T-259: Polkovskyi's re-solve of Couzo's packing of 130 squares, 2.08e-12 below T-254

S1 V3 C3 Upper bound confirmed

2026-10-30 published · Polkovskyi after Couzo, Xu, Daniel, Ostashev, 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 11.902430645982265758612919640554$$s(130)\le 11.902430645982265758612919640554$, 2.08e-12 below Couzo's certificate of issue 843 (T-254), the same arrangement, and 2.05e-3 below the case's house best packing when it was reported, T-174.

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: both read the certificate through the evand-cert reader, whose line filter and corner construction are transcribed from Daniel's checkers, the family of the source's verify_bound_certificate.py. The 31 October review decided it again on a clean-room checker of its own, by separating axes and by exact clipped areas with seven mutants at contact and 1e-60 past it, and found no blocking defect, so the bound is confirmed, independently re-implemented. The issue does not say what its Antigravity Autonomous Research Lab is, so whether the reviewer's system family overlaps the producer's is not known.

The issue says the certificate is valid and strictly valid under verify_bound_certificate.py --strict, Daniel's MIT separating-axis verifier with Couzo's modifications, byte-identical to the copy the issue-678 packet retains, with least wall and pair clearances of 9.66e-15 and 1.82e-14. Its header calls it a dilation, by dilate_cert.py with delta 2e-14, of isolated_lab/tmp_couzo_noalm.txt, and the issue says it beats Couzo's issue 843 by 2.08e-12. Those statements are the author's; no source program ran here.

Credit Couzo's packing of issue 843, found from PR #574's, and Polkovskyi (Mishapolk, https://github.com/Mishapolk/square-packing-records), with what the issue calls the Antigravity Autonomous Research Lab, for the re-solve, as the register credits a regularization. Measured by the 31 October review, it has Couzo's contact structure within 1e-9, 304 near-contact pairs and 38 wall contacts each; Couzo's pair gaps of about 2.16e-13 become about 2e-14, about ten of them making the 2.08e-12, and 14 squares move beyond 1e-9, the largest by 1.13e-6 (RV-6). The issue's six other counts are T-260's and the eight it reports beyond them are not recorded (T-260 names them).