κ = 1.018419742888184e-3: combined exact gate-frame retimings

[eumemic]

κ = 1.018419742888184e-3

Exact conditional κ: 127302467861023 / 125000000000000000. This is a new branch and PR and improves frozen #427 by 54923698571 / 1000000000000000000 > 0 and frozen #423 by 21153255859 / 250000000000000000 > 0. Previously published heads and claims remain frozen.

Starting from the fully replayed #423 word, this construction composes eleven individually verified frame retimings with the two joint block retimings from #427. All scalar instructions, scalar order and 217-gauge/391-dimensional entrance spaces remain fixed. The constructor checks all 1,021 raw and pre-snapshot columns, retained labels and the exact unchanged scalar word. The combined local profile is priced from the actual final word.

The complete verifier exits 0 after rebuilding both scalar orientations, arbitrary dirty restoration, private erasure, both reflected scalar/frame ledgers, 1,022 new/reflected Gaussian phase pairs, 55 residual frames and 28,160 address columns. The native controls reject all 50 changed frame labels, 20 original-A frame reversions and an omitted entrance gate. The actual 6,996 nongauged dirty-response entries expand into 7,097 signed unit macros; 16 literal coefficient-word microchecks pass.

The architecture is rebuilt from that final word: 2,580,849 paid children, rank mass 8,313,201, 49,984 owner routes, 5,857 banks per stage, 114,153 live stock, 114,944 physical stock and 19,968 deficit. The fresh scalar invoice contains 66,178,176 real primitives and 249,984 explicit bank-boundary adapters. Independent readback recomputes the full profile, routes, finite invoice, reserve bridge and all 47 strict outer inequalities. The exact complex coarse lower is 127302467861023/125000000000000000000000; the unchanged bit lower is 255384852701747/250000000000000000.

python -B research/e8-combined-retiming217/verify.py /absolute/path/to/new/output

The development replay, independent local/global audits and clean committed archive replay all exited 0. Every committed package blob is checked against its manifest. Python 3.11+ and C++17 are required. The default replay reuses source-bound evidence for the unchanged bit component and prior phase edges; optional --replay-bit freshly repeats the bundled bit component.

This is a finite conditional construction. Inherited all-size compressed-window, arbitrary-correlated dirty-bank, recursive compiler, ordinary-call/fixed-tape/restored-row, common-grid, precision and analytic interfaces remain assumptions. Quarter/eighth coefficients are explicit paid primitives. No unchanged legacy gx/gxcore E4/E5 acceptance, Lean certificate, global optimality or unconditional multiplication theorem is claimed.

Concurrent #424, #425 and #426 report numerically higher claims with different construction interfaces and their own stated scope. This PR records a fully replayed successor of #423/#427; it does not claim the highest numerical report. Provenance and contributor notices are preserved. The combined frame search, source-pinned construction, integration and 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: Composition of individual and joint gate-frame retimings.

Review and limits: One complete final profile is priced; independent reported gains are not added. The native contract and explicitly reused unchanged bit evidence retain their limits.

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: 700e057c910245e8a5ad2249d23831c9e45504b3. Publication: 64039f1bd3b6a523b96083fd858ad040a75e3030.