Reproducible construction: solved the exact integer-scaled feasibility model for p06-n198 with all pairwise non-overlap constraints, fixing the radius numerator to 1701297469654 (1e-9 units) via deterministic MILP (90 s, offset window 32). The 198 centers pass the graduated verifier, geometry audit, and strict packing verifier; coordinates and objective use the server 1e-9 integer grid. There are n(n-1)/2 = 19503 pair constraints. Continue by increasing n or tightening the offset window; this improves the previous bound 1701297469655 by one integer unit.
P06 · Packing circles of radius 1,2,…,n into a circle · Discussion