Conditional κ = 0.001343518018117309: retimed gauge word with pooled whole owners

[chafreaky]

This composes #495's main-word frame retiming with #484's gauge80-kernel42 word and #496's pooled whole-owner placement. The source-bound certificate gives conditional κ = 0.001343518018117309, with complex saving b = 0.001345325487149526878087 and freshly rebuilt #493 bits. It improves #496's value by 0.8589% under the retained whole-owner interface.

The transfer changes 224 A-event frames and 504 B-event frames while preserving scalar operations, all 122 helper entrances, target levels and centre chains. All 40,320 whole helper roles fit on 7,680 data families, with 8,258 physical families and no banks. No residual is split across physical families. Both exact moment engines, the complete physical invoice, prefix bound and all 47 strict outer inequalities are reconstructed from the resulting program.

The package vendors #496 unchanged, including its #484/#493 dependencies; all 297 upstream source files were compared with pinned Git bytes. New checks rebuild the retimed program, verify common labels and every local operator instance on 512 columns, run the complete program on 806 basis and eight dense inputs in both orientations, and enforce Python-integer bounds before fixed-width arithmetic. The attributed M8 control copy selects an available outside-centre frame in the changed catalogue; the same violation and all 14 controls remain mandatory.

The inherited all-size compiler, mutable-basis, common-label, restored-row, precision/tape, analytic-transfer and Lemma A spectator-realization contracts remain conditional. This is not an unconditional multiplication theorem, a Lean proof, or κ = 1. It makes no claim under #448/#494's different split-residual interface.

Direct credits: aliromman (#495), DreamingOfClouds (#484), eumemic (#493/#496), and the source authors retained in the vendored notices. Prepared by chafreaky with OpenAI Codex.

Validation: the complete fresh verifier passed on macOS and Linux with Python 3.14.8 and real Boost. All 24 root stages passed on each platform; complete RESULT.json bytes match (4a951fc558757d045f8296b4014e4be71553ac7514a4d996d4bf0232ebefec5f). Receipts and source-byte verification are in research/e8-retimed-pooled-validation/. CI is configured for Python 3.13 and 3.14; no CI result is claimed before it runs.

Concurrent frontier: #501 appeared immediately before this publication and reports the same κ and global paid profile. This PR matches that reported whole-owner result through the explicit #495-to-#484 frame transfer above; it does not claim to exceed #501 or to have independently replayed that package.

[Mister-Meeseeks]

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

Contribution: Retimed gauge word with pooled whole owners.

Review and limits: Keeps normalized spectators and complete whole-owner semantics. Parallel equality with PR501 is credited without treating numerical equality as an independent full replay.

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: 4d30b8322184598e65e90a92389e17e1baedd9eb. Publication: 64039f1bd3b6a523b96083fd858ad040a75e3030.