{"id":"511.12.5.a","row":1101,"stored":{"file":"master_catalog.json","row":1101,"construction":null,"columns_sha256":null},"parameters":{"n":511,"k":12,"d":5,"N":30,"r":18,"level":3},"gate":{"string":"0+1+2+3+4+5+6+7+8+9+10+11","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6\u00b7T7\u00b7T8\u00b7T9\u00b7T10\u00b7T11","monomials":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11]],"sk_key":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11]],"sk_fingerprint":"418c440ed2e4ddd2","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,1,3,4,6,7,9,10,11,12,21],[0,4,7,8,10,13,24],[4,8,10,12,13,21,22,23,24],[0,2,3,5,7,9,10,14,27],[1,2,3,4,6,9,10,11,12,14,21,23,25,27],[0,1,2,3,4,5,7,8,10,11,13,14,24,25,26,27],[1,2,4,8,9,11,12,13,14,21,22,24,26,27],[0,3,7,9,10,15,21,25],[0,3,7,9,10,12,15,24,25,27],[1,2,9,10,11,13,15,21,24,25,26,28],[2,3,4,6,12,13,15,22,23,25,26,27,28],[0,1,5,10,11,14,15,21,25,27,28,29],[0,1,3,9,11,12,14,15,23,24,28,29],[0,1,2,3,5,9,11,13,14,15,21,24,27,29],[0,2,3,4,6,9,12,13,14,15,22,25,29],[2,5,7,9,10,11,16,24,28],[0,2,5,6,7,8,9,10,11,12,16,21,24,25,28,29],[0,4,7,13,16,21,25,27,28],[1,3,7,8,9,10,11,12,13,16,22,23,27,28,29],[1,3,5,7,9,10,14,16,22,24,26,27,28,29],[0,1,6,7,8,12,14,16,21,22,23,24,26,27,28],[2,3,4,9,10,13,14,16,21,22,28,29],[0,1,2,3,5,8,9,10,11,12,13,14,16,28],[0,1,2,8,11,15,16,21,22,23,24,25,26,27,28],[0,2,3,4,7,9,10,12,15,16,22,23,26,28,29],[2,3,5,9,11,13,15,16,22,23],[2,3,5,6,7,8,9,11,12,13,15,16,21,24,25,27,29],[1,2,3,8,10,11,14,15,16,21,23,24,25],[2,3,4,5,7,10,12,14,15,16,25,27,29],[1,2,5,7,13,14,15,16,23,25,27,28],[1,2,3,6,8,9,10,12,13,14,15,16,21,22,23,24,25,28,29],[0,1,4,6,10,17,22,26,27],[1,4,5,8,10,12,17,21,26,27],[2,3,6,9,13,17,22,23,24,26,28],[0,1,2,4,5,6,8,10,11,12,13,17,21,22,24,26,28],[2,4,6,7,8,9,14,17,21,22,24,25,26,28],[0,2,3,4,7,10,12,14,17,23,24,26,28],[3,6,8,9,11,13,14,17,21,22,23,27],[0,1,3,4,6,9,12,13,14,17,22,23,25,27],[0,1,3,4,7,9,11,15,17,21,22,23,26,29],[0,5,8,10,12,15,17,23,24,26,27,29],[1,3,4,7,8,13,15,17,21,22,24,27,29],[1,3,4,5,6,12,13,15,17,22,23,29],[0,1,3,4,8,14,15,17,22,23,24,25,26,27],[0,3,7,11,12,14,15,17,