κ = 1.018364819189613e-3: two joint gate-frame blocks with complete replay

[eumemic]

κ = 1.018364819189613e-3

Exact conditional κ: 1018364819189613 / 1000000000000000000. This improves frozen #423 by 5937864973 / 200000000000000000 > 0 (about 0.00292%). This is a separate branch and PR; all previously published heads and claims remain frozen. Concurrent #424 reports 0.001018509848057013 and the updated #422 reports 0.001018475695250068, both numerically higher. This submission improves the fully replayed #423 construction; it does not claim the highest reported number. #424 explicitly leaves changed phases, target-125 native invoicing and fused-slot ownership open.

Two groups of gates change frames together. A2078–2081 and B376 move from frame 483 to the rank-five basis [193,49,9,5,3]; A2141–2144 and B428 move from frame 502 to [273,144,80,48,15]. Every scalar instruction and its order stays fixed. The local paid profile changes by {1:-2, 2:+10, 3:-14, 4:+6}, preserving both the number of children and their total rank while improving the exact moment. The constructor checks all 1,021 raw and pre-snapshot columns and the retained snapshot labels.

The portable verifier reconstructs the complete #423 chain: 217 gauges, 391 entrance dimensions, 701 entrance instructions, the enlarged shared entrances, chronological target 124/125 recovery, #376's frame edit, #402's target resynthesis and the target 124/144 prefixes. It then applies the source-pinned block changes. The actual 6,996 nongauged dirty-response entries are recomputed into 7,097 signed unit macros. Both scalar orientations restore arbitrary dirty inputs and erase private work; both reflected scalar/frame ledgers, the chronological entrance controls and all 990 new/reflected Gaussian phase pairs pass. The 16 literal coefficient-word microchecks and 55 residual charts covering 28,160 address columns also pass.

The full architecture is rebuilt from the final word. Sixty-four replicas and 576 complete invocations use 5,857 width-73 banks per stage with 2,729 rank-one pads. Live stock is 114,153, physical stock 114,944, paid children 2,587,185, rank mass 8,313,201 and deficit 19,968. All 49,984 owner routes and 249,984 explicit bank-boundary adapters are charged. The actual scalar invoice remains 66,178,176 real primitives. The complete bank audit, finite invoice, reserve bridge, two rational moment engines and 47 strict outer inequalities pass. The exact complex coarse lower bound is 127425367910454002819 / 125000000000000000000000; the unchanged bit lower bound is 255384852701747 / 250000000000000000.

python -B research/e8-joint-block217-retiming/verify.py /absolute/path/to/new/output

The full development replay, independent audit and clean committed Git archive replay completed before publication. All committed package blobs were checked against the final manifest. Python 3.11+ and C++17 are required; dedicated Linux CI covers Python 3.11 and 3.14. The default replay explicitly reuses source-bound evidence for the unchanged bit component and previously verified phase edges. Optional --replay-bit freshly repeats the bundled bit component. Historical proof documents retain their provenance banners.

This remains 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 lowered to explicit paid primitives. No unchanged legacy gx/gxcore E4/E5 acceptance, Lean certificate, global optimality or unconditional multiplication theorem is claimed.

Provenance: frozen #423 (997613cb3064b4096b996409a671e558251d55f8) and its #421/#420/#416/#414/#411/#410/#408 lineage; Dugongue #404; Chafik Boukhalfa/Anthropic Claude #402; applecrusher #376; Rohan Arun #409's grouped-entrance inspiration; and all retained E8, bit, compiler and analytic contributors. The block search, source-pinned constructor, integration and independent audits were prepared for eumemic with substantial OpenAI Codex assistance. Original licenses, contributor notices and AI disclosures are preserved.

[Mister-Meeseeks]

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

Contribution: Two joint gate-frame blocks on the enlarged word.

Review and limits: Scalar instructions stay fixed, but the reflected ledgers and complete charged moment must be recomputed. Native chronological/dyadic conditions remain distinct from legacy gx acceptance.

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: 360d1b182a5f098619d435339d060d9b0cd9f469. Publication: 64039f1bd3b6a523b96083fd858ad040a75e3030.