[jeremykothe2]

Summary

Conditional κ = 0.0016778199023144364336310551358776001013829401215770658599799349282716974076737897457922714197448847. Capped phase-cell fusion outer (PR1673, Vlado Vojdanovski) on this repository's T74 supplier (pivot-566 and pivot-554 helper-donor kernels, certified complex endpoint 0.00167975495612554452133567...), with the matrix boundary at tau=2.372864 above Francois Le Gall's published omega<2.3728639 as specialised by Chafik Boukhalfa in PR1699, free strict slacks at 1e-64 or below and b = certified endpoint - 1e-64, and a NEW radix-distributed sparse-union schedule (outer/UNION-SCHEDULE.md, not part of PR1673 or PR1699; executable check outer/sched_test.py) that replaces the per-axis scan of the union by flag-count rounds with stable radix distribution, a variable-length lockstep transpose and a LIFO interleave: union row eps+1/2-xi instead of eps+beta+1/2-xi, so the boundary row binds with main = fused Gaussian. The 50 strict inequalities, 7 rejecting controls (including reinstating the old g-factor union row, which fails) and the endpoint rejection are regenerated with an independent balance derivation; the supplier's full native admission is rerun. Conditional, with all inherited all-size hypotheses; the union schedule needs independent review; the exponent is a cited theorem.

Verification

Fresh checkout of f36701db17f6664c81d2eca80374b125fa014207. Manifest: 230db54ba751190542f2eb703214ff3063097bacb3d8f3fc04cc75c43217931a.
PASS package manifest: 372 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 419938739031386130333917748480... brackets the ledger's b = 4199387390313861303339177484801756442495778596256450738650818550407/2500000000000000000000000000000000000000000000000000000000000000000000. Outer (PR1673 capped phase-cell fusion): regenerated exact ledger (50 strict inequalities, 7 rejecting controls incl. the old g-factor union row, larger endpoint rejected by the native moment), independent balance derivation, the exact union-schedule simulation and 19 exact evidence replays all pass. Conditional kappa 0.0016778199023144364336310551358776001013829401215770658599799349282716974076737897457922714197448847 (union schedule: new radix distribution, outer/UNION-SCHEDULE.md; boundary tau=2.372864 from Le Gall's published omega<2.3728639, PR1699).

Full package-owned verification passed in 79.48 seconds. The fresh receipt binds the exact package manifest and score.

See research/capped-fusion-t74-k554/README.md for reproduction commands and proof qualifications.

Credits

PR1673 (Vlado Vojdanovski, with AI assistance): capped phase-cell fusion outer construction, its proof and exact evidence, vendored verbatim under vendor/pr1673. Chafik Boukhalfa (PR1699: classical-matrix specialisation of PR1673's boundary) and Francois Le Gall (omega<2.3728639, Powers of Tensors and Fast Matrix Multiplication, ISSAC 2014). The radix-distributed sparse-union schedule is new in this package; its independent review simulation outer/sched_review.py is by LeverRank. Supplier: PR1625 (mdumitrean) pivot-566 helper-donor kernel; PR1661 (midhatn) 400-digit endpoint-grid refinement of that stack; pivot-554 kernel (kernel566.py search by LeverRank/jeremykothe2 tooling, PR1672); PR1297, PR1319, PR1424, PR1485, PR1574 (Rohan Arun) T74 exact fill and cold kernels; PR1274, PR1479, PR1510, PR1513, PR1536, PR1578 (Jeremy Kothe) endpoint and outer-witness lineage; PR1534, PR1549 (midhatn); PR1519 (philippeVV) fine-Mercator soundness repair; PR1286, PR1193 (Jeremy Diviney), PR1148 (Thomas DiFiore) and the retained supplier lineage. Research direction, prioritisation and release strategy: jeremykothe2. Implementation assistance: oh-my-pi.

[Mister-Meeseeks]

Batch review at f36701db17f6664c81d2eca80374b125fa014207.

This remains open after scoped triage. Next review step: Resolve the inherited T74/#1319 supplier admission (controller, geometry, invoice and semantic regenerated-artifact checks) before accepting a stronger bound. Independently audit the new outer schedule/analytic cost argument and its precision, movement and recurrence interfaces; parameter inequalities alone do not establish it.

This is a specific continuation point, not a rejection or a request to redo already recorded checks. Completed local evidence is retained separately from outstanding whole-head obligations.

Batch review, attribution and evidence. Thank you for the contribution.