Conditional κ = 0.001274494971185576: four-replica whole bit hosting

[rohanarun]

Conditional candidate κ = 0.001274494971185576, 0.006235410670839051% above #460. Pool four replicas of #459's unchanged bit word when assigning whole helper residuals to idle data families; retain #458's complex supplier unchanged. The bit side binds.

Submitted first as a draft before full replay. The default full Python3.14.8 replay has now passed, including the repaired full PR460 supplier chain and every changed pooling check. Receipts are published in research/bit-whole-pool4-validation/python314-full. GitHub CI remains separate.

Each of the32,560 residual occurrences stays whole on one physical family. The owner may be in another replica, and every owner remains idle throughout the required window. There are no split residuals or helper banks. Four replicas use4,800 live /4,809 physical families. The exact bit endpoint is 1276121381468881130487/10^24. Eight and sixteen pooled replicas reached the same normalized endpoint in the scoped screen; this is not a global optimality claim.

The ownership change requires a new register-growth bound. The emitted physical-family chronology and a separate audit give a529-bit cancellation-free prefix, charged576bits. The three-level coefficient takes1640bits, charged1664bits in the bootstrap cutoffs. The previous192/1024-bit charges are not reused. Two extra routing factors per helper selector are charged. The complete row coefficient is19428, below the retained20161 contract.

Passed changed checks: official unchanged-word records/columns; all9,340 unbanked scalar columns;1,320 geometry routes;18 residual isometries;3,407 exact nested/reflected projector pairs; all owners, idle windows and remainder children;860,464 emitted events;24 omitted-bridge controls;22 ownership mutations; independently recomputed physical-family prefix; both exact moment engines; fresh bit invoice; six bootstrap steps and all47 strict outer inequalities plus controls. The complex supplier is initially cited from pinned #458 evidence.

Reproduce: python -B research/bit-whole-pool4/verify.py /absolute/new/output. Default runs the full #460 composition before the changed checks. Explicit --parent-output reuse of a completed full parent emits a distinct receipt status. Source pins, proof, receipts and Python3.11/3.14 CI are included.

The whole-call correlated-hosting, compiler, mutable-basis/target-label, compressed-window, restored-work, common-grid/tape, precision, row and analytic assumptions remain. No unconditional theorem, new Lean proof or cross-family splitting claim is made.

Credits: Rohan Arun with Claude Opus5.5 for #459's bit word; chafreaky with OpenAI Codex for #458's complex supplier and inherited audits; DaysSky for hosting; DreamingOfClouds for target mixing and solver extensions; icekylinx, eumemic, Zhihao Chen, Dylan Crow, Jacob Sussman, Henry Grant and all inherited authors. Four-replica selection, physical-prefix audit and composition by Rohan Arun with OpenAI Codex. Licenses and notices retained.

Verification update: the original PR460 full run stopped at PR458's non-proof discovery-float metadata comparison after its full PR454 chain passed. This draft now pins PR460's documented metadata-only portability repair; no pinned operator or exact check is changed. The exact kernel reconstruction passes with that normalization. The repaired full Python3.14.8 replay has now passed; the original failed run remains retained.