κ = 1.017812636706245e-3: one further chronological closure with exact target prefixes

[eumemic]

κ = 1.017812636706245e-3

Exact conditional κ: 203562527341249 / 200000000000000000. This improves frozen #416 by 1825176939 / 125000000000000000 > 0. This is a new branch and new PR; all earlier published heads and claims remain frozen.

One further entrance gauge is admitted at helper 672 in the rank-one space [48]. Its literal preparation is helper345 += helper672; helper673 -= helper672. A single existing A instruction involving helper 345 and center 504 moves from frame 47 to frame 305, [274,48], so its frame contains the new entrance space. The scalar instruction is unchanged. The complete construction has 215 gauges, 373 entrance dimensions and 699 entrance instructions.

This extends the frame-propagation construction of #416. All original A scalar groups are preserved; exact full-column and retained-snapshot operators, nested paths and both reflected ledgers are reconstructed. All six required frame reversions are rejected, an omitted new entrance leaks gauged dirt, and every chronological entrance omission witness is checked. The target 124/125 recovery, #376 target 201 frame edit, #402 target 177/220 resynthesis and target 124/144 donor prefixes are rebuilt on the resulting word. Nongauged response is freshly recomputed: 7,012 entries expand to 7,113 signed unit macros. Quarter/eighth coefficients are explicitly lowered and paid.

The new residual inventory uses 64 data replicas and 576 complete invocations, with 5,875 width-73 banks per stage and 2,891 rank-one pads. Live stock is 114,315, physical stock 115,106, paid children 2,580,003, rank mass 8,325,027 and deficit 19,968. All 247,680 boundary adapters and 49,984 inverse owner routes are charged. The finite invoice counts 66,238,080 real scalar primitives, local bound 9,502,548,302,688 and row 15,451 < 20,161.

Fresh verification passes all 1,021 scalar columns, arbitrary dirty restoration, private erasure, both reflected scalar/frame ledgers, 858 new/reflected exact Gaussian phase pairs, 43 residual charts and 22,016 address columns, six frame-reversion controls, six response controls, 13 bank controls, 16 coefficient-word microchecks, the complete paid profile and finite invoice, the reserve bridge, two rational moment engines and all 47 strict outer inequalities. Exact complex coarse lower: 25471240868484668881 / 25000000000000000000000; unchanged bit lower: 255384852701747 / 250000000000000000.

python -B research/e8-frameclosure215-target-prefixes/verify.py /absolute/path/to/new/output

The complete development replay and clean committed Git archive replay passed before publication. All 297 staged package blobs were compared with the manifest. Python 3.11+ and C++17 are required; dedicated Linux CI covers Python 3.11 and 3.14. The default replay explicitly reuses pinned evidence for the unchanged bit component and old local phase edges. Optional --replay-bit freshly repeats the bundled bit component; reused checks are not represented as freshly executed.

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. The native chronological and dyadic conditions extend older sufficient guards; no unchanged legacy gx/gxcore acceptance, Lean certificate or unconditional multiplication theorem is claimed.

Provenance: frozen #416 (c76d101df11ad4152c52fd9d68344c064e453d3a), #414, #411, #410 and #408; Dugongue #404 (12f488264cdd74a3b60d0fb534f4955792384f5c); Chafik Boukhalfa/Anthropic Claude #402 (7883c63ec724999b921c2304b66648cbb9e7a112); applecrusher #376; Rohan Arun #409 (212e03d7665d08fc6a037d3e33612cb7fc60874d) as inspiration for the preceding grouped ordered-entrance search; and the retained E8, bit, compiler and analytic lineage. Concurrent #412/#413/#415 were read as comparison claims; no implementation was imported from them. The new gauge, frame propagation, prefix relocation, 64-replica bank construction and complete audits were prepared for eumemic with substantial OpenAI Codex assistance. Original licenses, 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: One further chronological frame closure.

Review and limits: Native paid construction with 64-replica bank inventory and exact prefixes; source-bound unchanged bit reuse is explicit.

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: 079d514cdb40b2152ffa743853556b0117b98438. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.