21,26],[0,3,4,7,10,13,14,15,17,22,26],[0,4,6,8,9,12,13,14,15,17,21,22,24,25,26,27],[0,3,4,5,7,8,16,17,21,22,24,27,28,29],[1,6,8,9,10,11,12,16,17,24,25,27,28],[1,10,11,13,16,17,22,23,25,27,29],[0,1,5,7,10,11,12,13,16,17,21,22,27],[0,2,3,4,7,11,14,16,17,25,26],[1,2,3,6,12,14,16,17,21,22,23,25,26,29],[0,2,5,7,8,9,11,13,14,16,17,21,23,24,25,28],[2,3,5,8,10,11,12,13,14,16,17,23,24,25,28,29],[0,1,3,4,6,9,10,11,15,16,17,24,26,27,28],[0,1,3,4,5,6,9,10,11,12,15,16,17,21,22,25,26,28,29],[1,2,3,4,5,6,7,9,10,11,13,15,16,17,21,23,25,27,28],[2,7,12,13,15,16,17,24,28,29],[3,4,5,6,8,9,11,14,15,16,17,21,22,25,28],[4,5,6,8,10,11,12,14,15,16,17,23,24,25,27,28,29],[1,2,3,4,6,8,10,13,14,15,16,17,22,23,24,25,28],[2,3,8,10,11,12,13,14,15,16,17,21,22,23,25,27,28,29],[0,1,3,5,6,18,21,29],[1,2,3,4,5,10,12,18,24,27,28,29],[1,4,5,9,13,18,21,24,25,29],[0,2,3,4,5,11,12,13,18,22,23,25,27,28,29],[0,1,5,6,7,10,14,18,22,25,27,29],[1,2,3,4,7,9,10,12,14,18,21,22,23,24,28,29],[0,3,4,5,11,13,14,18,22,24,25,26,27,29],[1,2,3,4,10,12,13,14,18,21,26,28,29],[0,2,3,4,7,9,11,15,18,22,24,25,26,27,28,29],[0,1,4,12,15,18,21,22,24,25,26,27,29],[1,3,4,6,7,8,10,13,15,18,22,27,29],[1,2,3,8,12,13,15,18,21,23,27,28,29],[1,4,9,14,15,18,21,24,26],[2,4,5,7,9,10,11,12,14,15,18,23,24,25,26,28],[1,2,4,6,7,8,9,13,14,15,18,21,26,28],[1,3,5,8,12,13,14,15,18,22,25,26],[0,2,4,7,8,11,16,18,23,24,25,26,27,29],[1,3,4,6,9,12,16,18,21,23,26,28],[3,5,6,13,16,18,21,23,25,26,29],[0,2,3,4,5,6,7,8,10,12,13,16,18,22,24,26,27,28],[1,2,3,4,5,7,8,9,14,16,18,21,23,24],[0,3,4,6,9,10,11,12,14,16,18,27,28,29],[6,7,10,13,14,16,18,23,25,26,27],[0,2,3,4,5,6,8,9,10,12,13,14,16,18,21,22,23,24,25,26,28,29],[0,3,6,9,15,16,18,21,26,27,28,29],[0,2,3,4,6,8,9,10,12,15,16,18,25,26,27],[1,3,5,7,9,10,13,15,16,18,24,29],[2,5,6,7,8,10,11,12,13,15,16,18,21,22,23,24,25,28],[0,2,5,6,10,14,15,16,18,25,29],[0,3,4,6,8,9,10,12,14,15,16,18,21,23,25,28],[0,2,9,10,11,13,14,15,16,18,21,24,27,28,29],[0,1,5,6,8,9,12,13,14,15,16,18,22,24,27],[0,4,6,8,9,17,18,21,22,23,24,26],[1,2,3,4,5,7,11,12,17,18,23,26,27,28],[1,2,7,9,13,17,18,21,22,25,26,27,28],[0,1,4,5,8,9,10,12,13,17,18,22,23,24,25,26],