Conditional κ = 0.001703676387993676: a fifth #2436 alias on the entrance-raised T74 words

[jeremykothe2]

Summary

Conditional κ = 0.001703676387993676489033949045348121170345872741703307776154… (3046 decimals; the exact value is kappa in research/gmx-t74-borrow43-handoff/outer/OUTER-CLAIM.json, SHA-256 of the decimal string abb2d9752086cdf67572b0183ec2e17315e49c758153f2cf1b8d100ea80dbff7). This package adds a fifth PR2436 (tekuuu) alias to our PR2462 words: helper 637 borrows retired source register 31 (the PR2436 pair, with its G columns taken from PR2436's composed word), stacked on PR2436's four lifted-target aliases (helpers 640, 641, 642 and 644 borrowing from lenders 33, 55, 74 and 85, an A-phase prelude of 28 events, and the 4 centre COPY 8 to 7+1 splits) and on our entrance-raised words of PR2435/PR2447. The whole stack rests on PR2322's handoff construction (Vlado Vojdanovski) and our PR2312 words. PR2436's other removal, 653 borrowing from 73, does not stack here: it would force register 533 to lose its cold end (width 7 back to 8) and lowers the ideal below the four-alias value, so it is not used. This is not PR2436's whole construction: our word has 429 helpers per call. New in this package, by Jeremy Kothe (jeremykothe2), with AI assistance: the stacking of the fifth alias, its exact pricing, the audit of both words (forward and dual, with tamper controls on the new reads and the warp), and an exact owner fill for the 429-helper words (leftover idle {1:21857, 3:7308, 5:35, 48:25752}; same call order, windows and plan; every window, bin, helper and family rule checked literally); local profile {1:2363, 2:632, 3:326, 4:120, 5:33, 7:4, 8:4}, width inventory {4:33, 5:8, 7:62, 8:86, 9:240} per call. Also carried: private cleanup-buffer stock accounting (PR2309, PR2315), the pooled-slot time binding (PR2301, PR1959), the entrance-width binding stage and the 1e-3000 endpoints with the fixed-grid-maximum outer kappa C - 1/F - B (PR2180 / PR2161; PR2168). Conditional final kappa = 0.0017036763879936764890339490453481211703…(3046 digits) (supplier strict-assembly kappa 0.0017007788112916789027998352489828975646…(2995 digits)). It exceeds PR2462 (our previous package, kappa 0.0017035523129795943854...) by 1.24075E-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 71b5b0e383b2f4b57dd2177b424612da9c988fe4 (text-only follow-up to 5298f86c5193db65f869121eab3cac16d557196c: the README comparison now prints PR2462's kappa, not this package's own; kappa unchanged). Manifest: d910790cf2d05723bb270c02c1e5cebe7832c280fbbbbcd25d372674e70d351d.
PASS package manifest: 444 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 212959548499209561129243630668... brackets the ledger's b = 1703676387993676489033949045348121170345…(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 0.0017036763879936764890339490453481211703…(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 208.3 seconds on the new head (PASS_RELEASE, kappa identical). 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/). PR2436 (tekuuu): the four lifted-target aliases, the alias 637 pair and the A-phase prelude and verifier/transport edits (new/borrow/inputs/lowfour_43*.json, alias637_43*.json, new/borrow/audit_local.py, new/code/borrow/bw_transport.py). Jeremy Kothe (jeremykothe2), with AI assistance: the entrance raise of 24 copy-buffer helpers (PR2435/PR2447, new/borrow/inputs/entrance_43*.json) and the optimal owner fill for the 430-helper words (new/borrow-fill/FILL.json.gz). PR2442 and PR2446 (thakrarsagar): owner-move finding and verification of PR2435. PR2374 (ours), PR2349 and PR2363 (mason-hale): the preceding owner improvements. 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]

Text-only corrections for this series, from the pinned ledger in #2485. No κ value and no release gate is affected. All 82 predecessor gates in your verify_release.py scripts that name pinned PRs pass, and they use exact or conservative literals. The one exception is PR2265's published 43-digit κ, which is 9.7e-45 below the pinned value, which is immaterial here.

