Conditional κ = 0.001698511343697629: entrance raise of 24 copy buffers on the handoff T74 words

[jeremykothe2]

Summary

Conditional κ = 0.001698511343697629329051733814187744630805511096704593311278… (3046 decimals; the exact value is kappa in research/gmx-t74-borrow43-handoff/outer/OUTER-CLAIM.json, SHA-256 of the decimal string 13ad8a24e7456aebd54902329c433eacf69faa3780d2f33d8661a5204e3ea2a6). This package continues PR2322's (Vlado Vojdanovski) handoff construction and our own PR2374 exact owner fill on it (owner-map line: PR2349, PR2363 mason-hale). The circuit change of PR2322 (four coherent helper handoffs, helpers 438 to 434), its call order and windows are unchanged. New in this package, by Jeremy Kothe (jeremykothe2), with AI assistance: the entrance frames of 24 entering width-8 copy-buffer helpers per word are raised from dimension 1 to 2 (width 8 becomes width 7; start_extra and frames re-solved, gates, warps and restore order unchanged; local profile {1:2359, 2:632, 3:330, 4:120, 5:38, 8:8}, width inventory {4:33, 5:9, 7:62, 8:90, 9:240} per call; audited forward and dual with tamper controls), and an exact owner fill for the new inventory (leftover idle {1:20824, 3:6695, 5:1, 48:25302}). Also carried: the private cleanup-buffer stock accounting (PR2309 Dugongue, PR2315 thakrarsagar; physical stock 66826), the pooled-slot time binding (PR2301, PR1959), and the supplier endpoints certified to 1e-3000 with the fixed-grid-maximum outer kappa C - 1/F - B (PR2180 / PR2161, dataisfire; PR2168). Conditional final kappa = 0.0016985113436976293290517338141877446308…(3046 digits) (supplier strict-assembly kappa 0.0016956312947088376702639978708509688232…(2995 digits)). It exceeds PR2374 (our previous package) by 1.31639E-6 and PR2312 by 1.62028E-6. 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 0c87da874b82035082ba576b19f98dcec06874ba (text-only README follow-up to 324d7d3590dc21003940a44cb0cbdc32b3620f25: stated comparison figures corrected per #2485; kappa unchanged). Manifest: a2171d3f38a22a4f8728c9d241e46312dc1e5bdcf7e8a20d7867b205e0036633.
PASS package manifest: 437 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 849255671848814664525866907093... brackets the ledger's b = 1698511343697629329051733814187744630805…(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 0.0016985113436976293290517338141877446308…(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 154 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 entrance raise of 24 copy-buffer helpers and the exact owner fill for it (new/borrow/inputs/entrance_43*.json, new/borrow-fill/FILL.json.gz). PR2374 (ours), 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]

Owner-fill audit of this PR's fill in #2442 (no κ claim; pattern relaxation only). Both words at head 324d7d3 recount to your reported profile and inventory, and your idle multiset reproduces your κ to within 1e-15. However, the exact pattern-integer optimum for this inventory is not {1:20824, 3:6695, 5:1, 48:25302} but {1:20822, 3:6694, 5:2, 48:25302}, with root 0.0016985119240 (+5.80e-10). Every legal whole-helper fill has b ≤ that + 1e-15, and the optimum is unique within 1e-12. Its full pattern counts are in research/t74-owner-fill-optimality/owner_optimum.receipt.json; it uses, for example, two (32: 9,9,9) bins and 1,156 (48: 4,8,9,9,9,9) bins. I have not checked whether your windows and families admit it. If they do, it is a small owner-level gain on top of this PR.

[thakrarsagar]

Independent check in #2446, using this author's #2387/#2315 checkers, which are independent of your code.

What reproduces:

• Both words match your report.
• All 46 warps pass, and the exact replay passes forward and dual with dirty inputs, restoring all 78 buffers.
• OWNERS.json.gz passes R-a..R-g, with windows rebuilt from GLOBAL-TEMPLATE.
• Idle, global profile, roles, rank mass, physical stock 66,826 and the 9,129 charts all equal your SPEC.
• The root of the recounted profile is within 1e-15 of your κ.

One scope note. Your words differ from #2322's only in frames: 24 start_extra entrances, 24 A-gate frames and 48 B-gate frames per word. The scalar word is unchanged. So the only new obligation is the parent delivering those copy buffers at the two-dimensional entrance frame, and #2446 does not check that.

[thakrarsagar]

A pricing note on this PR's mechanism is in #2453 (no κ claim).

What the raise changes. Your 24 raises change 96 registers' climbs:

• the raised helpers each go rank-3 → rank-2 and width 8 → 7;
• 72 gate partners (6 X registers, 66 helpers) each split a rank-3 child into 2 + 1.

The width-aware LP reproduces your gain: +1.3166e-6, against your +1.3164e-6.

Further raises. With your average per-raise partner cost, more raises peak at about +3e-7 after roughly 10 and then turn negative as packing saturates. Raises whose partners don't split would be worth up to about +4.3e-6.

Remaining sites. 112 dimension-1 entrances remain, and 26 have the same shape as your 24. All of them have entrance-frame gates, and 96 of those are in B. A frame re-solve that treats entrance frames as variables and filters for split-free partners looks like the efficient way to find any remaining value.