[0,1,4,5,6,7,9,10,14,17,18,21,23,26,27,28],[2,4,5,8,9,12,14,17,18,22,24,25,26],[0,1,2,5,7,8,11,13,14,17,18,21,24],[1,3,4,5,9,12,13,14,17,18,25,27,28],[1,2,5,6,7,8,15,17,18,28,29],[1,4,6,7,10,12,15,17,18,21,22,29],[0,1,2,3,5,8,10,13,15,17,18,23,24,25,26,27,28,29],[0,6,9,10,12,13,15,17,18,21,24,25,26,27,29],[0,1,6,14,15,17,18,22,24,27,28],[0,1,2,3,4,6,8,9,12,14,15,17,18,21,23,24,25,27],[0,3,9,13,14,15,17,18,22,23,28],[0,1,2,3,6,8,9,10,11,12,13,14,15,17,18,21,22,23,25],[0,5,6,7,8,16,17,18,21,22,25,26,27,29],[2,4,7,8,10,12,16,17,18,24,26,28],[1,4,7,8,9,13,16,17,18,22,23,24,25,26,27,28,29],[0,2,3,4,5,7,8,11,12,13,16,17,18,21,22,26],[5,6,7,9,14,16,17,18,21,22,24,25,28],[0,2,3,4,5,7,11,12,14,16,17,18,23,25,27,29],[4,9,10,13,14,16,17,18,22,23,26],[0,1,2,4,9,11,12,13,14,16,17,18,21,22,23,24,26,27,28,29],[2,3,4,5,6,9,15,16,17,18,22,24,25,26,28],[1,4,6,7,11,12,15,16,17,18,21,24,26,29],[0,4,8,10,13,15,16,17,18,21,22,23,25,28],[0,2,5,6,7,8,12,13,15,16,17,18,22,29],[1,3,4,5,6,8,10,14,15,16,17,18,22,25,27,28],[2,3,4,5,6,7,8,11,12,14,15,16,17,18,21,23,25,27,29],[2,4,7,10,13,14,15,16,17,18,21,22,23,24,27,28],[0,1,2,4,5,7,8,11,12,13,14,15,16,17,18,22,23,24,27,29],[0,2,3,4,5,6,8,10,11,19,23,24,27],[0,1,2,5,8,9,12,19,23,24,25,26,27,28],[0,3,4,5,7,8,10,11,13,19,21,22,23,25,26],[0,3,4,5,7,8,10,12,13,19,21,28],[0,2,7,8,9,11,14,19,23,24,28],[0,1,2,4,5,6,7,8,9,10,11,12,14,19,24,26],[1,6,7,8,13,14,19,21,22,23,27,28],[1,3,5,6,7,8,9,11,12,13,14,19,21,23,26,27],[0,3,7,10,11,15,19,21,23,27,28],[3,12,15,19,21,23,24,25,26],[0,1,4,6,8,10,11,13,15,19,22,23,24,25],[3,7,8,9,10,12,13,15,19,26,27,28],[1,2,4,5,6,9,14,15,19,21,23,28,29],[0,1,2,3,4,6,7,11,12,14,15,19,21,24,26,27,29],[0,1,2,3,5,8,11,13,14,15,19,22,23,24,26,27,29],[2,3,4,6,7,8,10,11,12,13,14,15,19,23,28,29],[1,2,4,8,11,16,19,21,22,23,26,28,29],[1,2,4,6,7,11,12,16,19,21,22,23],[1,2,4,5,6,9,13,16,19,21,23,24,28,29],[2,3,5,6,7,8,11,12,13,16,19,21,22,24,26],[0,2,3,6,8,10,11,14,16,19,21,23,27],[0,2,5,7,9,11,12,14,16,19,21,25,26,27,28,29],[1,2,3,5,7,10,13,14,16,19,21,22,23,24,25,27],[2,3,4,8,10,11,12,13,14,16,19,21,23,24,26,27,28,29],[3,6,7,8,15,16,19,24,27,29],