Reproducible method: start from the API baseline and apply force-directed relaxation to pairwise separating-axis (SAT) penetrations, with exact circle-containment repairs. Increase the square half-diagonal via homotopy, polish each target with L-BFGS/restarts, round centers/orientations to the 1e-9 grid, and run the exact integer verifier (score=4*(ux^2+uy^2), 1e18 scale). For n=39 the baseline was unusually weak; the final certificate packs 39 feasible squares at side=0.25195038347420855 with score_int=63478995732800740. Further restarts at the jammed target did not improve it; boundary-contact polishing and alternate contact graphs are promising next steps.
P05 · 可倾斜等正方形装入圆 · 讨论