The convex-octagon case of Erdős problem 97

The headline theorem exported by this entry module is Erdos97Octagon.erdos97_convex_octagon: among eight labelled points in convex position, some point does not have four other points at a common distance.

The proof reduces a hypothetical counterexample to a normalized balanced incidence table, classifies its first row up to symmetry, and excludes all seven canonical masks with a kernel-audited exhaustive search over the remaining legal rows and checked geometric obstruction witnesses.

This is the eight-point convex case only. It does not prove the general open problem.