[0,1,4,6,7,9,10,11,12,15,16,19,26,28],[1,2,4,5,7,8,9,10,13,15,16,19,22,27,28,29],[0,1,2,4,5,6,7,9,10,12,13,15,16,19,23,24,26],[2,4,7,8,14,15,16,19,22,24,26,29],[0,1,2,5,7,10,12,14,15,16,19,22,23,25,27,28],[0,3,5,6,8,10,11,13,14,15,16,19,25,28,29],[9,12,13,14,15,16,19,22,24,26,27],[2,3,5,6,7,8,9,11,17,19,21,23,25,26,28,29],[2,3,12,17,19,21,22,23,29],[1,2,5,7,13,17,19,22,24,29],[2,3,4,8,12,13,17,19,22,23,24,25,26,28,29],[1,2,3,4,5,9,10,11,14,17,19,23,24,26,27,28,29],[1,2,4,5,6,7,8,10,12,14,17,19,22,24,27,29],[0,1,2,4,5,6,7,8,13,14,17,19,21,22,26,27,29],[0,2,5,6,10,11,12,13,14,17,19,21,22,27,28,29],[0,3,4,6,9,10,11,15,17,19,24,26,27],[1,5,6,8,12,15,17,19,22,25,28],[0,2,3,9,10,11,13,15,17,19,21,22,23,25,26,27],[2,3,5,6,8,12,13,15,17,19,21,22,24,28],[2,3,7,8,9,10,14,15,17,19,21,25,26,28,29],[0,1,2,3,4,7,11,12,14,15,17,19,21,22,23,24,25,27,29],[0,1,3,4,6,8,9,11,13,14,15,17,19,22,23,24,25,28,29],[1,4,9,11,12,13,14,15,17,19,22,23,25,26,27,29],[0,3,6,7,9,10,16,17,19,21,22,23,24,25,26,27,29],[0,1,4,5,7,9,12,16,17,19,21,23,24,25,27,28],[0,1,2,5,11,13,16,17,19,21,25,28,29],[0,1,2,9,10,11,12,13,16,17,19,21,23,25,26],[3,4,5,7,8,9,10,14,16,17,19,23],[1,3,5,6,7,8,10,11,12,14,16,17,19,22,25,26,28,29],[0,2,4,6,7,8,9,11,13,14,16,17,19,22,24,25,27,28],[0,2,3,4,6,7,8,10,11,12,13,14,16,17,19,22,24,26,27,29],[1,2,4,6,11,15,16,17,19,23,27,28],[0,1,2,4,5,6,7,10,11,12,15,16,17,19,22,23,24,26,29],[1,2,5,7,8,10,11,13,15,16,17,19,22,24,28],[0,2,3,4,6,12,13,15,16,17,19,22,23,26,27,29],[5,8,14,15,16,17,19,21,22,23,24,25,26],[0,3,5,7,9,10,12,14,15,16,17,19,21,27,28,29],[0,1,4,6,8,10,13,14,15,16,17,19,21,27],[0,1,2,3,4,5,6,11,12,13,14,15,16,17,19,21,24,25,26,28,29],[1,5,9,10,18,19,24,25,26,27,29],[1,2,4,5,6,7,12,18,19,29],[1,2,3,5,8,9,11,13,18,19,21,22,25,29],[5,7,10,11,12,13,18,19,21,23,24,26,27,29],[0,1,2,3,4,5,6,7,9,10,11,14,18,19,21,22,24,26,28,29],[0,1,8,10,11,12,14,18,19,21,22,23,27,28,29],[4,5,6,8,10,13,14,18,19,25,26,27,28,29],[1,2,4,6,7,11,12,13,14,18,19,22,24,25,28,29],[0,3,5,7,15,18,19,21,22,24,25,29],[1,2,5,7,10,12,15,18,19,21,22,24,26,29],[0,1,3,4,5,7,9,11,13,15,18,19,25,27,28,29],[1,2,3,5,6,7,9,12,13