Re-instantiated phase-stop on the p = 11 paired cubes: conditional κ = 5.108294e-4

[geckods]

Conditional improvement

$$T(n)=O\big(n(\log n)^{1-\kappa}\big),\qquad \kappa=\frac{2554147}{5000000000}=\mathbf{5.108294}\times10^{-4}.$$

Stacked on #152 (ae9baba, eumemic's paired cubes at p = 11 with the h = 21 bit word). Please review/merge that dependency first; its changes are not claimed here. The only files of this branch are research/paired-cube-p11-tightened/ (README, verifier). The branch carries a single squashed commit on top of main because the push credential lacks workflow scope; relative to #152 the diff is exactly those two files.

Change

One assembly instantiation constant is re-chosen. #152 inherits the merged #144 value PHASE_STOP = 1/10^6; the phase-stop beta is a free positive constant of the retained assembly (it enters only the (1-beta)*AC - 10^-10 ceiling term and the 47 strict inequalities). #152's complex side binds (AC = 5113520/10^10), so the ceiling moves directly onto kappa at the grid:

	phase-stop	kappa
#152	10^-6	5108289/10^10
this branch	10^-12	2554147/5*10^9

The same re-instantiation, at the same constant and for the same reason, is the move of #104 over #97 and of #135/#137/#138. No word, plan, row, bridge or interface changes; every inherited interface remains an assumption exactly as in #152.

Verification

python3 research/paired-cube-p11-tightened/verify.py (stdlib, ~1 min): reproduces #152's published 5108289/10^10 exactly at the inherited constants, then rebinds PHASE_STOP to 10^-12 and reruns #152's own 47-constraint assembly: kappa = 2554147/5000000000 with the next 10^-10 grid point rejected, 47 strict constraints and 7 margins.

Credits

• eumemic: Paired cubes at p = 11 with an h = 21 bit word: conditional κ = 5.108289e-4 #152 (p = 11 instance, h = 21 word) and Deferred bit word and a 28,705-role complex producer under stopped-product accounting: conditional κ = 1.044939e-4 #117, with Anthropic Claude assistance.
• icekylinx: Paired cubes and shared completed cores for conditional kappa = 4.609169e-4 #144/Three-stage Cayley covers for conditional kappa = 3.146011e-4 > 2^-12 #130 (paired cubes, shared cores, assembly).
• Zhihao Chen (Deferred endpoints and signed phase correction for a conditional 63965813/10^12 > 2^-14 bound #97), Swapnil Jain (round-seven checkers), an664 (Completed-core sharing: conditional kappa > 2^-13 #128).
• Re-instantiation and this package: Abhinav Ramachandran with Hermes (Nous Research) assistance.

Conditional; no unconditional multiplication theorem is claimed.

[ploniaaaaaaa]

wow

[Mister-Meeseeks]

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

Contribution: Phase-stop tightening on the pinned PR152 construction.

Review and limits: Fresh unchanged patch replay on parent ae9baba; standalone checkout intentionally lacks that dependency. Historical parameter witness, not a new network.

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: 4ead11e6e10cc7f13a340563990f50f86cc2668b. Publication: 50d768818f579d4e165b4c257c6ee25bca300802.