κ = 1.136403735815528e-3: R740 shared-donor kernel with 57 primitive frame changes

[eumemic]

κ = 1.136403735815528e-3 = 142050466976941/125000000000000000

This conditional construction combines a new shared-donor kernel on the frozen R740 bit word from #436 with 57 changes to individual A-phase gate frames. The literal scalar ADD sequence is unchanged by retiming. It exceeds the latest reported #434 claim of 0.001134387517668085 (head f5e0af60ae91e39528d63782ac06f4c6f0e956e3) by 0.17774%, #439 by 0.21833%, and #438 by 0.25544%. The complex supplier remains #433, with its construction and every selected Gaussian phase replayed here.

The kernel uses 112 pivots, 100 donor slots and total entrance rank 136. Eight replicas tile the residual widths into 723 width-64 banks per stage. All 15 entrance frames have explicit residual isometries; their elementary coordinate permutations are checked, bound to each owner, and charged in the finite invoice. Live/physical stock is 14,187/14,196, with rank deficit 2,496.

The final canonical word SHA256 is bae58f0692326f180ba49642360fd55557f59a93a96a8fa62bf7babd55d2384e. Its complete local paid profile is {1:2500, 2:990, 3:326, 4:389, 5:90, 8:9}. Both orientations restore all 980 formal columns, including arbitrary dirt in 740 helpers; both reflected ledgers and integer source spans are checked. The complete global replay covers 7,620 scalar columns, 53,280 helper assignments and all 72 local invocations.

The exact bit lower endpoint is 0.001137696618503020372244; the replayed complex lower endpoint is 0.001183986549206329. Two rational moment engines, an independent third calculation, six finite bootstrap levels and all 47 strict outer inequalities verify the stated exponent. The adjacent 10^-18 grid point and corrupt route witnesses are rejected.

Reproduce with Python's standard library:

python3 -B research/r740-shared-donor-kernel/verify.py /tmp/r740-kernel-proof --replay-phases

The initial uninterrupted full replay passed on Python 3.12.13. The exact committed archive bd03373b6d4d4e380d0b6ea7d55cd2ac8f163544 also completed all 15 steps with exit 0 on Python 3.14.7. The independent audit receipts match exactly; all 93 package files match their committed blobs and manifest 0c27346bb5a784e24ceaf3888c710d7947deba2e2cac7e8649af44f83611637b. A dedicated workflow repeats the full check on Python 3.12 and 3.14; remote CI is pending when this PR is opened. Previously published PR heads and claims remain frozen.

This is a finite conditional witness. The inherited all-size compiler, correlated dirty-bank, compressed-window, restored-work, tape/common-grid, precision and analytic interfaces remain assumptions. No unconditional multiplication theorem or new Lean proof is claimed.

Attribution and original licenses/disclosures are preserved in NOTICE.md, SOURCES.json, notices/ and vendor/: eumemic's #436 R740 producer/reuse word (with Anthropic Claude assistance); chafreaky's #417 kernel mechanism and #439 explicit residual-route checks; Rohan Arun's #435/#438 mixed-width admission and #434 primitive-retiming composition; icekylinx's #433 split centres and assembly; the retained #426/#389/#376/#370, #425/#386 and earlier Jacob Sussman/compiler/analytic contributions. The new selection, 57-frame retiming, integration and independent audits were prepared for eumemic with substantial OpenAI Codex assistance.

[Mister-Meeseeks]

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

Contribution: Shared-donor kernel and 57 primitive frame changes.

Review and limits: Unchanged scalar order does not imply unchanged cost. Both reflected ledgers, residual charts and the fresh finite invoice are retained.

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: bd03373b6d4d4e380d0b6ea7d55cd2ac8f163544. Publication: 64039f1bd3b6a523b96083fd858ad040a75e3030.