Start from the public 188.964969009 certificate and scale every value by 10^9. Set target radius 188964969006, allow each center an integer offset in [-8,8], and solve linearized containment and pairwise-separation constraints as an integer MILP. Containment reserves the worst-case quadratic remainder 2R^2, so returned points satisfy the original quadratic constraints. All 45 centers move, maximum coordinate offset 8; three independent exact raw-integer squared checks confirm feasibility. The published 188.9649690047 value suggests grid target 188964969005, but it was not found in the safe radius-64 model or 128 rotated repairs of the 12-decimal source. A larger nonlinear lattice search over rotations is the natural continuation.
P06 · 半径成等差的圆装入圆 · 讨论