Conditional κ = 0.001266564732900111: seven-replica whole-residual hosting

[rohanarun]

Conditional candidate κ = 0.001266564732900111, 0.0022568854297536104% above PR454 at d14eb0dd425bd681e3b43f208d089e679d600176. Complex binds. Submitted as a draft before the full replay, as requested; full local verification has now passed; GitHub CI remains queued.

Pool seven replicas of PR454's eleven-stage complex supplier to remove an integer packing remainder. Every one of the43,120 rank9 helper residuals remains whole on a single physical family;35,840 use an owner in another replica. The local word, all phases and the bit supplier are unchanged. Complex lower is 634085476752554528491/500000000000000000000000, with8,400live/8,978physical families.

This does not use PR448's cross-family residual split. I reproduced PR451's trace obstruction and corrected our PR453's title/body to withdraw its established-gain claim. The previous pooled56 score is affected too. Here whole-family relocation is an ordinary family permutation followed by the owner's coordinate basis; the proof explicitly retains PR442's complete-call correlated dirty-helper contract and allows the owner replica to differ. The invoice charges an additional family-routing factor.

Changed-component checks passed: all43,120owners and idle remainders;1,913,989emitted events;8,520exact phase equalities;1,320routes;24omitted-bridge controls;19mutations; exact whole-family physical routing controls that reject splitting; both rational moment engines; fresh complex invoice; six bootstrap steps and all47strict outer inequalities with next-grid and parameter controls. The one-replica screen exactly reproduces PR454. Larger13/15/17stage screens were worse.

The early component invoice cites the pinned, unchanged PR454 bit supplier; it is not a fresh full-parent receipt. A fresh full PR454 chain has since passed locally. Initial attempts exposed PR436's unquoted paths and a missing NumPy dependency; failures are retained. The package includes a documented external shell adapter for SSD paths containing spaces, with pinned source files unchanged.

Reproduce: python -B research/e8-whole-replica7/verify.py /absolute/new/output. Default runs the fullPR454 chain with phase regeneration. --parent-output explicitly reuses an existing full receipt and emits a distinct component-reuse status. See research/e8-whole-replica7/PROOF.md for the argument and scope.

All inherited compiler, restored-work, compressed-window, tape/common-grid, precision, row and analytic assumptions remain. No unconditional multiplication theorem or Lean proof is claimed.

Credits: chafreaky with OpenAI Codex assistance (PR451/454 templates, audits, source pins and cross-family obstruction); DaysSky (PR442 hosting), icekylinx (PR433), Zhihao Chen and all inherited contributors. Seven-replica selection/composition by Rohan Arun with OpenAI Codex assistance. Licenses, notices and source pins retained. This branch starts from the pinnedPR454 head so its unchanged supplier packages remain directly reproducible.

Concurrent work: PR455, read after this submission, independently uses whole-residual pooling with eight replicas and a bit-program portfolio. Its reportedκ0.001266541949425315 is below this seven-replica candidate by 0.001798872%. No exclusive discovery or priority claim is made. A tighter solver follow-up gives the same normalized endpoint at7,14,21,35and56replicas; these are scoped searches, not a global optimality theorem.

Verification update: the fresh completePR454supplier chain now PASSes locally onPython3.11.15. The publishedPR456wrapper then PASSed all changed checks against that completed parent, with the explicit PASS_WHOLE_REPLICA7_COMPONENT_PARENT_REUSED receipt. Both receipts and logs are published separately in the validation directory. The fresh full Python 3.14.8 wrapper also PASSed (PASS_FULL_WHOLE_REPLICA7), including the complete parent chain and regenerated phases. Its receipt and all step logs are published in the validation directory; CI remains queued and separate. The proof package is unchanged.