[rohanarun]

Conditional κ = 0.001289283116193775, 0.45219346286431% above PR465. A fresh shared-donor kernel and retiming on PR463's R715 word, with four-replica whole-residual hosting and PR458's unchanged complex supplier. The bit side binds.

Submitted first as a projected draft; the changed physical component, fresh finite invoice and exact outer assembly now pass. Complete changed-component wrappers pass on Python3.11 and3.14, each reusing its own completed full PR458 complex replay. Their receipt status explicitly distinguishes completed-parent reuse from a fresh default full run. The fresh default full Python3.14 replay also passes (PASS_FULL_R715_KERNEL_POOL_COMPOSITION), rebuilding the pinned complex supplier and all changed bit checks. Receipt and stage logs are in research/r715-kernel-pool-validation/python314-full/. GitHub CI is separate and is not claimed passed; this remains a draft.

The construction uses99 kernel pivots, entrance rank118,56 target-prefix receivers,60 single-gate retimings and14 connected-pair retimings. All31,460 helper residual occurrences stay whole on one physical family. Four replicas use4,800 live /4,809 physical families. No cross-family residual splitting is used. The actual final word and every frozen selection are included; the word is reconstructed independently from PR463's published pre-kernel source.

The new physical-family growth envelope takes604bits and is charged640; the three-level coefficient takes1864bits and is charged1920. The prior529/1664-bit charges are not reused. Fresh routing and selector work is included, and the full row coefficient is19428<20161.

Checks passed:

• Exact reconstruction, rational source spans and all955 local columns; official legality,1195 five-stage and1915 eleven-stage formal columns; six record corruptions and24 omitted-bridge controls rejected.
• Twelve coordinate-permutation residual isometries,959 exact frame projectors and3395 nested/reflected projector pairs;1320 geometry routes and every whole owner/window/remainder.
• All9065 unbanked global columns;859100 emitted instructions; independent ownership, profile and physical-prefix recomputation;22 global mutations rejected.
• Both rational moment engines, fresh invoices, six bootstrap levels,47 strict outer inequalities, adjacent-grid and invalid-parameter controls.

Exact bit lower:645473756513106438971/500000000000000000000000. Complex lower:1297203880559577927527/10^24. Final κ:51571324647751/40000000000000000.

Reproduce: python -B research/r715-kernel-pool/verify.py /absolute/new/output. Default runs the full pinned complex supplier before the new bit checks. --complex-output explicitly reuses a completed full complex receipt and emits a distinct status. Python3.11/3.14 CI, source pins, proof, manifest and local receipts are included. verify_component.py remains a narrower arithmetic screen and is not full admission.

The first local GCC build failed on SDK configuration (stdlib.h missing); retained failure and successful compiler receipts are published. The complex replay retains PR460's metadata-only portability adapter for two non-proof floating report fields, without changing pinned sources, operators or exact reconstruction checks.

The complete-call correlated-hosting, compiler, mutable-basis/target-label, compressed-window, restored-work, common-grid/tape, precision, row and analytic interfaces remain conditional. No unconditional multiplication theorem, new Lean proof or global optimality is claimed.

Credits: DreamingOfClouds with Claude Opus5.5 for PR463's carrier/XOR word and target mixing; chafreaky and PR417 for shared-donor packing and exact engines; DaysSky for hosting; chafreaky for PR458's complex supplier; Jacob Sussman, Dylan Crow, icekylinx, eumemic, Zhihao Chen, Henry Grant and all inherited contributors. New selection, retiming, four-replica pooling and integration by Rohan Arun with OpenAI Codex. Licenses and notices retained.

Full-run portability update: the first default invocation encountered inherited shell splitting on the SSD path containing spaces. The wrapper now supplies the existing pinned PR460 shell-path adapter and Boost header location. The repaired Python3.11 complete component wrapper passes with its completed full complex supplier. The repaired default full Python3.14 run now passes; the initial failure and all receipts are retained. No proof data or bound changed.