Conditional kappa 0.001676854978651125: four composed helper-donor cold kernels

[rohanarun]

Locally verified conditional κ = 0.001676854978651125, 0.031187795% above our locally verified PR1286 (0.001676332167598458). Compose two further exact helper-donor cold kernels, pivots 555 and 567, with PR1286's pivots 531 and 543. This also exceeds PR1280's reported 0.001676377648122875 without importing its idle overlay.

Local verification completed. Both full words passed independent rational scalar/frame audits, fresh sequential native transport, ledger, local replay, wrapper and exact phase checks. The standalone package explicitly reused those just-completed, word-bound native runs while repeating all local controls and strict global admission. Two exact moment engines and all 47 outer inequalities pass. Hosted CI is reported separately.

The frozen constructor reproduces the inherited 159,840 owner roles and dispatch from the final provider interfaces. Re-bound PLAN/SPEC, emitted controller, exact invoice and strict assembly pass. Rejected controls: 24 new pivot-555/567 mutations, 12 inherited pivot-543 mutations, 20 inherited fusion, 8 X54, 8 flow, 114 admission, 15 controller, 12 bit, and 8 independent owner controls. Both words pass the retained leaver-premise checker. The independent owner audit reconstructs source-event windows, checks ordered widths, common ports/centre frames, family noncollision and pending-child axes.

Reproduce with python3 -B research/global-mixed-four-cold-kernels/verify.py --work /absolute/new/output-directory. Default runs fresh sequential native replay for both words. Explicit --base-native-from / --extra-native-from reuse checks raw-word identity and all required completed native stages. Requires Python 3.11+, C++ compiler and Boost; no solver or network. Parent geometry and analytic/theorem interfaces remain explicitly inherited, not rebuilt from the original paper. Vendored predecessor receipts retain their original scope; root CLAIM/VALIDATION apply to this composition.

Pivot 555: replace its three early uses with a donor pair 620 += 2555 / 620 -= 2555 around the output-127 read, then 383 -= 555 after its output-187 read and restore 383 += 555 at the end of early cleanup. Pivot 567: analogous donor 628 with coefficient 2 around output 151, partner 399 after its output-211 read, and a matching early-cleanup restoration. Frozen old/new-key recipes retain the jointly optimized frames and include the exact PR1286 inputs; COMPOSITION.json gives original edit indices. Five exact alternative donor hooks were found for each pivot; the committed choice uses the first coefficient-two hook in each relation census.

Base profile: H1=2346, H2=504, H3=414, H4=130, H5=82, H8=8.
Extra profile: H1=2338, H2=512, H3=418, H4=126, H5=82, H8=8.
The inherited 125 base / 208 extra dispatch and idle H1=2, H48=11374 nominate aggregate {'1': 779556, '2': 169496, '3': 138694, '4': 42458, '5': 27306, '8': 2664, '48': 11374}; live=33152, width=73, deficit=11840. Interface and owner compatibility pass local and strict global admission.

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: Jeremy Kothe / PR1274 for the helper-donor cold-kernel mechanism; Rohan Arun / PR1286, PR1218 and PR1207 for composition and the mixed X54 fusion construction; Jeremy Diviney / PR1193 for global flow and regular matching; Thomas DiFiore / PR1148, chafreaky / PR1196, Marius-Paul Dumitrean / PR1195, and the retained PR564/571/589/645 lineage. Prepared by Rohan Arun with substantial OpenAI Codex assistance. Apache-2.0.

Open next questions

• Independently review this concrete four-kernel composition. First step: run the frozen package with fresh native providers; blocker: all-size and analytic transfer obligations remain inherited.
• Extend the exact two-shock sensitivity search beyond the four analogous pivots. First step: identify cold pivots with a larger early-use pattern; blocker: rational endpoint equality alone does not establish frame or hosting feasibility.

[tomdif]

Independent fresh replay PASS at 4abf710a7f0d2a46f522f3f13c15769d003f9495, prepared for Thomas DiFiore with OpenAI Codex assistance.

I ran the unchanged default research/global-mixed-four-cold-kernels/verify.py from the pinned package, without native-reuse arguments. Both full words passed independent local audits and all five fresh native stages; literal construction and strict global admission then passed. The retained two exact moment engines and all 47 outer inequalities pass at κ = 13414839829209/8000000000000000 = 0.001676854978651125. Both native-reuse flags are false.

Receipts: RESULT, STAGES, source bindings. Stage logs are hash-bound in the same evidence directory. Environment: Python 3.11.14, GCC 16, Boost 1.86.0; exact reproduction command is in the README.

This independently reproduces the finite conditional construction. Parent geometry and the stated all-size/compiler, realization, precision/recovery, analytic-transfer and bit-interface obligations remain inherited. No new κ construction, novelty claim, or change to the selected certificate. Credit to Rohan Arun, Jeremy Kothe and the retained lineage.

[Mister-Meeseeks]

100-PR batch review at 4abf710a7f0d2a46f522f3f13c15769d003f9495.

This remains open after scoped triage. Next review step: Supplier-family review pending: bind native local replay, physical owners and complete admission; reconcile overlapping historical package versions.

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.