κ = 1.018335129864748e-3: fourteen entrance enlargements with shared frame costs

[eumemic]

κ = 1.018335129864748e-3

Exact conditional κ: 254583782466187 / 250000000000000000. This improves frozen #421 by 55661995487 / 125000000000000000 > 0, exceeds #419's reported value by 372724567903 / 1000000000000000000, and exceeds #422's reported value by 365754878021 / 1000000000000000000. This is a new branch and new PR; all previously published heads and claims remain frozen.

Fourteen existing entrance spaces gain one dimension. Twelve expansions fit their exact backward frame capacities, including the retained-snapshot and final-endpoint constraints. Eleven rank-one entrances become rank-two, and helper 941 grows from rank four to five. Helpers 914 and 960 then enlarge jointly from [60] to [48,12]: the two changes share five instruction-frame costs, making the pair profitable although each single-step discovery score loses. No scalar instruction is added or altered by these enlargements. The construction retains 217 gauges and 701 entrance instructions, while total entrance dimension rises from 377 to 391.

The constructor rebuilds the complete word through #421, propagates all necessary frame constraints, then rebuilds #404's chronological target 124/125 recovery, #376's target 201 frame edit, #402's target 177/220 resynthesis and the exact target 124/144 prefix recipe. Both A and B scalar groups equal the pinned #421 candidate. All 29 changed A/B frames are individually reverted and rejected; twelve original-A frame controls and the entrance-omission control also reject. Both full-word and retained-snapshot operators are checked on all 1,021 columns. The actual 6,996 nongauged response entries and 7,097 signed unit macros are recomputed.

Complete finite replay checks both scalar orientations, arbitrary dirty restoration, private erasure, both reflected scalar/frame ledgers, the chronological entrance certificate and target-only bracket, 968 new/reflected Gaussian phase pairs, 55 residual charts and 28,160 address columns. Six response controls, 13 bank controls and 16 literal signed coefficient-word microchecks pass. Quarter/eighth coefficients use explicit paid copy, halving, accumulation and clearing streams; the result does not claim unchanged legacy gx/gxcore E4/E5 acceptance.

The residual inventory is taken directly from the final word, not from additive search scores. Sixty-four replicas and 576 complete invocations use 5,857 width-73 banks per stage and 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 inverse owner routes and 249,984 explicit bank-boundary adapters are paid. The fresh invoice counts 66,178,176 real scalar primitives, local bound 9,504,208,100,088 and row 15,451 < 20,161. Independent decoding verifies the full owner schedule, padding, paid profile and invoice. The reserve bridge, two rational moment engines and all 47 strict outer inequalities pass. Exact complex coarse lower: 509686596699014261497 / 500000000000000000000000; unchanged bit lower: 255384852701747 / 250000000000000000.

python -B research/e8-grouped217-entrance-enlargement/verify.py /absolute/path/to/new/output

The complete development replay and clean committed Git archive replay passed before publication. Every committed package blob was checked against 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 described as freshly executed. Historical proof-stage documents carry banners directing readers to the current root proof and validation.

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. The native chronological and dyadic conditions extend earlier sufficient guards; no Lean certificate or unconditional multiplication theorem is claimed. Concurrent #419 and #422 retain their own stated changed-phase and assembly/invoice obligations; numerical comparison does not certify those constructions.

Provenance: frozen #421 (6dfe3f978e2fcf3701523bda73744d56a1f8ac6f), #420, #416, #414, #411, #410 and #408; Dugongue #404 (12f488264cdd74a3b60d0fb534f4955792384f5c); Chafik Boukhalfa/Anthropic Claude #402 (7883c63ec724999b921c2304b66648cbb9e7a112); applecrusher #376; Rohan Arun #409 as inspiration for grouped entrance search; and all retained E8, bit, compiler and analytic lineage. Concurrent #412/#413/#415/#418/#419/#422 were read as comparison claims; no implementation was imported from them. The backward-capacity search, joint enlargement, exact integration 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: Joint enlargement of fourteen entrance spaces.

Review and limits: Native chronological and paid-dyadic contract; not unchanged legacy gx E4/E5 acceptance. Unchanged bit and old phase receipts are explicitly reused.

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: 997613cb3064b4096b996409a671e558251d55f8. Publication: 64039f1bd3b6a523b96083fd858ad040a75e3030.