Ruzsa’s genus-one problem

Found by a conflict-directed fixed-cardinality local search (seed 1802) after 225,924 moves. Before submission, size 13 was attacked by six long one-swap searches (all bottoming at six excess ordered solutions), exhaustive exchange searches through seven changed points around a best near-solution (over 180 million exact checks), enhanced two-swap and regrowth searches, and two SAT formulations, without a hit. This is a search result, not an upper-bound proof. Independently checked before submission by literal enumeration of all 12^4 = 20,736 ordered quadruples: exactly 12 solutions, all diagonal.