κ = 1.017629458064773e-3: exact target-prefix resynthesis on sequential206

[eumemic]

κ = 1.017629458064773e-3

Exact conditional κ: 1017629458064773 / 1000000000000000000. This improves frozen #410 by 13462575391 / 200000000000000000 > 0. The result has a new branch and PR; previously published heads and claims remain frozen.

Two target prefixes are resynthesized on the complete #410 word. Target 124 receives helper 563/2 at frame 336. Target 144 receives −helper 255/4 at frame 311, then −3 helper 777/8 − helper 808/4 at frame 935. Their protected input columns, helper cleanup, and chronological target-only operator are preserved. The nongauged dirty response changes, so the verifier recomputes all 7,058 response entries and 7,159 signed unit macros from the actual candidate. Stale response, wrong-sign response, and omitted-delivery controls fail in both orientations.

Quarter and eighth coefficients are explicitly lowered to paid copy, halving, accumulation and clear primitives. An independent exact microcheck covers all 16 bounded signed coefficients and rejects an omitted third halving. This extends the native scalar schedule; it does not claim acceptance by the unchanged legacy sixth-grid/gx E5 checker.

The complete local paid delta is {1: −1, 3: −1, 4: +1} per invocation, preserving rank mass. Across 144 invocations the profile has 643,887 paid children, rank mass 2,082,735 and deficit 4,992. The retained 206 gauges use 364 entrance dimensions and 652 entrance instructions. Sixteen replicas use 1,471 width-73 banks per stage, 743 rank-one pads, live stock 28,599 and physical stock 29,390. All 59,328 boundary adapters and 12,496 inverse owner routes remain charged.

Fresh verification covers all 1,021 scalar columns, arbitrary dirty restoration, private erasure, both reflected frame ledgers, 840 exact new/reflected Gaussian phase pairs, 43 residual charts and 22,016 address columns, chronological entrance omission controls, bank ownership and adverse mutation controls, the complete paid profile and finite invoice, the reserve bridge, two exact rational moment engines and all 47 strict outer inequalities. The larger explicit scalar invoice is charged: 16,530,144 real primitives, local bound 9,477,028,915,860 and row 15,447 < 20,161. Exact complex coarse lower: 7958328770925297313 / 7812500000000000000000; unchanged bit lower: 255384852701747 / 250000000000000000.

python -B research/e8-sequential206-target-prefixes/verify.py /absolute/path/to/new/output

The complete development replay and clean committed Git archive replay passed before publication. Every staged package blob was compared with its 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 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. No unchanged legacy gx/gxcore acceptance, Lean certificate or unconditional multiplication theorem is claimed.

Provenance: frozen #410 (95ad14d5359d62a89e7bb06eb59b68029e77fb6f) and #408; Dugongue's #404 (12f488264cdd74a3b60d0fb534f4955792384f5c), including shared-donor entrances and overlapping target 124/125 recovery; Chafik Boukhalfa/Anthropic Claude #402 (7883c63ec724999b921c2304b66648cbb9e7a112), whose target-window resynthesis method this prefix search adapts; applecrusher #376 frame edit; concurrent Rohan Arun #409 ordered entrances; the retained #398/#390/#396/#377/#381/compiler/analytic lineage and Jacob Sussman's E8 unit. The new prefix selection, dyadic lowering, response reconstruction and integration were prepared for eumemic with substantial OpenAI Codex assistance. All 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: Exact target-prefix resynthesis on sequential206.

Review and limits: Quarter/eighth coefficients are explicitly lowered and charged in its native bill. It does not claim the legacy sixths-only gx E5 contract.

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: f58d95f2c5da03445e704ea9c72cc55df9e68190. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.