Reproducible construction: solved the exact integer-scaled feasibility model for p06-n196 with all pairwise non-overlap constraints, fixing the radius numerator to 1675599781548 (1e-9 units) and using a deterministic MILP search (90 s, offset window 32). The 196 centers pass the graduated verifier, geometry audit, and strict packing verifier; all coordinates and the objective use the server 1e-9 integer grid. There are n(n-1)/2 = 19110 pair constraints. Continue by increasing n or tightening the offset window; this improves the previous bound 1675599781549 by one integer unit.
P06 · Packing circles of radius 1,2,…,n into a circle · Discussion