• Conditional κ = 0.001696395766736081: exact pivot-518 and 506 helper-donor kernel(s) (PR1625 shape, KernelsOnBorrow) on the borrowed words, exact frame refit (WildIdeas), 1e-3000 certified supplier endpoint, fixed-grid-maximum kappa C - 1/… #2302 body: "exceeds PR2288 … and PR2269 by 8.48163E-8". 8.48163E-8 is the difference to PR2288; the difference to PR2269 is 1.48628E-7. The README already has the right value.
• Conditional κ = 0.001697194950901770: exact owner fill on #2322's handoff construction #2374 body and README: "… and PR2312 by 1.28957E-7". That number is the difference to PR2349; the difference to PR2312 is 3.03884E-7.
• Conditional κ = 0.001698511343697629: entrance raise of 24 copy buffers on the handoff T74 words #2435 body and README: "… and PR2312 by 1.31639E-6". That number is the difference to PR2374; the difference to PR2312 is 1.62028E-6.
• READMEs of Conditional κ = 0.001698511343697629: entrance raise of 24 copy buffers on the handoff T74 words #2435, Conditional κ = 0.001698511924002761: optimal owner fill on #2435's entrance-raised words #2447 and Conditional κ = 0.001703676387993676: a fifth #2436 alias on the entrance-raised T74 words #2474: "exceeds PR#### (our previous package, kappa X…)" gives this package's own κ as X. The predecessor values are PR2374 0.0016971949509017704…, PR2435 0.0016985113436976293… and PR2462 0.0017035523129795943854…. The Conditional κ = 0.001703676387993676: a fifth #2436 alias on the entrance-raised T74 words #2474 body quotes PR2462 correctly.
• READMEs of Conditional κ = 0.001696310950415050: exact frame refit of the borrowed gauge44 word (WildIdeas), 1e-3000 certified supplier endpoint, fixed-grid-maximum kappa C - 1/F - B at 1e-3080 slacks (PR2180 / PR2161 retune) and exact-integer coarse… #2288, Conditional κ = 0.001696395766736081: exact pivot-518 and 506 helper-donor kernel(s) (PR1625 shape, KernelsOnBorrow) on the borrowed words, exact frame refit (WildIdeas), 1e-3000 certified supplier endpoint, fixed-grid-maximum kappa C - 1/… #2302 and Conditional κ = 0.001696891067241618: helper width exchange on the borrowed T74 words #2312: "exceeds PR2265 by about 1.28e-5" is copied from PR2269. The values are about 1.29e-5, 1.30e-5 and 1.35e-5.
• Gate label slip: in the Conditional κ = 0.001697194950901770: exact owner fill on #2322's handoff construction #2374, Conditional κ = 0.001698511343697629: entrance raise of 24 copy buffers on the handoff T74 words #2435, Conditional κ = 0.001698511924002761: optimal owner fill on #2435's entrance-raised words #2447, Conditional κ = 0.001703552312979594: optimal owner fill for #2436's aliases on the entrance-raised T74 words #2462 and Conditional κ = 0.001703676387993676: a fifth #2436 alias on the entrance-raised T74 words #2474 scripts, the gate commented "PR2363 (mason-hale): exact claimed kappa" raises "does not exceed PR2322". The comparison itself is right. In Conditional κ = 0.001703552312979594: optimal owner fill for #2436's aliases on the entrance-raised T74 words #2462 and Conditional κ = 0.001703676387993676: a fifth #2436 alias on the entrance-raised T74 words #2474, the "PR2436: exact kappa" gate uses the 24-digit round-up, which is 1e-46 above the exact value and so conservative, and it appears three times.

python3 -I -B research/t74-claim-lineage-ledger/ledger.py --fetch reproduces all of this; the statement ids are in STATEMENTS.json. (Sagar Thakrar, with AI assistance.)

[philippeVV]

Independent audit of 5298f86: the claim holds. On Linux, verify_release.py fails on line endings at two points.

Artifact: research/pr2474-independent-audit @ 590c6379 (fork; own scripts plus details).

Independently confirmed with separate code:

• Alias 637←31. It is exactly the 7 declared renames plus one warp at B1041, whose G equals PR2436's. 31 retires at B574 and 637 had no cold end. A randomized non-commutative replay passes forward and dual, with the cleanup derived independently. The mutants are rejected for real reasons.
• Owner fill. 285,714 rows, all windows, bins, families and prefixes respected; idle {1:21857,3:7308,5:35,48:25752}, deficit identity 23680.
• κ. A 90-digit root of Σ n_r(r/73)^(1−s) = 66304 matches the claim to 79 digits.

Defects (none affects κ):

1. CRLF.
   • outer/run_outer.py:14 compares bytes against CRLF-committed LEDGER.json, so it fails on Linux. The regenerated file is identical modulo CR.
   • The new/PLAN.json provider_registry.*.artifact_sha256 pins for LOCAL-CHECKS.json and RESIDUAL-ADAPTERS.json are hashes of the CRLF files. Linux-regenerated natives hash to b7d12b86…/bbfe9033…/dd735bb6…; converted to CRLF they give the pinned 3dad2d64…/4b2348f0…/09f5320f….
   • So verify.py:116, and then bind_providers_portable.py:54, fail. With line endings normalised, every stage passes.
2. Verification mutates the package. The new/borrow/receipts/ files (12) are rewritten with nondeterministic elapsed_seconds, so a second run fails the manifest and entry-hash checks.
3. The alias-637 sign-flip, doubling and dropped-warp controls in rebuild_borrow.py:96-99 are vacuous. They don't re-derive the cleanup, so they are rejected only by "explicit cleanup differs" or "warp operator id". With the cleanup re-derived they are rejected for real reasons.
4. Minor.
   • lowfour_controls.py:35-38 still uses warps[-4:], which now hits lender 55.
   • "430-helper" appears in the credits.
   • verify_release.py:128-135 has the same gate three times.
   • Dependencies (numpy, gmpy2, sympy, mpmath, psutil) are undeclared.

I can open a small PR that normalises line endings and pins LF hashes if that helps.

Prepared with substantial Claude Code assistance. A sub-agent did the audit. I separately re-ran the fill check and confirmed the run_outer.py failure.