[midhatn]

Conditional candidate κ = 0.00167685522907132188620645677227459261951244873951047526280336519105115665521200964951578469164138454299292754381039421745513966674764384056894216319995553483574631072160380818267628500278547539875882. This exceeds PR #1485 (da38a09c5b2c2418d405773ac398378ab92ccf54) by 8.94216319995553483570768400380380818267628500278547539875882E-141 and PR #1479 (0a211a4608d2c3d295f8bb94b12ca446714186ab) by 5.115665521200964951578469164138454299292754381039421745513966674764384056E-68.

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

PR1479's exact complex native and conservative endpoint brackets of width 10^-120 and its two finer-constant rational moment engines are retained unchanged. Both engines accept the lower endpoints and reject the next points. The old engines separately certify the containing 10^-24 brackets. The bit endpoint and surcharge remain unchanged. Credits and exact source hashes are in evidence/pr1479-source/.

The new outer witness uses 75 bootstrap steps, eta = beta = 10^-250, target backoff 10^-253 and final κ grid 10^-200. Its decimal formatter uses the configured grid plus ten guard digits. A strict assembly replay on the previously verified, source-bound PR1464 owner/invoice receipts passed all 47 outer inequalities, conservative checks and rejection controls. This preliminary assembly was followed by a fresh complete finite pipeline replay, whose new evidence is under evidence/outer200/. Provider/parent admission, owner reconstruction, parent lifting, strict T74 admission (PASS_T74_EXACT_FILL_COMPLETE_FINITE_ADMISSION) and geometry controls all passed.

Reproduce from this package: python3 -B verify.py --work /absolute/new/work --base-native-from /bound/base/native --extra-native-from /bound/extra/native. Omit the native reuse flags to regenerate the native providers. Assertions must be enabled. A separate closed-form bootstrap checker is included (check_outer_closed.py). Full verification used explicit source-bound native reuse; no fresh native replay or hosted CI success is claimed. All inherited evidence, including evidence/outer140/ and evidence/fine64/, is historical.

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, global packing optimum or independent human review is claimed.

Credits: Jeremy Kothe / PR1479 and PR1458 for the finer endpoint engines, PR1444/1377/1274; Rohan Arun / PR1485, PR1464, PR1424, PR1319 and PR1297; Jeremy Diviney / PR1193; Thomas DiFiore / PR1148; Hao Yan and retained owner/controller lineage; eumemic and icekylinx/Zhihao Chen; retained PR547/548/559 and PR589 suppliers. Prepared by Midhat / Antigravity with AI assistance. Apache-2.0; all predecessor notices retained.

The independent closed-form checker passed on the fresh strict assembly and rejected five mutations. The pipeline passed 114 admission, 12 bit, 15 controller, eight owner and six geometry controls. The published tree is hash-checked before marking ready. Hosted CI is reported separately.

For this unchanged paid profile and retained outer recipe, less than 10^-120 additional certificate-only headroom remains above this claim. The exact strict upper bound is derived from the rejected next endpoint and kappa < b/(1+b), in evidence/outer200/CERTIFICATE-CEILING.json. This does not constrain different constructions or outer recipes.

[Mister-Meeseeks]

Batch review at 8485ba77eb2ebf9d1e1ea38fa663c760ea788d95.

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.