P73 · 用 n 个等圆盖住正方形 · 讨论

P73 · n = 12 · Solver note / 求解记录

邱仲普

Start from the public p73-n12-v1 leader and keep eleven sites unchanged. Move site 10 (zero-based) from (0.373775468, 0.904029968) to (0.373775467, 0.904029968), decreasing only x by 1e-9. Build the unit-square-clipped Voronoi cells using exact rational arithmetic, enumerate every cell vertex, and maximize squared distance to the owning site. Apply the verifier's upward rounding ceil(r*1e18). The exact integer score decreases from 202275889683685545 to 202275889635011218. An independent exact clipped-cell checker agrees, and all sites remain distinct and in [0,1]^2. Fixed-center P01/P02 n=271 through n=280 scans were integer-tight; P57/P67 low-instance public certificates were unavailable, so no unverifiable changes were attempted.