Conditional κ = 0.0017177949841186346638272: #2802's construction with a 1e-3000 certified endpoint

[jeremykothe2]

Summary

Conditional κ = 0.001717794984118634663827229918428178904088584385462312200900… (3046 decimals; the exact value is kappa in research/gmx-t74-borrow43-handoff/outer/OUTER-CLAIM.json, SHA-256 of the decimal string 94b67ffa5832fb500a87936e1ac7b915eab03301cb73f014c29c3b4da9a3677d). This package is PR2802's (mdumitrean, Marius-Paul Dumitrean) construction, unchanged: seven retired-lender aliases (606<-550, 635<-551, 637<-552, 638<-553, 639<-562, 667<-401, 669<-403) and two hostee moves (401->564, 403->565) on PR2751's (tekuuu) twelve-alias words with PR2766's (DavidAriasC) frame refit; its words, owner fill, order and dispatch are PR2802's (local profile {1:2382, 2:648, 3:268, 4:128, 5:26, 8:8}, leftover idle {1:17316, 3:6594, 5:9878, 32:1, 48:26558}). Our contribution is only the finer endpoint certificate (the supplier endpoint certified to 1e-3000 and the fixed-grid-maximum outer kappa C - 1/F - B, as PR2767 did over PR2766) and the integration into our verifier: the construction as one declared patch stage retired7 with tamper controls, our guards and private-buffer accounting, PR2768's (tekuuu) exact sparse native replay as the default native stage, and a stale-bytecode guard after PR2788 (jeremydiviney). Prepared by Jeremy Kothe (jeremykothe2), with AI assistance. Conditional final kappa = 0.0017177949841186346638272299184281789040…(3046 digits) (supplier strict-assembly kappa 0.0017148492247218876758214032268877614551…(2995 digits)). It exceeds PR2802 (exact kappa_decimal from its claim) by 2.29918E-25 only through the finer endpoint grid; the construction gain is PR2802's (exact gate in verify_release.py). grid_digits 2995, margin_digits 3005, bootstrap_steps 1116; 63 strict inequalities, 17 rejecting controls.

Verification

Fresh checkout of 175822aee7a1858ec653f7f92d7a750aec2c2795. Manifest: ee9c141a4e65c2c3769384bf4458c9d38007c7bd806ca6795c8c2b49a60fc484.
PASS package manifest: 539 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 171779498411863466382722991842... brackets the ledger's b = 1717794984118634663827229918428178904088…(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 0.0017177949841186346638272299184281789040…(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 292.19 seconds. 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

PR2802 (mdumitrean, Marius-Paul Dumitrean): the construction, credited first: seven retired-lender aliases and two hostee moves, their words, owner fill, order, dispatch and certified frames (new/borrow/inputs/retired7_43*.json). Our contribution is only the finer 1e-3000 endpoint certificate and the verifier integration. PR2751 (tekuuu): the twelve-alias reassignment; PR2768 (tekuuu): the exact sparse native replay (new/fastnative/), with PR662 (Charles Bethin) tables and the PR1029 (Ali Romman) sparse evaluator. PR2766 (DavidAriasC): the frame refit of PR2751's words (priority over PR2767, which has the same construction value on a finer grid); PR2733 (mdumitrean) found the same refit concurrently. PR2788 (jeremydiviney): the stale-bytecode finding (code/pyc_guard.py, with a planted-.pyc control). GaugeFix: the Theorem 4.1 correction applied to outer/GAUGEFREE-INTERIORS.md and outer/check_gaugefree.py. PR2696 (mason-hale), PR2679 (philippeVV), PR2588 / PR2530 (zxv), PR2621 (themilkman216) and PR2559 (philippeVV): the lineage. Jeremy Kothe (jeremykothe2), with AI assistance: the 1e-3000 endpoint certificate and the integration. PR2696 (mason-hale): the concentrated eight-lender source-partner assignment (new/borrow/inputs/alias8_43*.json) and its construction. PR2679 (philippeVV): the six pre-life hostings, the frame refit and the retired-lender alias 653<-563 (new/borrow/inputs/prelife_43*.json, refit563_43*.json, alias1_43*.json; word_patch.py and rebuild_borrow.py stages and controls), the base package, and the owner-fill evacuation method of PR2559. PR2588 (jeremykothe2) and PR2530 (zxv): the words they build on (the eight source-partner aliases, the helper-label swap) and the realize flows. PR2621 (themilkman216): the priority re-ordering idea applied here to the call order. PR2733 (mdumitrean): concurrent independent work with the same composition (concentrated assignment plus pre-life hosting); our refinement is the 1e-3000 endpoint grid. Jeremy Kothe (jeremykothe2), with AI assistance: stacking PR2696's assignment with PR2679's hostings and alias, the priority-ordered window-optimal fill (the offset search for the order and the fill) and the integration. PR2530 (zxv): the eight source-partner aliases, the order, the words and the starting owner map (new/borrow/inputs/alias8_43*.json, new/borrow-fill/ORDER.json, DISPATCH.json, independent_core.py). PR2559 (philippeVV): the owner-fill evacuation method, and the portability fixes (line endings, receipts outside the package, re-derived controls, dependency declaration) reused here; philippeVV's audit of PR2474. Jeremy Kothe (jeremykothe2), with AI assistance: running the evacuation on PR2530's owner map (new/borrow-fill/FILL.json.gz) and the integration. PR2436 (tekuuu): the lifted-target aliases and the A-phase prelude mechanism that PR2530 extends. PR2322 (Vlado Vojdanovski): the handoff construction; PR2435/PR2447/PR2462/PR2474/PR2526 and PR2312 (ours): the entrance raise, the supplier chain and the borrowed words. PR2478 (mdumitrean) and PR2508 (ywz65): the cut-centre and helper-index guards. PR2309 (Dugongue) and PR2315 (thakrarsagar): private-stock accounting; PR2301 (navinor / Aaron Wang) and PR1959 (Josie Elliston): pooled-slot time binding; PR2161 / PR2180 (dataisfire): fixed-grid maximum; PR2168 / PR2184: exact-integer coarse exponential. PR2226 (Cinna Davis / 1337isnot1337 with OpenAI Codex): anticipatory dirty borrowing. 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.