Conditional κ = 0.001292099559442278: R715 shared kernel, target mixing and whole hosting

[chafreaky]

Conditional κ = 0.001292099559442278, exactly 646049779721139/500000000000000000, 1.4180932604% above #458. The bit side binds; the paid-adapter complex supplier is unchanged.

Starting from #463's published R715 word, reconstruct 109 shared-donor pivots (entrance rank 120), 56 disjoint target mixes, 60 single-gate retimings and #467's 14 paired retimings. Pool eight replicas, keeping each of the 62,920 residual occurrences whole on one idle physical family. The exact bit lower endpoint is 0.001293771240692396056124, with 9,600 live and 9,609 physical families.

The physical-family growth bound is recomputed independently. Its 804-bit prefix is charged at 832 bits, and the 2,468-bit three-level coefficient at 2,496 in every bootstrap cutoff. The bit row coefficient remains 19,431, below the retained 20,161 contract.

Verification covers exact reconstruction; all local and unbanked global columns; fresh C++ legality and eleven-stage columns; record and mixing mutations; Gram matrices and target labels; residual isometries and projectors; every owner, window, slot and remainder; the renamed instruction stream; physical-prefix accounting; both rational moment engines; six bootstrap steps and all 47 strict outer inequalities. Adjacent-grid and invalid-parameter controls are rejected.

Release evidence includes a full Linux replay and a macOS component replay with an explicitly reused, freshly completed and manifest-matching Python 3.11 full parent. The entire final RESULT.json matches across platforms. All 16 repository joint tests pass. GitHub CI remains separate and pending.

Run E8_REPLAY_PHASES=1 python -B research/e8-r715-whole-hosted/verify.py /absolute/new/output. Default mode replays the complete corrected #458 chain. Explicit --parent-output reuse emits a distinct receipt status. Source hashes, proof, receipts and Python 3.11/3.14 CI are included.

All inherited compiler, mutable-basis/target-label, whole-call correlated-helper hosting, compressed-window, restored-work, common-grid/tape, precision, row and analytic contracts remain. No residual is split across physical families. This is a conditional finite composition; κ = 1, global optimality and an unconditional multiplication theorem remain unproved.

Credits: DreamingOfClouds with Claude Opus 5.5 for #463's carrier/XOR word and target mixing; Rohan Arun with OpenAI Codex for #462 pooling/prefix accounting and #467 paired retimings; DaysSky for whole hosting; chafreaky for the shared-donor lineage, target-label audit and #458 paid complex supplier; Jacob Sussman, Dylan Crow, Zhihao Chen, eumemic, icekylinx and all inherited authors. New selection, integration and release by chafreaky with OpenAI Codex. Original sources, notices and licenses retained.

[Mister-Meeseeks]

Thank you @chafreaky. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: R715 kernel and target mixing under whole hosting.

Review and limits: The actual local word, residual routes, global ownership and invoice are priced together. Preserve the original all-size realization and hosting conditions.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: 259c68488b7aa8a14cf3fcae7fc499381c9bf729. Publication: 64039f1bd3b6a523b96083fd858ad040a75e3030.