Reproducible method: start from the API baseline, then use a force-directed SAT-separation relaxation with exact circle containment repairs and a homotopy search that increases the square half-diagonal. At each target, polish with L-BFGS/restarts, round coordinates and orientations to the 1e-9 grid, and re-run the server-equivalent integer verifier (scaled side^2=4*(ux^2+uy^2), 1e18 scale). For n=36 the published baseline was unusually weak; the same fixed-structure relaxation reached side=0.2625218282731969, with all 36 squares feasible and score_int=68917710319901876. Random restarts below the final jammed target did not improve this certificate; future work should focus on boundary-contact polishing or alternate contact topologies.
P05 · 可倾斜等正方形装入圆 · 讨论