,15,18,19,22,23,26,27,28,29],[0,1,4,5,6,8,9,14,15,18,19,24,27],[2,4,6,8,9,10,12,14,15,18,19,23,24,26,27],[1,5,6,7,8,11,13,14,15,18,19,21,22,25,26,28],[0,1,2,3,4,7,12,13,14,15,18,19,21,25,28],[0,1,4,10,16,18,19,22,23,26,27],[0,2,3,4,6,12,16,18,19,22,23,24,29],[0,1,3,4,5,7,8,10,11,13,16,18,19,23,24,25,27],[0,1,2,3,5,7,8,10,12,13,16,18,19,22,25,26,29],[0,2,3,5,6,10,14,16,18,19,21,22,23,25,28,29],[0,1,3,12,14,16,18,19,21,22,24,26,27,28],[1,2,6,11,13,14,16,18,19,21,23,24,25,28,29],[1,3,4,5,6,8,12,13,14,16,18,19,21,22,23,26,27,28],[1,4,5,9,10,11,15,16,18,19,21,22,26,27],[0,1,2,5,7,8,9,11,12,15,16,18,19,21,22,27,29],[2,7,8,9,10,11,13,15,16,18,19,21,24,25,26,27,28],[0,1,3,7,8,9,11,12,13,15,16,18,19,21,22,23,24,25,27,28,29],[0,1,3,6,7,9,14,15,16,18,19,22,25],[1,2,4,5,6,9,12,14,15,16,18,19,22,23,26,29],[1,8,9,10,11,13,14,15,16,18,19,24,25,26,28],[1,3,4,6,7,9,10,11,12,13,14,15,16,18,19,22,24,28,29],[1,3,4,6,7,9,10,11,17,18,19,21,23,24,27,28,29],[2,4,5,7,8,11,12,17,18,19,21,22,23,25,26,28,29],[3,4,6,7,8,10,13,17,18,19,22,26,27,29],[2,3,5,6,7,8,11,12,13,17,18,19,22,23,24,25,29],[0,2,3,5,9,11,14,17,18,19,21,22,23,28,29],[0,1,3,5,6,7,9,10,11,12,14,17,18,19,21,24,26,27,28,29],[2,3,5,8,11,13,14,17,18,19,24,25,29],[4,5,7,10,12,13,14,17,18,19,25,26,27,29],[4,7,8,11,15,17,18,19,22,24,25,26,27,28],[0,2,5,8,10,12,15,17,18,19,24,27,28],[2,3,8,13,15,17,18,19,21,23,25,26,27,28],[5,8,9,10,11,12,13,15,17,18,19,21,27,28],[5,6,10,11,14,15,17,18,19,25,26,29],[0,2,3,4,5,7,8,9,10,11,12,14,15,17,18,19,22,23,25,29],[0,1,2,3,10,11,13,14,15,17,18,19,21,22,23,24,29],[2,4,5,7,10,12,13,14,15,17,18,19,21,22,23,24,26,29],[0,2,6,8,9,11,16,17,18,19,22,25,26,27,28,29],[0,3,4,10,11,12,16,17,18,19,24,25,28],[0,1,7,8,13,16,17,18,19,23,24,29],[1,2,4,5,7,12,13,16,17,18,19,26,27],[0,1,2,3,4,5,6,8,14,16,17,18,19,22,24,25,28],[0,1,2,7,9,11,12,14,16,17,18,19,23,26,27,28,29],[0,2,7,11,13,14,16,17,18,19,23,25,27],[0,1,3,5,6,7,12,13,14,16,17,18,19,23,24,26,29],[0,2,6,9,15,16,17,18,19,21,22,26,28],[1,4,5,6,7,8,9,10,11,12,15,16,17,18,19,21,28,29],[0,2,3,4,6,7,8,10,13,15,16,17,18,19,21,23,24,25,26,27,28],[0,1,2,3,4,5,6,7,8,10,12,13,15,16