T-248: Daniel's new arrangement at 299, 1.92e-2 below the catalogue's construction

S3 V3 C3 Upper bound confirmed superseded by T-258

2026-10-26 published · Daniel after Deotte · $n=299$$n=299$

One complete rational source certificate reports a finite upper-bound improvement at the exact side it states: $s(299)\le 17.803695435332337695435314533642$$s(299)\le 17.803695435332337695435314533642$, 1.92e-2 below the case's house best packing, the Kingbird catalogue's 33/2 + √7/2, which is 17.8228756555…, as T-101's exact ceiling verifies it, and below every report at 299.

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 own checkers, the ones the certificates name. The 31 October review decided it again on a clean-room checker of its own, by separating axes over every pair and by exact clipped areas with ten sharp controls each, 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 recorded only: the 29 October update's certificate (T-258), which continues this packing, is 2.46e-3 lower, and the house rule adopts that one.

It is search/packer/candidates/s299-1025.cert in Daniel's watched repository (https://github.com/evand/square-packing), committed on 26 October 2026 at 03:30:38Z, 21 minutes before issue 824 reported it as 17.803695435333, its side rounded up at 12 places.

The certificate's header calls it a dilation by dilate_cert.py, delta 1e-12, of the binary64 packing s299-1025.input.txt, side 17.803695435314534, and names verify_cert.py, byte-identical to the copy the n183 packet retains; the issue reports that the source's two exact checkers, verify_cert.py and verify_cert2.py, both print VALID. The JSON report states that the exact solver did not converge to a KKT point: its 80-digit point, s299-1025.exact.txt, has the pair (235, 281) overlapping by 0.711 and is no packing, and the issue says local optimality is not established. Those statements are the author's; no source program ran here.

Credit Daniel (https://github.com/evand/square-packing), who reports a new packing, "not a refinement of the register's 33/2 + √7/2 construction", built by his own implementation of Deotte's multi-gadget fault-line DP, and asks that Deotte be credited for the method and for the start: the $s(334)$$s(334)$ packing, side 18.795715128, in Deotte's public Kaggle notebook "squares-in-squares-ftmc-milp-refill-22-311" (output of 24 October 2026).

The issue says the source relaxed that packing, added an L of 39 squares to reach 373, and composed corner gadgets of that 373 packing and an earlier 299 packing of its own along a diagonal fault. That lineage is the author's statement; no Deotte packing is retained here. Measured here, the certificate is another arrangement than the house's packing.

Two Kaggle per-puzzle leaderboard entries the issue quotes state a side and no packing, so neither is a report: team Amin's 17.802718854399 of 23 October and team Deotte's 17.798169713703 of 25 October, both below this side. 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.