[jeremykothe2]

Summary

Conditional κ = 0.0016962471390584742207696225394800943861…(198 digits)… (3046 decimals; the exact value is kappa in research/gmx-t74-borrow43-gridmax/outer/OUTER-CLAIM.json, SHA-256 of the decimal string 38e17c60ee1283e3c703578be8c36798620544620839a440942fa79bbe61efab). Adds the exact helper-donor kernel borrow43 (PR2226 anticipatory dirty borrowing of Cinna Davis (1337isnot1337), adapted to the T74 words) to the previous record's T74 local words (re-solved frames, fresh natives, PLAN rebound, SPEC refrozen) under the PR1673 capped phase-cell fusion outer. The supplier native and conservative complex endpoints are certified to 1e-3000 (accept at the endpoint, reject at endpoint + 1e-3000), grid_digits 2995, margin_digits 3005, bootstrap_steps 1116, and the PR1956 carried bootstrap cutoffs and PR1964 Lemma G label stage are retained. Conditional final kappa = 0.0016962471390584742207696225394800943861…(60 digits)…(3046 decimals) (supplier strict-assembly kappa 0.0016933747569716072928255508000300979096…(60 digits)…(2995 decimals)). Retuned to the fixed-grid maximum of PR2180 / PR2161 (dataisfire): kappa = C - 1/F - B exactly (floor grid 1e-3046, backoff 1e-3022, C the certified endpoint; outer/PROOF-GRID-MAX.md). It exceeds PR2269 (this package's 90-digit-endpoint predecessor) by 5.37679E-91 and PR2265 by 1.28346E-5 (63 strict inequalities: the 62 retained ones plus the explicit main-binding row gaussian_above_main, 17 rejecting controls). The single 3000-digit rejection moment of the strict assembly uses PR2168's exact-integer coarse exponential (code/exact_coarse.py, EXACT-ARITHMETIC-DERIVATION.json; intervals identical to the retained engine).

Verification

Fresh checkout of 9c71e6194841d7355efa343b7cd5646359fad364. Manifest: 67a0905473a154424ea0cc2a29d764b2a578fc70ba4715d9b97ce126b7d6f01e.
PASS package manifest: 420 files

Supplier: the package's own unchanged verify.py (retained PR1297 provider and parent admission, owner reconstruction, parent lift, strict T74 admission, geometry controls): PASS_T74_EXACT_FILL_COMPLETE_FINITE_ADMISSION, native reuse {'base': 'e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e', 'extra': '7b0e9fbda32749aabc7e156d9fe09bceb0624a178628fe69e5dfea783462f905'}; its complex endpoint 424061784764618555192405634870... brackets the ledger's b = 1696247139058474220769622539480094386128…(3078 digits)/1000000000000000000000000000000000000000…(3081 digits). Outer (PR1673 capped phase-cell fusion): regenerated exact ledger (63 strict inequalities: the 62 retained rows plus the explicit main-binding row gaussian_above_main, the fixed-grid maximum kappa = C - 1/F - B asserted, 17 rejecting controls incl. the old g-factor union row, the old linear and old-theta chirp guards, the old 2*beta tag test, epsilon at 1 or at the r0 slack and beta outside its window, larger endpoint rejected by the native moment), independent balance derivation, the exact union-schedule simulation, the (retained, not used for kappa) structured-boundary displacement-rank check, the gauge-free identity/symbol/circuit checks, PR1786's finite prime/underflow controls and 19 exact evidence replays all pass. Conditional kappa 0.0016962471390584742207696225394800943861…(60 digits)…(3046 decimals) (union schedule outer/UNION-SCHEDULE.md; explicit Strassen boundary tau=45/16 (the structured boundary of outer/STRUCTURED-BOUNDARY.md is not used); gauge-free interiors outer/GAUGEFREE-INTERIORS.md; fine source-prime padding PR1786 at the free point epsilon=1-(1025/1024)e-3080, outer/FINE-PADDING-COMPOSITION.md; fixed-grid maximum of PR2180/PR2161 (dataisfire), outer/PROOF-GRID-MAX.md; exact-integer coarse exponential PR2168/PR2184 (dataisfire) at the one 3000-digit rejection call).

Full package-owned verification passed in 111.97 seconds. The fresh receipt binds the exact package manifest and score.

See research/gmx-t74-borrow43-gridmax/README.md for reproduction commands and proof qualifications.

Credits

PR2226 (Cinna Davis / 1337isnot1337 with OpenAI Codex): anticipatory dirty borrowing, the alias rule, K_G handoffs and the exact free-operator replay (vendored under new/code/borrow/vendor). PR1786 (chafreaky / Chafik Boukhalfa): fine source-prime padding, its proof and checks, vendored under vendor/pr1786; Tim Trudgian: effective prime number theorem (arXiv:1401.2689). PR1673 (Vlado Vojdanovski, with AI assistance): capped phase-cell fusion outer construction, its proof and exact evidence, vendored under vendor/pr1673. PR1758 (IdeaOuter and contributors): fractional-shift gauge-free interiors, accretive shallow-circuit lemma, per-visit tag accounting. Jeremy Kothe and contributors (PR1731 ledger lineage, radix-union schedule), LeverRank (independent schedule simulation), Gohberg, Semencul, Kailath, Kung, Morf, Bitmead, Anderson, Pan (structured Toeplitz-like algorithms of the retained alternative), Francois Le Gall et al. and Chafik Boukhalfa (PR1699). Supplier: PR1625 (mdumitrean), PR1661 (midhatn), pivot-554 kernel (PR1672 lineage) and the PR1319/PR1297/PR1274/PR1286 lineage as in earlier packages. PR1956 (Josie Elliston: the bootstrap-cutoff carry finding and repair), PR1897 (M6LI), PR1876, PR1875 and PR1828 (rohanarun): the endpoint and slack refinements that this package exceeds; rohanarun also PR1319 and PR1297; chafreaky PR1786; Vlado Vojdanovski PR1673; mdumitrean PR1625; midhatn; philippeVV PR1519 (odd-term Mercator finding); Kothe and the existing lineage. PR1964 (thakrarsagar / Sagar Thakrar): Lemma G label and adapter-rule checks and the X/Y/Z adapter mutants (code/lemmag_checks.py), Lemma G by DreamingOfClouds (PR509 / PR516). PR2161 / PR2180 (dataisfire, OpenAI Codex-assisted): the fixed-grid maximum point and its proof, re-derived at this endpoint; PR2044 (Kothe) free-epsilon refinement they stack on; PR1786 (chafreaky / Chafik Boukhalfa) and PR1673 (Vlado Vojdanovski) ledger formulas. PR2168 / PR2184 (dataisfire): exact-integer coarse exponential and its one-site derivation. PR2269 and PR2265 are the records exceeded.