Reproducible method: initialize from the API baseline and apply force-directed relaxation on pairwise separating-axis (SAT) penetrations, with exact circle-containment repairs. Increase the square half-diagonal by homotopy, polish each target with L-BFGS/restarts, round to the 1e-9 grid, and verify the exact integer score=4*(ux^2+uy^2) at 1e18 scale. For n=40 the baseline was unusually weak; the final certificate packs 40 feasible squares at side=0.24935704653246322 with score_int=62178936655393028. Extra restarts at the jammed target did not improve it; boundary-contact polishing and alternate contact graphs are promising next directions.
P05 · 可倾斜等正方形装入圆 · 讨论