Conditional κ = 0.001697194950901770: exact owner fill on #2322's handoff construction

[jeremykothe2]

Summary

Conditional κ = 0.001697194950901770426594081877309541199782925447437522970580… (3046 decimals; the exact value is kappa in research/gmx-t74-borrow43-handoff/outer/OUTER-CLAIM.json, SHA-256 of the decimal string b14d377d6aa465aafd8d8f23953a210763744fbc7a538fd378f89c48704885be). This package refines PR2322's (Vlado Vojdanovski) construction; the owner-map line continues through PR2349 and PR2363 (mason-hale). The circuit change, the words, the call order and the windows are PR2322's, reproduced on the PR2312 supplier: four coherent helper handoffs replace four high roles by retired source registers (helpers 438 to 434, local profile {1:2335, 2:512, 3:426, 4:120, 5:38, 8:8}). PR2322 builds on PR2312 (anticipatory dirty borrowing of PR2226, Cinna Davis / 1337isnot1337, the width exchange, frame refit and pivot-518/506 kernels of Jeremy Kothe (jeremykothe2), with AI assistance). Our additions, by Jeremy Kothe (jeremykothe2), with AI assistance: (1) an exact window-free-optimal owner fill on PR2322's words, order and windows (every window, bin and family rule checked literally), with leftover idle ranks {1:21978, 3:8592, 5:2552, 32:1, 48:24560}, which raises the exact outer kappa beyond the earlier owner improvements PR2349 and PR2363 (mason-hale); (2) the private cleanup-buffer stock accounting, which PR2322 does not charge: 78 private zero buffers are charged as physical stock (66304 + 434 + 8 + 78 + 2 = 66826) with CLEAR charges, the warp routing reserve and the adapter bound, following PR2309 (Dugongue) and the audit PR2315 (thakrarsagar); (3) the supplier endpoints certified to 1e-3000 with the fixed-grid-maximum outer kappa C - 1/F - B (PR2180 / PR2161, dataisfire; exact-integer coarse exponential PR2168). Conditional final kappa = 0.0016971949509017704265940818773095411997…(3046 digits) (supplier strict-assembly kappa 0.0016943193606376810384632624188834507488…(2995 digits)). It exceeds PR2363's exact claimed kappa 0.001697147064845350 by 4.78861E-8 and PR2312 by 3.03884E-7. grid_digits 2995, margin_digits 3005, bootstrap_steps 1116; 63 strict inequalities, 17 rejecting controls; the PR1956 carried bootstrap cutoffs and PR1964 Lemma G label stage are retained.

Verification

Fresh checkout of 42669f5111e2e79a5796c7fa36e17ea81556f5c0 (text-only follow-up to fdd605d27b124d8f562368e14acd504182cf5728: README title line corrected; kappa unchanged; then text-only README follow-up correcting stated comparison figures per #2485; kappa unchanged). Manifest: bcd7f692061179fbf5d25772b21f115226eb62a8962639814f1994a6ba97f680.
PASS package manifest: 435 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 169719495090177042659408187730... brackets the ledger's b = 1697194950901770426594081877309541199782…(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 0.0016971949509017704265940818773095411997…(3046 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-(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 147 seconds on the new head (PASS_RELEASE, kappa identical to the previous head). The fresh receipt binds the exact package manifest and score.

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

Credits

PR2322 (Vlado Vojdanovski): the coherent four-helper handoffs, the words, call order, windows and the starting owner map, and the generator and checks this package builds on (new/borrow/inputs/handoff_43*.json, new/borrow-fill/). Jeremy Kothe (jeremykothe2), with AI assistance: the exact owner fill (new/borrow-fill/FILL.json.gz). PR2349 and PR2363 (mason-hale): the preceding owner improvements on this construction. PR2312 and the series it continues: anticipatory dirty borrowing PR2226 (Cinna Davis / 1337isnot1337 with OpenAI Codex); the width exchange, exact frame refit and pivot-518/506 kernels (the kernel shape of PR1625, mdumitrean) by Jeremy Kothe (jeremykothe2), with AI assistance. Added here: PR2309 (Dugongue) and PR2315 (thakrarsagar) for the private cleanup-buffer stock accounting; PR2301 (navinor / Aaron Wang) and PR1959 (Josie Elliston) for the pooled-slot time binding; PR2161 / PR2180 (dataisfire) fixed-grid maximum and PR2168 / PR2184 exact-integer coarse exponential; PR2286 (thakrarsagar) and philippeVV for the side-condition text corrections. 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. PR2309, PR2302 and PR2265 are the records exceeded. PR2286 (thakrarsagar) side-condition audit and philippeVV (PR1897 / PR2044 comments): the text defects (minimum-margin claim, xi aside, HALO K0^2 branch, p^10 umbrella, vacuous or-True guards, stale xi digits) corrected in outer/FINE-PADDING-COMPOSITION.md section 4, outer/check_ledger.py, outer/struct_check.py and outer/check_gaugefree.py. Jeremy Kothe (jeremykothe2), with AI assistance: change of the lender of alias 651 to 530 and dropping of alias 653, the exact owner fill for the new width inventory, the exact frame re-solve of both borrowed words and the exact kernel search and pricing, new work in this package (new/borrow/inputs/refit_43*.json, kernel_43*.json, new/borrow-fill/FILL.json.gz). PR1625 (mdumitrean): the helper-donor kernel shape reused here at pivots 518 and 506. PR2309 (Dugongue): concurrent independent work, a 44th dirty alias with owner repacking that also borrows from lender 530; the leader this package exceeds. PR2301 (navinor / Aaron Wang) and PR1959 (Josie Elliston): the unbound pooled-slot time field, bound in code/audit_allcold.py here. PR2315 (thakrarsagar): the audit finding that the private cleanup buffers must be charged. PR2309 (Dugongue): the private-stock accounting (physical stock, CLEAR charges, warp routing reserve, adapter bound, controls) ported here.

[thakrarsagar]

Independent check in #2442: your window-free-optimality claim holds, and more strongly. Over the bin-pattern integer relaxation of all legal whole-helper fills of #2322's words, your idle multiset is the unique optimum within 1e-12, and every fill has b ≤ your κ + 1e-15. The check uses an exact rational dual with 800-bit enclosures and exact enumeration. An adversarial reviewer also ran a Gomory group-relaxation check and local search, and could not refute it.