Conditional κ = 0.001717256973467002: post-cut partner correction on #2696's lender assignment with #2679's pre-life hosting

[jeremykothe2]

Summary

Conditional κ = 0.001717256973467002308270944796906915212611876978096502828100… (3046 decimals; the exact value is kappa in research/gmx-t74-borrow43-handoff/outer/OUTER-CLAIM.json, SHA-256 of the decimal string 93818aeaa04a53feeb6ff18e8cdf0d4be95a99dcbc89ddd8a078b3c789a00198). This package stacks PR2696's (mason-hale) concentrated eight-lender source-partner assignment with PR2679's (philippeVV) six pre-life hostings (cold hosts 273/275/289/291/305/321 host helpers 482/483/494/495/507/519) and the one-gate frame refit with the retired-lender alias 653<-563, adds a post-cut partner correction (the four partner helpers' prelude warps and correction gates move after the centre cut, as explicit signed B-phase warp items; the lifted-target set shrinks to eight offsets and the four rank-7 plus rank-1 centre splits become rank-8 children) with a frame re-solve of the final word, and gives the result a priority-ordered call order and the window-optimal owner fill for it. The eight-lender words (new/borrow/inputs/alias8_43*.json) are PR2696's; they sit on PR2588's words (PR2530's (zxv) eight source-partner aliases with our swap of the helper labels of lenders 80 and 88); 415 helpers per call, local profile {1:2370, 2:646, 3:297, 4:120, 5:26, 7:4, 8:4}. PR2751 (tekuuu) was published earlier and reaches the same all-rank-8 centre profile by a different mechanism (its twelve-alias reassignment); the post-cut route is an independent alternative, not an improvement over it, and the only gain over PR2751 is the B1149 frame re-solve (+1.15e-7), found concurrently by PR2733 (mdumitrean). What changes: the words (the post-cut partner correction, stage postcut of new/rebuild_borrow.py with new/borrow/inputs/postcut_43*.json: verified by new/borrow/audit_local.py (extended to accept signed B-phase warp items) and the transport and tamper controls of new/code/borrow/, with controls rejecting a flipped inverse sign, a wrong operator, a wrong register, a misplaced timing and an omitted inverse or forward warp; PR2696's eight-lender assignment carried through PR2679's pre-life, refit and alias stages, which are re-checked on the combined state with their controls and both guards) and the owner side: the call order and dispatch (new/borrow-fill/ORDER.json, DISPATCH.json) and the owner fill for that order (FILL.json.gz; leftover idle {1:17316, 3:6594, 5:5216, 32:1, 48:26558}). The priority re-ordering idea is PR2621's (themilkman216); the evacuation method is PR2559's (philippeVV); the realize flows are PR2530's (zxv). New in this package, by Jeremy Kothe (jeremykothe2), with AI assistance: the post-cut partner correction with its verifier extension and controls, the stacking of PR2696's assignment with PR2679's hostings and alias, and the priority-ordered window-optimal fill, its exact checking (every window, bin, helper and family rule literal) and the integration into our pipeline. Conditional final kappa = 0.0017172569734670023082709447969069152126…(3046 digits) (supplier strict-assembly kappa 0.0017143130574144518034056624282464037255…(2995 digits)). It exceeds PR2751 (exact kappa from its claim, the live leader when this package was built) by 1.15387E-7 (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 e8b771ba132fe632796b28c1742a8d096c04519f. Manifest: b78a248db5539549710565e1d1a3e3c39b3791fbf09d05c19043b593a53c9b44.
PASS package manifest: 493 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 none (fresh replays); its complex endpoint 171725697346700230827094479690... brackets the ledger's b = 1717256973467002308270944796906915212611…(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 0.0017172569734670023082709447969069152126…(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 682.92 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

PR2766 (DavidAriasC) was published about 43 s before this PR with the same construction value: PR2751's twelve-source reassignment plus PR2733's B1149/B1151 frame refit. This PR's κ exceeds PR2766's kappa_decimal by about 9.45e-25 only because its supplier endpoint is certified more finely (1e-3000 grid); the construction gain is identical, and PR2766 has priority on it.

PR2751 (tekuuu) was published earlier and reaches the same all-rank-8 centre profile by a different mechanism (its twelve-alias reassignment, no phase-B warps); this package's post-cut route is an independent alternative, not an improvement over PR2751. The only gain over PR2751 is the B1149 frame re-solve (+1.15e-7), which PR2733 (mdumitrean) also found concurrently. The exact gate in verify_release.py is against the kappa of PR2751. 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: the post-cut partner correction (words, audit extension, controls), 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. 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.

Follow-up fd7c7a7

Theorem 4.1 in outer/GAUGEFREE-INTERIORS.md is restated with the absolute-scale guard log(2+Λ+1/μ) (thanks to Mister-Meeseeks' review on #1758; the unit-diagonal application and κ are unchanged). new/PLAN.json now pins regenerated natives including the 7 postcut_* controls, and verify.py LF-normalises regenerated text artifacts, so a fresh no-cache verify_release reproduces on Windows and Linux. Fresh PASS_RELEASE: Windows no-cache 1058 s, WSL no-cache 839 s, cached 699 s; κ identical.