f52642e4fab86e02) is included unchanged. Every pinned input matches current main. This addresses the inherited joint-dual CI failure without changing its mathematics.

[Mister-Meeseeks]

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

Contribution: Coupled bit-frame changes after weighted matching.

Review and limits: Retains complete staged transcript checks and exact pricing; the source's native bank/projector and all-size obligations remain distinct.

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: d3d84202e528d6e147a8ea62463ae5c0125997cf. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.