Conditional κ = 0.001636269762440408: combined cold ends and PR635 owner repair

[vectorsss]

Raises conditional κ to 0.001636269762440408, exactly 204533720305051/125000000000000000. This improves pinned PR635 (a6895a69f8ad98ab45777b03e9e6f48888c39f6f) by 0.000000028260864020. The conservative rate is 0.001636269759573274.

The improvement comes from a literal owner repair on PR635's map: 6,967 recorded row replacements, with the same 71 JP8 / 1 CK dispatch (CK at time 5). The idle profile becomes {1:42,23:1,32:1,39:1,48:2221}. All 35,424 roles are checked; rank mass 520,704, live families 7,168 and physical families 7,670 are unchanged. A bounded search nominated the map; the entire actual profile is priced by exact assembly. No optimality claim.

The package uses our independently reconstructed combination of PR629's four dimension-eight ends and PR627's two dimension-seven factored ends. Its helper widths and paid profiles match PR635. One same-frame absorption (q95 += S403/4 at original anchor 1665) and ten rank-zero basis corrections resolve the interaction. A separate Fraction proof checks the repair. All 23 core verification files are byte-identical to pinned PR629.

Verification complete: a fresh macOS/Python 3.14.8 wrapper run passed all 64 stages with no reused baseline or local supplier results. All 51 receipt artifact hashes and 64 stage-log hashes match. The run includes the physical controller, finite invoice, both exact moment engines, outer inequalities and all 114 admission rejection controls. Supplemental checks passed the independent basis proof, positive control and 12 composition mutations, independent native-owner/rational-moment verification and five mutations, declarations, and exact recipe/owner reconstruction with four exporter mutations.

The full replay archive and receipts are retained in research/combined-cold-ends-20261013/validation635/. Execution is bound to immutable commit 4988e425009a1a94ebd5f4281a251fa5cc9cb162; the later README-only status/manifest update is explicitly recorded, with all other 320 manifested inputs verified unchanged. GitHub CI and Linux execution are not claimed.

The new witness is research/combined-cold-ends-20261013/witness635/; the deterministic owner exporter and pinned provenance are also available in research/kappa-packing-pr635-20261013/. The package vendors all six source packages, preserves notices and pins, and includes reproducible construction, independent owner/moment checks and targeted rejection controls.

Credits: Jeremy Kothe (PR635, PR629), Jeremy Diviney (PR627), Chafik Boukhalfa (PR632, PR626), GamingPuzzled, DreamingOfClouds, eumemic, and the preserved contributor lineage. Prepared by Chi Zhao with substantial OpenAI Codex assistance.

The inherited compiler, common-label/mutable-source realization, whole-call hosting, precision/tape/exact recovery, analytic-transfer and bit H1–H5 assumptions remain. PR543's bit supplier is repriced rather than rebuilt. This is a conditional finite certificate. Selected certificates and archived packages are unchanged.