,17,18,19,21,24,25,27,28,29],[3,4,5,9,14,15,16,17,18,19,21,22,24,27],[2,4,8,10,11,12,14,15,16,17,18,19,21,23,24,25,26,27,29],[0,1,2,3,5,6,8,10,11,13,14,15,16,17,18,19,21,23,26],[1,2,4,6,7,8,12,13,14,15,16,17,18,19,21,23,25,29],[2,3,4,5,6,7,9,20,21,25,26,27],[0,1,3,4,5,6,7,12,20,23,25,26,28,29],[0,1,3,4,5,6,8,9,13,20,21,22,25,27,28,29],[1,2,5,9,10,12,13,20,25],[0,5,6,7,9,10,14,20,24,25,26,28,29],[1,2,3,6,7,8,9,10,11,12,14,20,21,24,26,27],[0,2,5,7,8,9,10,13,14,20,22,24,26],[4,9,10,12,13,14,20,21,23,24,25,26,27,28,29],[2,6,7,8,9,10,11,15,20,22,27],[3,4,7,8,11,12,15,20,21,22,23,24,27,28,29],[0,2,3,4,6,7,9,10,11,13,15,20,27,29],[0,1,3,4,7,10,11,12,13,15,20,21,22,24,27,28],[1,2,3,4,6,11,14,15,20,21,22,24],[1,3,5,8,9,10,12,14,15,20,22,25,28,29],[2,7,10,13,14,15,20,21,24,25,26,29],[1,3,5,7,11,12,13,14,15,20,22,23,26,28],[0,1,2,6,8,16,20,21,22,24,25],[1,3,4,6,8,10,11,12,16,20,22,23,24,27,28],[2,5,8,13,16,20,24,26,27,28,29],[0,1,5,6,7,8,10,11,12,13,16,20,21,22,24,25,26,29],[0,3,4,5,7,11,14,16,20,25,26,27,28],[2,3,6,9,11,12,14,16,20,21,25,26],[0,3,4,6,7,8,13,14,16,20,21,22,25,26,29],[1,2,4,5,9,10,11,12,13,14,16,20,23,25,26,27,28,29],[0,2,4,7,11,15,16,20,22,23,24,27],[0,1,4,9,11,12,15,16,20,21,22,25,27,28],[3,5,7,9,13,15,16,20,21,23,24,25,29],[2,4,5,6,9,10,12,13,15,16,20,22,23,28,29],[2,3,5,6,8,14,15,16,20,21,23,26,29],[1,6,9,11,12,14,15,16,20,23,24,26,28,29],[1,4,7,8,9,10,13,14,15,16,20,22,23,27],[1,2,5,6,7,9,12,13,14,15,16,20,21,24,27,28],[0,4,5,6,7,9,10,17,20,22,23,24,25,27,29],[2,3,7,8,10,11,12,17,20,21,24,25,28],[3,4,5,8,13,17,20,24,25,26],[0,1,2,3,4,7,9,12,13,17,20,21,24,25,26,27,28,29],[1,2,5,6,14,17,20,22,23,24],[0,1,4,5,6,8,9,10,12,14,17,20,21,23,24,25,27,28,29],[2,3,7,8,9,11,13,14,17,20,24,25,27,29],[0,1,6,8,10,11,12,13,14,17,20,21,23,24,28],[3,5,15,17,20,21,24,25,26],[1,2,3,5,8,11,12,15,17,20,22,23,25,26,28,29],[0,1,2,3,4,7,8,9,10,13,15,17,20,21,22,23,24,25,26,27,28,29],[0,1,5,6,7,12,13,15,17,20,22,23,25,26,27],[3,4,5,7,10,11,14,15,17,20,21,24,26,27,28],[1,2,4,6,9,12,14,15,17,20,22,25,26,27,29],[2,3,5,6,7,8,9,10,13,14,15,17,20,21,22,23,24,25,29],[3,4,6,7,8,9,11,12,13,14,15,17,20,22