Conditional κ = 7.54077687633330e-4: 438 early restorations (endpoint-aware banks) after the squares on #310's w3 word (+0.0755% over #311)

[rohanarun]

Conditional κ = 754077687633330234295251/10^27 = 7.54077687633330234295251e-4, +0.0755 % over #311 (7.53508664880762e-4), +0.157 % over #310's w3 word. Below #312 (draft, 7.54550e-4, kernels/squares/plateau/reorder with #304's supplier); this PR contributes the stage #312 reports as blocked — early restorations with endpoints below the full frame — and its composition with #312's stages follows.

One self-contained package, research/w3-restore/ (#311's package with one more native transcript stage), with its own workflow; branched from main, no existing file changed.

Full replay: PASS (verify.py --output, ~10 minutes locally): both prerequisite source verifiers fresh, the squares, the restoration stage, legality, all 23,627 global and 22,172 compact F₂ columns, the endpoint-aware bank allocation, 22,806 changed charts, geometry admission, exact price (nine ordinary levels, two engines, 47 strict constraints, adjacent grid point rejected), finite invoice, complex guard and finish.py; prints PASS conditional kappa = 754077687633330234295251/1000000000000000000000000000.

Change

438 early restorations on w3 — #280's rule and its own screen/emitter (code/cleanup_screen.py, code/cleanup_emit.py, re-pinned to this word). At the first cleanup_gate ADD (record 962,945) every data target already has its scalar endpoints (checked on the exact F₂ prefix); 440 helpers a have a single later scalar incidence a −= b with a donor unwritten in between, both at rank-22 frames with a nondegenerate 23-dimensional span E (#280's shape; 477 further multi-incidence candidates at dimension 3 are not moved). With 40 physical replicas the restored width-3 slots must tile width-120 banks, so 438 are moved (438·40 = 146·120 — #280's own 438/440 distinction). The write commutes over the integers with every crossed gate; a and b advance to E, the ADD runs there and a retires at E. The emitter checks each new frame's full-rank annihilator and nonzero cleared Gram determinant mod 2¹²⁷ − 1, the commutation conditions, forward/inverse/roundtrip F₂ replays and an omitted-restoration control. Local delta {1: +1314, 2: −876}; rank mass 398,897 → 398,459; endpoint residual 317,409 → 316,971.

Admission of endpoints below the full frame. code/cohort-bank-review.cpp now reads the candidate's COHORT249-FINAL.json and a tiling plan (inputs/bank-plan.json): each helper's residual width is dim(endpoint) − dim(entrance) (#310's census is reproduced when nothing is restored); the plan is an exact integer tiling (small ILP over patterns of ≤ 3 widths; 105,657 banks per stage) that the C++ verifies in full — width census, collision-free tiling of all 3,026,400 role/replica/stage slots, every bank a full 120-coordinate partition, the per-pattern endpoint and omission/repetition controls, exact charts (3,911 new, ≤ 320 factors) — with the generic stock invariant. Legality runs against the candidate's declared endpoints with the export's base frame table; the changed-chart audit covers the 2,703 retired endpoints (≤ 342 factors). Literal stock 810,615 → 809,885 (normalized 161,977); finite coefficient 58,322,299,353,183,001 < 2⁸⁰; selector charge 571,950,385,600 < 2⁴⁰. Re-pinned: code/admit_geometry.py, code/price.py (word hash 8f05b2af…, 3,687,240 calls, mass 19,402,040, κ, 9 levels), code/finish.py.

With #233's complex supplier the complex side would bind at 7.5413e-4 for any further bit-side gain; the composition with #312 therefore uses #304's supplier as #312 does.

Verify

python3 -m pip install -r research/w3-restore/requirements.txt

python3 -B research/w3-restore/verify.py --output /tmp/w3-restore-proof --cxx g++ --boost-include /usr/include

Scope and credits

Exactly #310/#311's conditional interfaces; no Lean build. utcorvusvolat-dotcom (#310 w3 word and admission chain; #280 early restorations and endpoint banking), eumemic (#268, #249 lineage), Dugongue (#283 endpoint-aware composition), chafreaky, DreamingOfClouds, hcg890, Jacob Sussman, Evan McKinney and the retained lineage. Prepared by Rohan Arun with Anthropic Claude assistance; Apache-2.0; NOTICE.md.

🤖 Generated with Claude Code

[rohanarun]

CI note: the only failing check here was the repo-wide 'Verify research artifacts' job (make joint-dual-verify), which fails on main itself because the root Makefile/README changed while research/joint-dual/SOURCE.json pins their digests (see #318). To make this PR's checks green now, the branch carries that same one-line repin commit (research/joint-dual/SOURCE.json and the two joint-dual certificates' recorded manifest hash) — no package content changes; it can be dropped once #318 or an equivalent fix lands on main.

[Mister-Meeseeks]

Thank you @rohanarun. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Early restorations after w3 target squares.

Review and limits: Endpoint-aware banks must be rebuilt on the changed word. Seven unrelated root-wrapper differences in CI are disclosed; contributed package sources match.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: 9646345a82f7858e266f71a005a06aaf2c30eba9. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.