κ = 7.69556690340075e-4: four frame retimings after PR320 restoration

[eumemic]

κ = 7.69556690340075e-4

This conditional finite construction improves the independently replayed #320 snapshot 1b37957d1520c80b6ea796bf418e52be5109c2d4 from 769553898621543/10^18 to 30782267613603/40000000000000000. The exact gain is 2791718532/10^18; the bit supplier still binds.

Four kernel_setup ADD gates receive larger admissible frames after early restoration and before terminal sink removal: three ranks 8→9 and one rank 13→14. Their exact local paid-profile change is {1:+12, 2:-8, 8:-3, 9:+3, 13:-1, 14:+1}. This preserves rank mass while improving the complete moment bound. The stage preserves its scalar/COPY projection and all input/output frames, including the 240 restored helper endpoints. The subsequent seven sinks and 133 reorder moves are reselected and fully replayed on the changed word; the final scalar ordering is separately verified.

The self-contained package is research/p10-presink-retiming/. It includes an immutable archive of the exact #320 source, explicit four-frame witnesses, complete paid profiles, both reflected ledgers, endpoint banks, scalar restoration checks, determinant/prime witnesses, both rational moment engines, all 47 assembly inequalities and finite invoices. A dedicated CI workflow repeats the strict offline verifier:

python -m pip install -r research/p10-presink-retiming/requirements.txt
python -B research/p10-presink-retiming/verify.py --output /tmp/p10-presink-proof

Validation: two fresh complete immutable replays, plus a separate C++ audit of the literal final word. The latter checks both F₂ directions, dirty restoration, reflected and required paid ledgers, and the complete 60-replica tiling. The final word has 386,909 records, 336,253 scalar ADDs, 8,223 dirty helpers, 85,578 banks per stage and literal stock 658,290. Omitting the early restoration operations makes 240 rows fail. Exact bit root: 770149364272199/10^18; unchanged complex supplier: 772714351296671/10^18.

This is a conditional finite construction, retaining the all-size compiler, weighted-selector, common-chart, restored-row, routing, prime-supply, recovery, complex-symbolic and analytic interfaces. The finite checks do not establish those inherited hypotheses.

Provenance: builds on DreamingOfClouds' #315 p=10 word, Chafik Boukhalfa's #320 stage stack and shared-donor closure, the earlier transcript methods including Rohan Arun's concave descent, and the prior source527/five-stage lineage. Original attribution and Anthropic Claude disclosures remain in the package. The new selection, restored-endpoint adaptation, packaging and audits were prepared with substantial OpenAI Codex assistance, under Apache-2.0.

This is a new branch and new PR. Previously published heads and claims remain frozen.

[Mister-Meeseeks]

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

Contribution: Four frame retimings before p10 terminal sinks.

Review and limits: Restored endpoints and subsequent sink/reorder selections are rechecked, rather than assuming unchanged scalar instructions imply unchanged cost.

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: 8ce22e5e487e9d1017c26702adc09d5646565d0c. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.