T-183: Mykhailo Polkovskyi's certificate for 237 squares, the smallest known side there when registered

S3 V3 C3 Upper bound confirmed superseded by T-190

2026-10-13 published · Polkovskyi after Friedman, Daniel, Xu, Chaoweeraprasit, Barnett, Couzo, Ostashev, Ellsworth, Fang, Levy · $n=237$$n=237$

One complete rational source certificate reports a finite upper-bound improvement at the exact side it states: $s(237)\le 15.902705057866366799436476453482$$s(237)\le 15.902705057866366799436476453482$.

All nine retained jobs, three certificates with their 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 this entry cites 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 author's runs of this repository's sqpack verifier, from copies outside the pinned tree, are his and decide nothing here, so the replay is independently re-implemented. The 14 October review found no blocking defect.

The author reports that Daniel's verify_cert.py and verify_cert2.py and this repository's sqpack/verify.py, run from copies outside the pinned tree, accept all 73 certificates with zero tolerance in 219 runs taking 43.9 seconds. Those statements are the author's; no source program ran here.

Credit Polkovskyi (Mishapolk), as he asks on the issue, with the certificate at 237. The issue's lineage column, headed 'Lineage / Baseline Holder', names Couzo's issue 561 (itself a continuation of Chaoweeraprasit's SQUISH packing) as the baseline at 237; it does not call the 237 a refinement, as it does at 146 and 261. Measured pose by pose by the 14 October review, the 237 is Couzo's issue-561 design moved, every square paired one to one, 63 moved beyond 1e-03 and seven beyond a tenth: another arrangement of that design.

The issue claims all 73 as beating or tying every standing and pending record; measured here, 13 of the files are byte for byte certificates by Daniel (70, 102, 123, 269, 292, 295) and Couzo (105, 108, 127, 209, 267, 305, 306), 40 have the case's exact side, and at 129, 176, 204, 303 and 304 the side is within 1e-30 of Ostashev's earlier issues 562 and 575, at 211 and 241 it equals Couzo's issue-586 certificates exactly, and at 156 and 271 it equals Couzo's issue 561 exactly.

The same review compared the poses: at 211 and 241, where the issue asks to be recorded jointly with issue 586, its certificates are issue 586's pose for pose, at 241 all but one square, which lies 1.9e-04 from issue 586's, and both are exact re-solves of Couzo's issue-583 arrangement, first committed at 13:53:57Z on 13 October, two hours before the issue's first commit of its 211 and 241 at 15:51:54Z; issue 586's commit followed at 17:30:53Z. Identity of poses is what was measured: two exact solves of one contact graph from one start give the same poses, so it establishes no copying, and the owner decides the joint credit. The source discloses Gemini assistance with solver scripting, precision checks and formatting.

On 15 October 2026 the case record at 237 adopted this entry as its house, its reported and verified upper bounds moving together and Couzo's certificate (T-140) kept as history, with T-161 verified and not selected; private-worker custody was closed in the same change (packing/devtools/house-custody-2026-10-11.json).