T-171: An exact contact refinement of SQUISH's packing of 272 squares

S1 V3 C3 Upper bound confirmed superseded by T-174

2026-10-12 published · PingYou Ltd after Chaoweeraprasit, Daniel, Levy · $n=272$$n=272$

One complete rational source certificate reports a finite upper-bound improvement at the exact side it states: $s(272)\le 1696558647483767063575600703342204556962987576825904423514291493830293022275118026464939778830359993334240647227/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000$.

All three retained jobs, the positive with its duplicate-square and outside-container controls, were decided again here on 14 October 2026 by both maintained exact routes and equal their retained rows. A third exact route, half-extent containment and exact intersection area, decided the certificate with six controls each and held the derived fact to the pinned file it is derived from, fetched at the pin. No route here is the source's code; the source's runs of this repository's two maintained routes on its corners witnesses are its own and decide nothing here, so the replay is independently re-implemented. The 14 October review found no blocking defect.

The author reports that exact separating-axis and rational polygon-intersection implementations accept all 272 squares, 1,088 wall conditions and 36,856 pairs, for the new witness, the prior certificate and a pre-stationarity projection, with duplicate and outside controls refused and the conversion to its corners Witness/v2 lossless; and that this repository's sqpack exact_verify and check_rational_witness_independent, run unchanged, accept that witness. Those statements are the author's; no source program ran here.

Credit PingYou Ltd (https://github.com/BuddenPing/square-packing-certificates) with this contact refinement, as the source asks, of Chaoweeraprasit's SQUISH n272 (T-151, issue 500), whose components the source names as SQUISH's $s(240)$$s(240)$ and the former Kingbird $s(182)$$s(182)$ catalogue construction, with Daniel's exact contact solver. The issue states: 'Computation, checking and submission preparation were AI-assisted; the requested attribution is as stated above.' The pinned source makes no statement about AI assistance.

Measured pose by pose by that review, it is Chaoweeraprasit's SQUISH packing (T-151) re-solved, no square moved beyond 2e-07. At 272 PR 574's certificate (T-174) is smaller, by 1.70e-99, and the house rule of 16 October 2026, which lifted the hold of 15 October, made T-174 the house there, and the adoption of 17 October 2026 (think-3mry) moved the case to it. This entry held the case until then, the smallest certificate there that the hold left in.