[rohanarun]

Conditional candidate κ = 0.0016768552290713218862064567722745926195124487395104752628033651837667029477836, an absolute increase of 1.948448994029477836E-61 over PR1458 at fec30ff23f972fdc59aeec24bc5bd64b8638d8aa.

Complete local finite admission passed. Certificate refinement only; the physical construction, native words, provider inventory, owners and paid profile are unchanged. This is an extremely small numerical certificate improvement, not a new algorithm or practical speedup.

The complex native and conservative endpoint grids are refined from PR1458's 10^-60 to 10^-64. Both retained rational Mercator and PR1458's finer base-two moment engine accept each lower endpoint and reject the next grid point. The bit endpoint and surcharge assumptions stay unchanged. A strict outer assembly on source-bound, previously verified PR1424 owner/invoice receipts passes all 47 inequalities and rejection controls. That preliminary assembly was followed by the fresh full finite replay documented below.

The exact witness uses 30 finite bootstrap steps, eta = beta = 10^-86, target backoff 10^-89 and final κ grid 10^-80. Every integer cutoff is recomputed. The decimal formatter uses the configured grid plus ten guard digits, avoiding truncation of the exact rational claim. All mathematical engines and inequalities are inherited; PR1458's fine engine is unchanged and credited.

Full reproduction: python3 -B verify.py --work /absolute/new/work --base-native-from /bound/base/native --extra-native-from /bound/extra/native. Omit the reuse flags for fresh native replay. Assertions must be enabled. The native reuse flags are explicitly recorded; no fresh native run or hosted CI success is claimed. A separate closed-form bootstrap checker is included. Ancestor evidence under evidence/pr1424/ and evidence/pr1377/ is historical evidence, not new verification.

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.

Credits: Jeremy Kothe / PR1458 and PR1444 for finer endpoint enclosures and outer refinement, PR1377 and PR1274; Rohan Arun / PR1424, PR1319 and PR1297; Jeremy Diviney / PR1193; Thomas DiFiore / PR1148; Hao Yan and retained owner/controller lineage; eumemic and icekylinx/Zhihao Chen; the retained PR547/548/559 recurrence and PR589 bit suppliers. Prepared by Rohan Arun with substantial OpenAI Codex assistance. Apache-2.0; predecessor notices retained. No independent human review or proof-assistant verification is claimed.

The complete replay passed provider/parent admission, owner reconstruction, parent lifting, strict T74 admission and geometry controls. Controls: 114 admission, 12 bit, 15 controller, eight independent owner, six geometry, plus five rejected independent outer mutations. Native receipts were explicitly reused. Fresh evidence is under evidence/fine64/; all other inherited stage receipts are historical. The standalone closed-form checker passed on the fresh strict assembly. Published tree hashes are checked before marking ready. Hosted CI remains separate. Continue the search for a lower paid physical profile.

The retained paid profile and outer recipe have less than 10^-64 further certificate-only headroom above this candidate: both engines reject the next complex endpoint, and kappa < b/(1+b). The exact ceiling and scoped argument are in evidence/fine64/CERTIFICATE-CEILING.json. This does not bound changed constructions or outer recipes.

[Mister-Meeseeks]

100-PR batch review at 2ffb640826106f01184c818ecd0cccb683f2aabf.

This remains open after scoped triage. Next review step: Refines only the outer witness of the pending PR1319 family. Review the arithmetic separately, but whole-head admission requires resolving the parent regenerated-container binding and completing its controller/invoice/geometry replay; do not promote an unadmitted parent through a finer numerical grid.

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.