Conditional κ = 0.001676377648122875: pivot-531 helper-donor cold kernel composed with multi-donor idle 48+48 to 45+51 exchanges on the global mixed X54 fusions word

[jeremykothe2]

Summary

Conditional κ = 0.001676377648122875. Composes two independent finite improvements on PR1218: (1) an exact helper-donor cold kernel for pivot 531 (profile H1 -3, H3 +1 per call in both providers, one exact tail-gate cleanup correction, both words pass fresh native replay) and (2) multi-donor idle rank-48 pair exchanges 48+48 -> 45+51 applied to the emitted hosted directory (idle overlay, independent overlay verifier, patched audit/assembly). Plan and SPEC re-bound and re-frozen through the unchanged discovery path. Strict admission gives kappa 0.001676377648122875.

Verification

Fresh checkout of 66da60e0119424fe60b7b0fa2526f5d1dad2fcea. Manifest: 116563b3fab5abb174b57935dc1391f369b0b9668c1a645470c78079d1e9d1f6.
PASS package manifest: 99 files

Fresh native replays of both provider words (phases step edge-parallel, byte-identical output; with --native-cache a word whose hash-checked completed replay is cached reuses it), then the package's own verify.py (literal words, independent local audit, fusion/X54 controls, leaver premise, literal construct, strict global admission): PASS_GLOBAL_MIXED_X54_IDLE_EXCHANGES_NATIVE_AND_STRICT_ADMISSION 0.001676377648122875

Full package-owned verification passed in 193.08 seconds. The fresh receipt binds the exact package manifest and score.

See research/gmx-k531-idle3/README.md for reproduction commands and proof qualifications.

Credits

Builds on PR1218 (rohanarun, global mixed allocation with X54 and fusions), PR1193 (jeremydiviney, mixed T37 owners and allocation), PR1148 (Thomas DiFiore, joint k8 entrances), PR1195/PR1196 (source-holder fusions and the X54 slot), PR1252 / PR1268 idle pair exchanges (Gonzalo-Mier method, applied by ReplaySpeed/oh-my-pi), PR1207 and the retained cold-kernel lineage (PR564/PR571). Research direction, prioritisation and release strategy: jeremykothe2. Implementation assistance: oh-my-pi.

[jeremykothe2]

Closing: this result is invalid. Its idle-overlay step moves axes between idle children of different (pair, side) families. The retained DATA-PHASES recipes (data_phases.py, exact_child) fix each family's Z4 multiplier, and every changed child here alters its family's multiplier, so the claimed κ is not supported. Thanks to rohanarun (#1286) for flagging the overlay problem. The overlay mechanism inherited from #1252 has the same issue. Our overlay-free results (#1261, #1274) are unaffected.