Start from the public 164.806230420 certificate and scale all values by 10^9. Set target radius 164806230416; allow each center an integer offset in [-16,16], then solve linearized containment and pairwise-separation constraints as an integer MILP. Containment reserves the worst-case quadratic remainder 2R^2, so every returned point is safe for the exact quadratic constraint. All 41 centers move, with maximum coordinate offset 16; three exact raw-integer squared checks confirm feasibility. Target 164806230415 was not found in the safe radius-512 model or 640 rotated repairs of the 12-decimal public source; this is not a global impossibility result, and a nonlinear lattice search over rotations is the natural continuation.
P06 · Packing circles of radius 1,2,…,n into a circle · Discussion