T-243: Daniel's new arrangement at 182, 3.17e-3 below T-174

S3 V3 C3 Upper bound confirmed

2026-10-25 published · Daniel after Couzo, Ostashev, Levy · $n=182$$n=182$

One complete rational source certificate reports a finite upper-bound improvement at the exact side it states: $s(182)\le 13.970916436214678735385725854133$$s(182)\le 13.970916436214678735385725854133$, 3.17e-3 below T-174, the case's house best packing when it was reported, and below every report at 182.

The certificate and its duplicate-square and outside-container controls were decided here on 25 October 2026 by both maintained exact routes. Those routes share components with the producer: both read the certificate through the evand-cert adapter, whose reader's line filter and corner construction are transcribed from Daniel's own checkers, the ones the certificate names. The 25 October review decided it again on a clean-room checker of its own, by separating axes and by exact clipped areas with fourteen 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.

It is search/packer/candidates/s182-1024.cert in Daniel's watched repository (https://github.com/evand/square-packing), committed on 25 October 2026 at 04:11:15Z and pushed at 04:16:05Z, 19 seconds before issue 806 reported it as 13.970916436215, its side rounded up at 12 places.

Credit Daniel (https://github.com/evand/square-packing), from an L-cut of Couzo's 211 packing (T-188), an arrangement of Ostashev's design (T-175). The issue asks that "the register's $s(211)$$s(211)$ packing (Ostashev; also in Couzo's repository)" be credited as the start; the register's packing at the side the issue gives for it is T-188's, and where T-188 differs from Ostashev's own 211 packing the certificate follows T-188 (M-1 of the 25 October review).

The issue says one L-cut job removed a strip of 29 squares, a row and a column along two walls, and relaxed the rest, and a local search took that to this side. Measured square for square by the review, the 29 squares the 182 do not use are T-188's right column and top row, and of the other 182, 17 move beyond 0.1 (largest 0.464), 156 beyond 1e-2 and 173 beyond 1e-3. Against T-174's packing no symmetry pairs it one to one, so it is another arrangement.

Two Kaggle per-puzzle leaderboard entries the issue quotes state a side and no packing, so neither is a report: Subramanya N's 13.9709164362306 of 24 October, 1.59e-11 above this side and listed before the source's search found the packing, by the issue's account, and Prathamesh Chavan's 13.9727613470647 of 23 October. The source's credits say its work was produced by Claude (Anthropic) under human direction, and the commit carries a Co-Authored-By trailer naming Claude.