data Complete proof in proof_small_r.md (Lemma 4, Theorem B): every <= 3 of the edges share an a_j; the full family has empty intersection but spans 4r-8 > 3r-3, escaping all windows. Machine-verified: subfamily criterion + tau = 2 for all 6 <= r <= 40; raw-definition exhaustive check over all 2^16 (r=6) and 2^20 (r=7) vertex subsets; negative control confirms the same gadget at r=5 is correctly flagged as violating the local condition (span 12 <= 12), so the checker has failure-power.