κ = 1.017022657082799e-3: 205 shared-donor gauges with 64-replica banks

[eumemic]

κ = 1.017022657082799e-3

Exact conditional κ: 1017022657082799 / 1000000000000000000. This new branch and PR improve #406/#404; all previously published heads and claims remain frozen.

This extends Dugongue's #404 shared-donor construction from 194 to 205 pivots by reoptimizing three existing nested rank-one entrance groups, then repacks the complete residual program over 64 replicas. It retains the #404 chronological target124/125 recovery and credited #376 target201 frame edit, and relocates Chafik Boukhalfa's #402 target177/220 resynthesis through the 405 added entrance instructions. The package checks the complete combined word; separate gains are not added.

The fresh verifier passed all 1,021 raw columns, arbitrary dirty helper and target inputs, both scalar orientations and reflected frame ledgers, 816 new/reflected Gaussian phase pairs, 37 residual charts and 18,944 address columns, 49,984 owner routes, and 13 adverse bank controls. The local paid profile, finite invoice, reserve bridge, two exact moment engines and 47 strict outer inequalities are regenerated from the emitted word.

There are 205 gauged helpers, 645 entrance gates, 355 entrance dimension, 5,893 width-73 banks per stage and 3,053 rank-one pads. Live stock is 114,477, physical stock 115,268, rank mass 8,336,853 and deficit 19,968. The complete assembly has 2,569,941 paid child calls, maximum child rank 48, local bound 7,984,248,503,128 and required row 15,451 < 20,161. The exact complex coarse lower is 254514511295243586371 / 250000000000000000000000; the unchanged bit lower is 255384852701747 / 250000000000000000.

python -B research/e8-shared-donor-205-bank64/verify.py /absolute/path/to/new/output

The committed clean archive replay passed with exit 0. The default replay reuses only the explicitly pinned unchanged bit and old phase receipts; --replay-bit optionally reruns the bit component. This remains a finite conditional construction under inherited all-size, dirty-bank, compiler, fixed-tape, restored-row, precision and analytic interfaces; it is not an unconditional theorem or Lean certificate.

Credits: Dugongue's #404 (12f488264cdd74a3b60d0fb534f4955792384f5c) and #401; Chafik Boukhalfa/Anthropic Claude's #402 (7883c63ec724999b921c2304b66648cbb9e7a112); applecrusher's #376 frame edit; #398/#390/#396/#377 lineage; Jacob Sussman's E8 unit; and concurrent rohanarun #406 (5d0d8dff39db99f922ead6d11963aa643511e3ee). The 205 selection, packing, integration and audits were prepared for eumemic with substantial OpenAI Codex assistance. Original licenses, notices and AI disclosures are retained.

[Mister-Meeseeks]

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

Contribution: 205 shared-donor gauges with 64-replica banks.

Review and limits: Native finite contract with complete dirty response and phase/bank checks. The legacy gx rejection recorded by PR412 concerns a different interface; neither claim is silently substituted for the other.

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: 26332a3a4bed23484d5cde2c9d4f72b6de130a9b. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.