T-254: Couzo's new packing of 130 squares from PR #574's, 2.05e-3 below T-174

S3 V3 C3 Upper bound confirmed superseded by T-259

2026-10-27 published · Couzo after Chaoweeraprasit, Gupta, PingYou Ltd, Levy · $n=130$$n=130$

One complete rational source certificate reports a finite upper-bound improvement at the exact side it states: $s(130)\le 466915711841738962256077475351530705109199164124122993/39228601764570445403995003040207131754000000000000000$. It is 2.05e-3 below the case's house best packing, PingYou Ltd's certificate of Chaoweeraprasit's packing (T-174), and below every earlier report at 130.

The certificate and its duplicate-square and outside-container controls were decided here on 31 October 2026 by both maintained exact routes. Those routes share components with the producer: the sqpack route decides through sqpack/verify.py, the checker the source's manifest names first, and both read the certificates through the evand-cert reader. The 31 October review decided it again on a clean-room checker of its own, by separating axes and by exact clipped areas with ten controls, by a Claude agent, a system family the producer also used, and found no blocking defect, so the bound is confirmed, independently re-implemented.

Polkovskyi's issue 846 re-solves the same arrangement 2.08e-12 lower (T-259), and the case adopts that certificate under the house rule, with this packing's credit.

The issue says both of the source's exact checkers accept the certificate in exact rational arithmetic: verify_bound_certificate.py, Daniel's MIT separating-axis verifier with modifications by Couzo with Codex, byte-identical to the copy the issue-678 packet retains (valid and strictly valid, 1,624 candidate pairs), and exact_finish.py, an exact corner replay; both read the same certificate format. The source's commit of 27 October says the packing was read from a database salvaged after a host crash of 26 October and ends with a Co-Authored-By trailer naming Claude; the issue says Claude did the certification, the comparison and the report at the author's direction. Those statements are the author's; no source program ran here.

Credit Couzo (https://github.com/franciscouzo/square-packing), after the packing his searches started from, PR #574's at 130: found by Chaoweeraprasit (itsnaka), improved by Gupta and PingYou Ltd, as the issue asks. The issue says thirteen successive improvements of his live searches of 24 and 25 October took the side from 11.904483032516 to this one, ten by the web app's fq quench (a browser adaptation of Daniel's fq optimizer), two by its basin hopping and one by native SLP, all on his own computers, and that matched one to one against PR #574's packing the largest move is 0.704, 11 squares move beyond 0.1 and 26 beyond 0.01, so it calls it a new packing found from #574's.

A Kaggle per-puzzle side the issue quotes, 11.902430646006 for the team Cats and boxes, states no packing and is no report.