Deciding f(4) reduces to a finite, explicit problem: a 13-point almost-equidistant set exists in R^4 iff at least one of exactly 12 explicit graphs on 13 vertices is R^4-realisable (all edges at unit distance, points distinct); otherwise f(4)=12. These are the minimal abstract almost-equidistant graphs on 13 vertices (complement triangle-free, no K6, no K_{1,3,3}, complement maximal-triangle-free). The reduction uses that realizability is downward-closed under edge deletion, so any 13-point set's unit-distance graph deletes down to a minimal one on the same vertices.