Conditional kappa 0.001676855229071321: verified exact fill on 74 replicas

[rohanarun]

Conditional κ = 0.001676855229071321, a 0.00001493392089% improvement over PR1297 (0.001676854978651125). Doubling the four-kernel construction to 74 replicas admits one more extra-provider call and fills all four leftover rank-one gaps.

The complete package-owned finite replay passes. It reconstructs all 319,680 owner roles and the exact doubled parent; checks emitted chronology, charts, finite invoice, both exact moment engines and 47 outer inequalities; rejects 114 admission, 12 bit, 15 controller, eight independent owner and six new geometry/charge mutations. The generalized formulas also retain the 37-replica regression with 114 rejected admission mutations.

The scalar words are byte-unchanged from PR1297. This local release run explicitly reused their word-bound completed native receipts and reran their independent local, fusion, kernel and phase-premise checks; it does not claim fresh native runs. Hosted CI is separate and was queued at the last exact-head check.

The dispatch is 249 base / 417 extra among 666 calls. Exact alternating paths change whole width-four and width-five owner assignments. Idle H48=22,748 and no H1 gaps remain. Prefix use is 1,441 bits, charged at 2,048; row coefficient 19,545 is below the unchanged 20,161 limit. PROOF-NOTE.md explains the direct sum, namespace sharing and larger prefix charge. No pending idle axis is transferred between data streams.

Reproduce offline with Python 3.14 and SymPy installed:

python -B research/global-mixed-t74-exact-fill/verify.py --work /absolute/path/to/new/work

Default operation runs both native suppliers sequentially. Explicit --base-native-from and --extra-native-from accept completed predecessor native directories only after word and stage binding checks. Work must be outside the package and must not exist. reconstruct.py --out /absolute/path/to/new/owners runs the separate standard-library owner construction. See evidence/FULL-ADMISSION.json and the exact pinned predecessor under vendor/pr1297.

Conditional finite construction only. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact recovery, analytic transfer, PR559 recurrence correction and PR589 bit H1-H5 assumptions remain. No unconditional theorem, full Lean certification, or global packing claim.

Credit: Rohan Arun / PR1297 and PR1286 for the four cold-kernel composition; Jeremy Kothe / PR1274 for the first helper-donor kernel; Jeremy Diviney / PR1193 for the mixed-provider flow and regular matching; Hao Yan / PR1074 for source-event windows and direct-sum lifting; Thomas DiFiore / PR1148, PR1195/1196 and the retained X54, owner and PR589 bit lineage. PR1240/1264 motivated the packing-headroom screen. Prepared by Rohan Arun with substantial OpenAI Codex assistance. Apache-2.0; predecessor notices retained.

Open next questions

• Seek a new local paid profile or a compatible centre-path change. This result only removes the integral packing remainder of the existing two-provider construction.
• Further replication alone is not claimed to improve this exact-fill profile, and global optimality remains open. All inherited theorem obligations remain conditional.

[Mister-Meeseeks]

100-PR batch review at 603defe58aac018c6a8457840481390a15846fe4.

This remains open after scoped triage. Next review step: Fresh native providers and retained-parent admission passed. Reconstructed owners have identical decompressed SHA256 417903ae… but different gzip bytes; the supplied verifier stops at PLAN.json assignment_sha256 and replica_lift.owners_file_sha256. Normalize regenerated-container bindings while preserving immutable pins, then finish T74 controller/invoice/assembly and geometry controls using the retained native receipts.

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.