Conditional κ = 7.55120411314104e-4: 438 early restorations after #312's kernel/target/plateau/reorder stages on the w3 word (+0.0756% over #312)

[rohanarun]

Conditional κ = 151024082262820774685631/(2·10^26) = 7.55120411314104e-4, +0.0756 % over #312 (7.54549816771013e-4), +0.214 % over #311, +0.296 % over #310's w3 word. Priced against #304's complex supplier as #312 is; the bit side binds (nine ordinary levels).

One self-contained package, research/w3-stages-restore/ (#312'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, ~12 minutes locally): both prerequisite source verifiers, #304's supplier admission, #312's three stages, the restoration stage, recompaction, legality, all global and compact F₂ columns, the endpoint-aware bank allocation, 23,870 changed charts, geometry admission, exact price (nine ordinary levels, two engines, 47 strict constraints), finite invoice, complex guard and finish.py; prints PASS conditional kappa = 151024082262820774685631/200000000000000000000000000.

Change

438 early restorations after #312's reorder stage — the stage #312 reports as blocked ("they would need final-frame changes that #310's legality checker rejects"), admitted as in #313: #280's own screen and emitter re-pinned to #312's final word. At the first cleanup_gate ADD (record 925,515) 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 an unwritten donor, both at rank-22 frames whose span E is a nondegenerate 23-dimensional frame (477 multi-incidence dimension-3 candidates are not moved). With 40 replicas, 438 are moved (438·40 = 146·120 width-3 slots). 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. New-frame annihilators and cleared Gram determinants (mod 2¹²⁷ − 1), commutation, forward/inverse/roundtrip F₂ replays and an omitted-restoration control are checked. Local delta {1: +1314, 2: −876}; rank mass 398,057 → 397,619; endpoint residual 316,569 → 316,131.

Admission of endpoints below the full frame. #312's plan-driven code/cohort-bank-review.cpp now reads the candidate's COHORT249-FINAL.json: each helper's residual width is dim(endpoint) − dim(entrance) (#312's census is reproduced when nothing is restored), with the generic stock invariant (all slot coordinates fill the banks exactly). stages/bank-tiling.json carries the new census (438 at width 3, 1,762 at width 4, #312's kernel widths unchanged) and an exact integer tiling (ILP over patterns of ≤ 3 widths; 105,377 banks per stage) that the C++ verifies in full — collision-free tiling of all 3,026,400 slots, every bank a full 120-coordinate partition, per-pattern endpoint and omission/repetition controls, exact charts (4,703 new, ≤ 320 factors). Legality runs against the candidate's declared endpoints with the export's base frame table; 23,870 changed projector charts (3,221 retired endpoints, ≤ 342 factors). Literal stock 809,215 → 808,485 (normalized 161,697); finite coefficient 58,519,066,603,435,601 < 2⁸⁰; selector charge 571,949,825,600 < 2⁴⁰. Re-pinned: code/admit_geometry.py, code/price.py (word hash a972abfe…, 897,241 ADDs, 3,709,480 calls, mass 19,368,440, deficit 35,200, κ), code/finish.py (also cross-binding the restoration receipt and the pre-restoration word hash to #312's reorder output).

Verify

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

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

Python 3.11+, a C++17 compiler and Boost headers; about 12 minutes.

Scope and credits

Exactly #310/#312's conditional interfaces; no Lean build. chafreaky (#312: the w3 stage composition this extends; kernel/plateau/reorder stages), utcorvusvolat-dotcom (#310 w3 word and admission chain; #280 early restorations and endpoint banking), DreamingOfClouds (#304 supplier), Dugongue (#309 adapter, #283 endpoint-aware composition), eumemic (#268, #249 lineage), 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 the complete w3 stage stack.

Review and limits: Joint stage replay and revised bank endpoints are required. CI merge-checkout wrapper differences do not change this package's source bytes.

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: 3984049ab4658f8126475aa1860367bdb79b40cc. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.