Conditional κ = 0.001325117552367841: moment-directed complex hosting

[chafreaky]

A different whole-residual packing of #484's unchanged complex gauge/kernel word raises its saving from 0.001326789535340266 to 0.001326875818805153. With #493's freshly replayed R489 bit supplier, the conditional assembly is κ = 0.001325117552367841, +0.00649456% over the #484/#493 pairing. The complex side binds.

All entering helpers now fit on data families. The 66 remaining banks contain only width-nine helpers, so their pads have rank one. Live stock stays 7,746 and physical stock stays 8,324; the largest paid complex child drops from rank nine to rank eight. The profile change is exactly +66·rank1 −528·rank5 +528·rank6 −66·rank9. The proof shows this improves the complete charged moment for every saving in (0,1). No local scalar gate, frame, phase, wrapper, or global schedule changes.

python -B research/e8-gauge-moment-hosting/verify.py /absolute/new/output freshly runs #484's complete --all verifier and #493's full verifier with real Boost arithmetic, then the new packing, the unchanged hosting audit, an independent integer count check with five rejection controls, both rational moment engines, the finite invoice, and all 47 strict outer inequalities. Fresh macOS and Linux runs pass with identical deterministic results. The inherited source packages are byte-identical to their published commits; 277 source/manifest entries were checked against staged Git blobs. CI is pending.

Use Python 3.13 or 3.14: the unchanged #484 receipt compares gzip byte hashes that differ on 3.12 and 3.15. Raw timing-dependent parent hashes remain in the receipts; only the inherited geometry timer is excluded from the deterministic bit-template fingerprint. Optional SciPy discovery is separate from verification, and no optimality claim depends on it.

This retains the parents' conditional all-size compiler, mutable-basis, whole-owner hosting, restored-work, and analytic interfaces. It does not adopt cross-copy routing, claim an unconditional theorem, or change main's selected result. κ = 1 remains open.

Credits: #484's gauge/kernel word and pipeline, #493's source-carrier bit word, #442's hosting, #458's whole-owner rule, and their source-pinned predecessors. Chafreaky with OpenAI Codex assistance; upstream notices and licenses are retained.

[Mister-Meeseeks]

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

Contribution: Moment-directed whole-owner packing.

Review and limits: Same local program, new actual owner map and smaller largest child. Exact profile comparisons establish the gain; no global packing optimum is claimed.

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: b1972da7c6d11eb9745273d81bbba3fe9e565e88. Publication: 64039f1bd3b6a523b96083fd858ad040a75e3030.