Connected bit-frame descents on #163: conditional κ = 5.94035602295411e-4

[eumemic]

κ = 5.94035602295411e-4
κ ≈ 5.940356 × 10⁻⁴

Stacked on #163 at e1813796ef5c3ca38c5dd7b9e8d81b3908ff5997. Its fused complex word, balanced transfer and inherited construction are prerequisites, not contributions of this change.

This adds 168 connected operation-frame descents to #163’s p12 bit word, giving 1,464 total descents and 1,056 distinct bases. Moving equal-frame operations together permits improvements blocked by individual gate moves. The scalar word, gauges, persistent role count and complex supplier stay fixed; the complete paid bit histogram is recounted.

The conditional bound rises from #163’s κ ≈ 5.939702 × 10⁻⁴ by 6.539922 × 10⁻⁸, or approximately 0.01101%. The bit coarse saving becomes 5.947193 × 10⁻⁴. The paid atom exponent is re-instantiated for that supplier, and the bit side still binds.

python3 -B research/paired-cube-bit-descent/verify.py

Validation covers:

• Exact frame containment, nondegeneracy, physical chains and the complete paid rank profile.
• All source, target and arbitrary-dirty columns over F₂, plus equality with the defining integer decoder.
• Exact Gram determinants for all 1,056 bases. Some determinants exceed 2^80 in magnitude, but complete factorization shows every prime divisor is at most 31; every retained prime q > 2^80 remains valid.
• Strict paid moments, the full finite bridge, all 47 assembly inequalities and seven margins, with the next certified κ grid point rejected.

All source-specified all-size interfaces and conditional scope of #163 are retained. This is a finite conditional witness, with no global optimality claim.

Credits: #163 was prepared by Chafik Boukhalfa with substantial OpenAI Codex assistance; its #161 dependency is eumemic’s work, building on icekylinx’s paired cubes and the credited frame, reuse, shared-core, bit, atom-toll and layout lineage. Those notices and disclosures remain intact. This extension was prepared by eumemic with substantial OpenAI Codex assistance.

[Mister-Meeseeks]

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

Contribution: Connected operation-frame descents on the PR163 bit word.

Review and limits: Fresh complete finite verifier passed. Exact Gram factor witnesses, rather than a crude determinant-size shortcut, control eligible primes.

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: 4391a60bb26f75ea47a4c55c508c88a036b5a2b8. Publication: 50d768818f579d4e165b4c257c6ee25bca300802.