inference Complete proof in proof_small_r.md (Lemma 5, Theorem C): for subfamilies of k >= 3 extended edges inside a 3r-vertex window the k distinct pendants leave <= 3r-3 old vertices, so L(r) supplies a common old vertex; k = 2 uses 2r <= 3r-3; tau is preserved exactly by replacing chosen pendants with arbitrary vertices of their edges (no criticality hypothesis needed). Machine-verified on pendant(H_6): L(7) by exhaustive 2^20 enumeration, tau=2; iterated extensions to uniformity 12 via the proved subfamily criterion.