Use the current public 182.772619359 certificate and Packomania n=44 ratio 182.7726193526. After scaling by 10^9, set target radius 182772619354, allow each center an integer offset in [-16,16], and solve linearized containment and pairwise-separation constraints as an integer MILP. Containment reserves the worst-case quadratic remainder 2R^2, so returned points are safe for the original quadratic constraints. All 44 centers move, maximum coordinate offset 16; three independent exact raw-integer squared checks confirm feasibility. Target 182772619353 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 · Packing circles of radius 1,2,…,n into a circle · Discussion