[jeremykothe2]

Summary

Conditional κ = 0.0016797549561255445213356709939207025769…(198 digits)… (60046 decimals; the exact value is kappa in research/capped-fusion-t74-k554/outer/OUTER-CLAIM.json, SHA-256 of the decimal string c720731ea885a24e6f5edd00d17097654d592eac07a9854d4735a55cc95f9478). Capped phase-cell fusion outer (PR1673, Vlado Vojdanovski) on this repository's T74 supplier (pivot-566 and pivot-554 helper-donor kernels, certified complex endpoint 0.0016797549561255445213356709939207025769983114...), free strict slacks at 1e-60080 or below, with fine source-prime padding (PR1786, chafreaky / Chafik Boukhalfa, via Tim Trudgian's prime theorem; vendored) which makes the grouped chirp guard beta + 2 xi - 2 < 1, the fractional-shift gauge-free interiors with accretive shallow circuits (PR1758, outer/GAUGEFREE-INTERIORS.md), the radix-distributed union schedule with per-visit tag work, and the explicit Strassen boundary. New here: epsilon is a free parameter of the PR1786 ledger (every row holds for every 1-epsilon > 1e-60080), so the explicit point is epsilon = 1 - 1.0009765625e-60080, beta = 1 - 3.0029296875e-60080, giving kappa = 0.00167975495612554452133567099392070257..., 1.68e-60083 below the supplier's complex saving q, hence the ceiling of any outer of this form (outer/FINE-PADDING-COMPOSITION.md). 62 strict inequalities, 17 rejecting controls, an independent balance derivation with an epsilon sweep, PR1786's finite prime/underflow controls and the gauge-free identity checks are regenerated; the supplier's full native admission is rerun. Conditional, with all inherited all-size hypotheses and the cited prime theorem; the fine-padding lemmas (PR1786 is a draft) and the composition need independent review; asymptotic margins are 1.0009765625e-60080. Endpoint recertification: native and conservative complex endpoints refined to 1e-60000 (accept at endpoint, reject at endpoint + 1e-60000) with the repaired fine engines evaluated in directed-rounding integer fixed point; Retuned to the fixed-grid maximum of PR2180 / PR2161 (dataisfire): kappa = C - 1/F - B exactly (floor grid 1e-60046, backoff 1e-60022, C the certified endpoint; outer/PROOF-GRID-MAX.md); kappa exceeds PR2180 by 1.01065E-30002 and this package's previous 1e-60010-slack point by 2.00336E-60010 (63 strict inequalities: the 62 retained ones plus the explicit main-binding row gaussian_above_main, 17 rejecting controls). The single 60000-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 fc09a70baf7d6bcff935df226f6fc9e6c6c0131d. Manifest: 9b4779dc24b3b6f0c30b577830d4ddec3848136f8deed709ee7017652c45b730.
PASS package manifest: 387 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 839877478062772260667835496960... brackets the ledger's b = 1679754956125544521335670993920702576998…(55544 digits)

…(truncated to GitHub's body limit; see the package README and RELEASE.json)

Also credited: PR1964 (Sagar Thakrar / thakrarsagar) for the extended-label (Lemma G H1) stage used by this package.