Conditional κ = 0.001635749838057164: two factored cold ends on the K492 supplier

[jeremydiviney]

Change

End two additional jp8 helpers early by factoring their cleanup, then repack the smaller residuals. This raises the conditional integer-multiplication saving from PR623's κ = 0.001635490664920455 to 0.001635749838057164, exact 408937459514291/250000000000000000. The conservative value is 0.001635749835187059.

Raw helpers 590 and 581 (helper indices 366 and 357) now end at a dimension-7 frame instead of FULL. For each helper, a free rank-zero premix and dead-port absorption permit a three-gate tail: combine two data registers with an accumulator at dimension 4, then read that accumulator once at dimension 7. The combined exact local paid-profile change is {1:+2,2:+2,5:−2}, and each helper's width falls from 9 to 7. Across the unchanged jp8 ×64 / ck ×8 dispatch, this frees 256 units of owner capacity. The combined supplier and literal owner map are invoiced and certified together.

All 23 inherited code files and verify.py are byte-identical to PR623. The existing cold_end constructor admits the new declarative recipe; no verifier rule is weakened or extended. FACTORED-END.md gives the exact gates, dual-row correction, cleanup argument and inherited interfaces. The deterministic construction and owner-map exporters reproduce the committed inputs from pinned PR623.

Dependency: PR623 at e39a615ca601ce5d62abeb24f3fcdb8644ca1005, using PR622's K-triangle supplier construction and all earlier credited work. PR623 and the preceding K-triangle chain were merged during preparation; this branch preserves their original commits. Our change is confined to research/complex-571-cold14-k492b/ and its two sibling audit directories (the single-helper evidence is retained as historical provenance). It does not change the repository's selected certificate.

As checked immediately before submission, main selects the newly merged #626 at 0.001635527380375392. This candidate is higher by 0.000000222457681772 (about 0.0136% in κ). This comparison is time-specific, not a claim of lasting priority.

Validation

• Fresh strict default-SPEC replay: 64/64 stages pass, 471.5 seconds, with no reused baseline or provider outputs. All 51 receipt artifacts and 64 raw stage logs were independently hash-checked against the final package manifest.
• The unchanged audits reject 23 owner mutations, 114 assembly mutations and 38 cold-end mutations. Both exact moment engines, the conservative calculation, strict outer constraints, native/reflected programs, wrappers, exact phases and generated-identity controls pass.
• Fourteen additional corruptions aimed specifically at the two new helpers all reject under the unchanged native auditor; the positive control passes. A portable runner and raw logs are included.
• Exact recipe/word and owner-map reconstruction passes; both exporters refuse optimized Python before output. All 23 inherited code files and verify.py remain unchanged.
• Full make verify passes on the pinned PR623 base, including gen4-bank-verify, the selected frontier617 replay, all 84 isolated test modules and patch applicability. All shared infrastructure is unchanged. The contributed package is separately verified by the fresh replay above; the audit identifies both scopes and retains the complete root-suite log.

Final source review corrected an outdated auxiliary WITNESS recipe hash; SPEC already pinned the correct recipe. EXPECTED and the manifest were rebound, and the complete replay restarted in a new directory. The final recursive source comparison verifies WITNESS/EXPECTED/SPEC correspondence. No circuit, owner map or κ changed.

The checked-in generic witness-spec-tools/spec.py does not support the predecessor's newer construction steps and rejects unchanged PR623 identically. We make no generic-verifier pass claim; the unchanged package-specific official verifier supports those steps. The audit records this limitation, exact hashes, raw logs, source comparison and search provenance.

Scope and credit

This builds on DreamingOfClouds' cold-end construction, jeremykothe2's extensions and K-triangle supplier, and all predecessors preserved in NOTICE. The two factored extra ends, dual-row correction, deterministic generators, owner repacking and contributor validation were prepared by Jeremy Diviney with OpenAI Codex assistance. This follows our earlier owner-repacking contributions #618 and #624, both merged and credited in the K-triangle integration review.

All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape/exact recovery, analytic transfer and bit H1–H5 assumptions remain. The cited PR543 bit supplier is repriced, not rebuilt. This is finite conditional contributor evidence awaiting independent review, not an unconditional theorem, full Lean proof, optimal packing or practical speedup.

Current construction: research/complex-571-cold14-k492b/. Current audit: research/complex-571-cold14-k492b-two-factored-audit/. The older single-helper audit is explicitly historical; the final two-helper inputs and fresh evidence supersede it.

Verified contribution commit: f95308a9afa5adc071fe75c8cd7feec172503d4f. Exact construction and reproduction; final validation receipt.

[Mister-Meeseeks]

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

Contribution: Two factored dimension-seven cold ends on K492.

Review and limits: The existing typed constructor and verifier are unchanged; exact premix, tail and owner changes are priced together. One-helper historical receipts are superseded by the final two-helper witness.

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: f95308a9afa5adc071fe75c8cd7feec172503d4f. Publication: 64039f1bd3b6a523b96083fd858ad040a75e3030.