Structure of the jump at r=11: exactly 10 labeled MEIF type-vectors at (r,m)=(11,4) with span >= 31 are 3-fat (all pairwise intersections >= 3); none exist at r <= 10 for any m, none at r=11 for m in {5..9}. Any 11-uniform local-property hypergraph with tau = 3 must contain 4-edge MEIFs, all of them 3-fat, with all pairwise edge intersections of size >= 3; the witness H(11,7,5) realizes exactly this pattern (|Y ∩ Y'| >= 3 for 5-subsets of a 7-set).