κ = 1.138798055343319e-3: R740 block retiming after shared-donor kernel

[eumemic]

κ = 1.138798055343319e-3 = 1138798055343319/1000000000000000000

This conditional construction improves frozen PR #440's κ by 0.21069% through joint frame changes on neighboring primitive B-phase ADDs. Individual-gate descent had reached a local optimum; moving compatible groups together permits a better complete paid profile while preserving every scalar ADD, operand and its order.

The construction reproduces the R740 word from #436, applies the 112-pivot shared-donor kernel and 57 A-phase changes published in #440, then applies two deterministic B-phase stages: 112 changes from paired gates and 42 further changes from larger windows. Because the stages overlap, there are 126 net changed B frames relative to #440. Every frame remains in the same 944-frame family.

The final canonical word SHA256 is 00d8aa8608e40b53fd8752399de06cb730cc55caaadc528f88379cb31b8460a6. The complete local paid profile is {1:2528, 2:1004, 3:284, 4:347, 5:118, 7:14, 8:9}. The 740 helpers retain total entrance rank 136, 723 banks per stage, 14,187 live families and rank deficit 2,496. All 15 explicit residual isometries and their elementary routing costs are checked again.

The bit lower endpoint is 0.001140096394900736521536; #433's complex lower endpoint remains 0.001183986549206329. Verification reconstructs both suppliers, replays all 2,918 complex Gaussian phase edges, checks all 980 local columns with arbitrary dirty restoration, both reflected ledgers, 7,620 global scalar columns, 53,280 helper assignments, complete paid profiles and finite invoices. Two rational moment engines and an independent third calculation support six finite bootstrap levels and all 47 strict outer inequalities; the adjacent 10^-18 grid point and corrupted witnesses are rejected.

python3 -B research/r740-block-retimed-kernel/verify.py /tmp/r740-block-kernel-proof --replay-phases

The initial complete replay passed on Python 3.12.13. The exact committed archive 6160c13526f5f957902910b462164c93c1d8f39a completed all 15 steps with exit 0 on Python 3.14.7; the independent audit matched the Python 3.12 result. The release manifest is bb78de6b1aca67601456fe9701d4bea70b09ba4b3ddef1373822076a35478634. A dedicated workflow covers both versions; remote CI is pending at creation. This is a new branch and new PR; #440 and all earlier published heads and claims remain frozen.

This remains a finite conditional witness under the inherited all-size compiler, correlated dirty-bank, compressed-window, restored-work, tape/common-grid, precision and analytic interfaces. It does not assert an unconditional multiplication theorem or a new Lean proof.

This joint-frame search, deterministic witnesses, integration and independent audits were prepared for eumemic with substantial OpenAI Codex assistance. Source-specific licenses, hashes and AI disclosures remain in NOTICE.md, SOURCES.json, notices/ and vendor/: eumemic #436/#440; chafreaky #417 kernel mechanism and #439 residual routes; Rohan Arun #434 primitive-retiming inspiration and #435/#438 mixed banks; icekylinx #433; Zhihao Chen #425/#386; Dylan Crow #370; ai-nanachi #426, applecrusher #376, Jacob Sussman and the retained compiler/analytic contributors.

[Mister-Meeseeks]

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

Contribution: Joint B-phase frame retiming after individual descent.

Review and limits: The combined final profile accounts for overlapping moves. Local search termination is not a global optimum; all-size interfaces 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: 6160c13526f5f957902910b462164c93c1d8f39a. Publication: 64039f1bd3b6a523b96083fd858ad040a75e3030.