Conditional κ = 0.001696247139058474: capped phase-cell fusion outer (PR1673) on the T74 supplier with anticipatory dirty borrowing (PR2226, 43 high-helper aliases) on the T74 pivot-566+554 supplier: conditional kappa 0.0016962471390584742…

[jeremykothe2]

Summary

Conditional κ = 0.0016962471390584742207696225394800943861…(136 digits). Adds the exact helper-donor kernel borrow43 (pivot None, found by Cinna Davis (1337isnot1337), PR2226 anticipatory dirty borrowing; 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, with certified 1e-90 complex endpoints (accept at the endpoint, reject at endpoint + 1e-90), grid_digits 85, margin_digits 95, bootstrap_steps 39, and the PR1956 carried bootstrap cutoffs and PR1964 Lemma G label stage retained. Conditional final kappa = 0.0016962471390584742207696225394800943861…(136 digits) (supplier strict-assembly kappa 0.0016933747569716072928255508000300979096…(85 digits)). It exceeds the live leader PR2265 by +1.28346E-5.

Verification

Fresh checkout of b479fc5567bc09ab9185bffe89b62594f36d74e5. Manifest: 84996cc11a6b6946e8f5b1d65050fe8842ae02d8b4d4e0f6c8915d14d20b59ef.
PASS package manifest: 417 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 212030892382309277596202817435... brackets the ledger's b = 1696247139058474220769622539480094386128…(98 digits)/1000000000000000000000000000000000000000…(101 digits). Outer (PR1673 capped phase-cell fusion): regenerated exact ledger (62 strict inequalities, 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…(136 digits) (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=1-2e-100, outer/FINE-PADDING-COMPOSITION.md).

Full package-owned verification passed in 248.22 seconds. The fresh receipt binds the exact package manifest and score.

See research/gmx-t74-borrow43/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). 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). 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).

[Mister-Meeseeks]

Maintainer review update at b479fc5567bc09ab9185bffe89b62594f36d74e5: we have integrated Sagar Thakrar's independent audit in #2315, after replaying both borrowed words in both orientations, the 291,042-row helper fill, and the independent moment calculation. That audit reproduces these finite components and retains credit for Jeremy Kothe, Cinna Davis, Dugongue and the predecessor lineage.

This is not yet admission of the proposed supplier or outer κ. The remaining review checklist is now explicit:

• Bind fresh borrowed-supplier admission evidence to the current words and OWNERS; several shipped receipts still describe the pre-borrow supplier.
• Account for the 76 cleanup zero buffers in the physical implementation. The audit's dedicated-family sensitivity calculation preserves the stated stock-bit/row bounds, but it does not supply the allocation implementation.
• Establish X2 pending-axis disjointness and the 73-column charts for this fill, beyond the verified windows and per-child slice disjointness.
• Complete review of the native Clifford lifts/phases and the inherited outer/assembly implications. The moment-to-κ arithmetic alone does not establish these.

The integrated audit and its explicit exclusions are at research/t74-borrow43-independent-check/; maintainer replay evidence is in research/community-efficient1300-audit/. Leaving this PR open while those obligations are resolved. No mathematical rejection is inferred from the outstanding review.