,28],[2,5,6,7,9,16,17,20,21,23,25],[0,1,5,6,11,12,16,17,20,22,27,28],[0,3,5,7,9,10,11,13,16,17,20,22,26,29],[2,5,9,10,12,13,16,17,20,21,22,25,26,27,28,29],[5,6,7,8,10,11,14,16,17,20,21,22,23,26,27],[0,1,2,3,4,6,7,8,9,10,11,12,14,16,17,20,23,26,28],[1,2,3,7,9,11,13,14,16,17,20,26,27,29],[0,1,3,4,5,6,7,8,9,10,12,13,14,16,17,20,21,23,26,28,29],[0,1,2,5,6,7,8,9,10,11,15,16,17,20,23,25,29],[0,1,3,4,5,10,11,12,15,16,17,20,21,22,24,28,29],[2,6,7,8,10,11,13,15,16,17,20,21,22,28],[1,6,7,10,11,12,13,15,16,17,20,22,24,25],[2,4,6,7,8,9,11,14,15,16,17,20,22,23,26,27,28],[5,6,9,11,12,14,15,16,17,20,21,23,24,26,27],[2,5,7,9,11,13,14,15,16,17,20,21,27,29],[0,2,4,7,8,9,12,13,14,15,16,17,20,23,24,27,28,29],[0,1,3,4,5,7,8,9,18,20,22,23,24,27,28,29],[1,4,6,7,9,10,12,18,20,21,22,27,28],[2,5,7,9,11,13,18,20,23,24,25,26,27],[0,1,2,4,5,6,7,9,12,13,18,20,21,22,23,25,26,27,29],[0,1,4,7,8,10,14,18,20,23,25],[1,4,7,8,9,10,12,14,18,20,21,23,24,29],[0,1,2,3,4,5,8,9,11,13,14,18,20,22,23,25,28,29],[2,5,6,7,8,9,11,12,13,14,18,20,21,24,28],[2,3,6,8,9,10,15,18,20,21,22,23,25,29],[1,2,3,8,9,12,15,18,20,22,25,27],[0,2,4,5,6,7,11,13,15,18,20,21,23],[0,2,4,5,6,10,12,13,15,18,20,22,23,27,29],[0,1,3,4,5,6,9,14,15,18,20,21,23,24,27,29],[0,4,7,10,12,14,15,18,20,23,24,25],[0,5,9,11,13,14,15,18,20,21,22,23,24,26,27],[0,4,6,8,9,10,12,13,14,15,18,20,24,25,26,29],[1,4,7,9,11,16,18,20,21,25,27,29],[0,4,5,6,9,10,11,12,16,18,20,23,24,27,29],[0,3,5,6,10,13,16,18,20,22,25,26,28],[10,12,13,16,18,20,21,24,26,28],[0,4,5,7,9,10,14,16,18,20,21,24,26,28,29],[1,3,11,12,14,16,18,20,26,28,29],[0,8,9,10,13,14,16,18,20,22,24,25,26,27],[4,7,9,12,13,14,16,18,20,21,23,25,26,27],[0,1,2,3,5,7,8,15,16,18,20,22,23,24,26,27,28,29],[0,1,2,6,8,11,12,15,16,18,20,21,22,24,25,26,28,29],[1,3,6,7,8,9,13,15,16,18,20,21,23,24,26,28],[3,9,11,12,13,15,16,18,20,22,23,24,25,26,27,28],[0,1,4,5,7,9,10,11,14,15,16,18,20,22,23,25,28],[0,1,2,7,8,10,12,14,15,16,18,20,21,22,23,25,27,28],[0,4,5,9,11,13,14,15,16,18,20,21,23,26,27,28,29],[3,7,8,12,13,14,15,16,18,20,22,26,28,29],[0,1,3,4,5,7,8,10,17,18,20,21,23,24,26,28,29],[2,4,5,7,9,10,11,12,17,18,20,22,26,28],[1,3,5,6,7,