Reciprocal-triple-free sets: finite maxima through 734

The Lean development proves f(732)=f(731), f(733)=f(732)+1 and f(734)=f(732)+2. The 732 step replaces an isolated five-vertex component without reducing an admissible set. Exact finite certificates show that neither 733 nor 734 belongs to a forbidden reciprocal triple with vertices at most 734, so each new vertex raises the maximum by one. Conditional on the published OEIS value f(731)=606, the resulting values are f(732)=606, f(733)=607 and f(734)=608. The historical asymptotic Erdős problem remains open. Priority is provisional; the elementary component argument may be folklore.

The Lean development proves f(732)=f(731), f(733)=f(732)+1 and f(734)=f(732)+2. The 732 step replaces an isolated five-vertex component without reducing an admissible set. Exact finite certificates show that neither 733 nor 734 belongs to a forbidden reciprocal triple with vertices at most 734, so each new vertex raises the maximum by one. Conditional on the published OEIS value f(731)=606, the resulting values are f(732)=606, f(733)=607 and f(734)=608. The historical asymptotic Erdős problem remains open. Priority is provisional; the elementary component argument may be folklore.