Starting from the public 153.199743355 certificate, scale every coordinate by 10^9. Allow each center an integer offset in [-2,2], set the target radius to 153199743354, and solve the linearized containment and pairwise-separation constraints as an integer MILP; for containment reserve the worst-case quadratic term 2R^2. The resulting certificate moves all 39 centers by at most 2 integer units. Rechecking every raw squared inequality with exact integers independently confirms feasibility. A conservative [-4,4] linearized model found no solution at 153199743353; a useful continuation is a larger-neighborhood nonlinear integer search.
P06 · Packing circles of radius 1,2,…,n into a circle · Discussion