κ = 1.017562145187818e-3: enlarged entrance spaces with sequential donor promotion

[eumemic]

κ = 1.017562145187818e-3

Exact conditional κ: 508781072593909 / 500000000000000000. This improves frozen #408 (0.001017022657082799) and concurrent #409 (0.001017250500928266). It is a new branch and new PR; previously published heads and claims remain frozen.

Eight entrance subspaces in #408's 205-pivot selection are enlarged, raising their total dimension from355 to363. Seven explicit elementary shears then promote donor760 to a new rank-one pivot. The completed word has206 gauges,364 entrance dimensions and652 entrance instructions. The chronological prefix permits a donor to become a pivot; the exact full raw operator and distinct dirty-input chart tokens are checked rather than assuming all entrance shears commute. An independently computed prefix/suffix formula certifies a nonzero gauged-input leak for omission of every entrance instruction.

The complete construction retains Dugongue's #404 overlapping target124/125 recovery, applecrusher's #376 target201 frame edit and Chafik Boukhalfa's #402 target177/220 resynthesis. Each step is freshly reconstructed and compared on all1,021 rational input columns. The #402 deliveries are relocated through the added entrance instructions and actual B chronology. Separate reported gains are not added.

Sixteen data replicas permit1,471 width73 banks per stage with743 rank-one pads. Across144 complete invocations, live stock28,599, physical stock29,390,644,031 paid children, rank mass2,082,735 and deficit4,992 are reconstructed. All59,328 boundary adapters and12,496 inverse owner routes are charged. The new invoice counts11,857,920 real scalar primitives, local bound7,998,149,307,350 and row15,447 <20,161; maximum child rank remains48.

Fresh verification passes arbitrary dirty restoration, complete private erasure, both reflected scalar/frame ledgers,836 new/reflected Gaussian phase pairs,43 residual charts and22,016 address columns,13 adverse bank controls, the complete finite invoice and reserve bridge, two exact rational moment engines and all47 strict outer inequalities. The exact complex coarse lower is 15915603634335785361 / 15625000000000000000000; the unchanged bit lower is 255384852701747 / 250000000000000000.

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

The complete original package replay and committed clean Git archive replay passed before publication. Every staged package blob was checked against the manifest. A dedicated Linux workflow covers Python3.11 and3.14; Python3.11+ and C++17 are required. Portable discovery sources and recorded logs are included; the fixed literal construction and exact replay establish correctness, not the heuristic search score.

The default offline replay explicitly reuses source-bound evidence for the unchanged bit component and old local phase edges; optional --replay-bit repeats the bundled bit component. Those reused checks are not represented as freshly replayed. Finite native admission uses the exact chronological target identity and generalized entrance-omission proof in place of old disjoint-role sufficient guards. This does not claim acceptance by unchanged legacy gx/gxcore or a Lean kernel.

This remains conditional on the inherited all-size compressed-window, arbitrary-correlated dirty-bank, recursive compiler, ordinary-call/fixed-tape/restored-row, common-grid, precision and analytic interfaces. It is not an unconditional multiplication theorem.

Provenance: frozen #408 (26332a3a4bed23484d5cde2c9d4f72b6de130a9b); Dugongue #404 (12f488264cdd74a3b60d0fb534f4955792384f5c) and #401; Chafik Boukhalfa/Anthropic Claude #402 (7883c63ec724999b921c2304b66648cbb9e7a112); applecrusher #376; the retained #398/#390/#396/#377/#381/compiler/analytic lineage and Jacob Sussman's E8 unit. Rohan Arun's concurrent #409 (212e03d7665d08fc6a037d3e33612cb7fc60874d) independently uses sequential donor promotions; we acknowledge it and claim no exclusive priority for that mechanism. The new enlargement, single-donor selection, packing, composition and 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: Enlarged entrances and sequential donor promotion.

Review and limits: Explicit acyclic chronological proof replaces a disjoint-entrance guard. Assess its native contract; do not claim unchanged gx/E4 acceptance or formalized all-size transfer.

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: 95ad14d5359d62a89e7bb06eb59b68029e77fb6f. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.