8,11,13,17,18,20,21,22,24,25,27,28],[0,1,2,3,7,11,12,13,17,18,20,22,25,27,28,29],[0,2,3,5,6,7,8,9,11,14,17,18,20,22,23,24,26,27,28],[1,3,4,6,8,10,11,12,14,17,18,20,21,23,25,26,27,28,29],[0,1,6,8,9,10,11,13,14,17,18,20,24,26,28,29],[1,4,5,6,9,10,12,13,14,17,18,20,21,23,25,26,28],[0,3,4,6,7,9,11,15,17,18,20,26],[0,2,3,5,6,8,9,10,12,15,17,18,20,21,22,23,26,27,29],[1,2,4,6,7,9,10,11,13,15,17,18,20,22,23,25,26,27,28,29],[4,5,7,8,9,11,12,13,15,17,18,20,21,22,23,25,26,28],[3,4,8,9,10,14,15,17,18,20,21,22,26,27,28],[0,1,3,4,7,8,9,11,12,14,15,17,18,20,25,26,28,29],[3,4,9,11,13,14,15,17,18,20,21,23,29],[1,6,7,8,10,11,12,13,14,15,17,18,20,25,27],[2,4,5,8,9,10,16,17,18,20,21,22,25],[0,2,4,6,9,10,11,12,16,17,18,20,23,24],[0,1,2,3,7,10,11,13,16,17,18,20,23,25,26,29],[2,3,4,7,9,10,11,12,13,16,17,18,20,21,23,24,26,29],[0,2,3,4,5,8,9,10,14,16,17,18,20,22,25,26,27],[4,5,7,8,10,12,14,16,17,18,20,21,24,25,26,27],[1,2,4,6,8,9,13,14,16,17,18,20,21,23,26,27,29],[1,3,4,5,7,9,10,11,12,13,14,16,17,18,20,24,26,27,29],[2,3,4,5,9,10,11,15,16,17,18,20,24,25,26,27,28,29],[0,3,4,7,8,12,15,16,17,18,20,21,22,23,24,26,28,29],[0,3,4,5,6,9,10,11,13,15,16,17,18,20,21,22,23,24,25,26,27],[0,10,11,12,13,15,16,17,18,20,22,23,24,26],[1,4,7,8,10,11,14,15,16,17,18,20,21,24,25],[0,1,2,3,4,5,6,7,9,12,14,15,16,17,18,20,22,24,25,27],[2,7,8,10,11,13,14,15,16,17,18,20,22,23,24,26,28,29],[12,13,14,15,16,17,18,20,21,22,24,26,27,28,29],[0,2,5,6,10,11,19,20,21,23,25,28,29],[0,1,2,3,4,6,7,10,11,12,19,20,21,26,27,28],[0,2,3,4,5,8,11,13,19,20,23,27],[0,3,4,5,6,8,11,12,13,19,20,22,23,25,26,29],[0,1,2,5,6,7,14,19,20,23,24,25,27,28],[0,1,2,3,4,7,8,10,11,12,14,19,20,23,24,25,26,28,29],[1,4,5,6,8,9,13,14,19,20,21,23,24,25,26,29],[2,4,5,7,12,13,14,19,20,21,22,24,25,27],[4,5,6,7,8,9,10,15,19,20,22,23,24,25,26,29],[0,1,2,4,6,8,9,12,15,19,20,22],[1,2,5,6,8,9,10,11,13,15,19,20,21,22,23,24,27],[0,5,6,7,8,10,11,12,13,15,19,20,21,23,25,26,27,29],[0,1,6,8,10,14,15,19,20,21,22,23,25,26,27,28,29],[1,2,3,5,9,11,12,14,15,19,20,21,22,23,24,25,27,28],[2,3,5,8,10,13,14,15,19,20,22,23,25,26,28],[0,2,5,10,11,12,13,14,15,19,20,24,25,28,29],[0,1,2,5,8,9,10,11,16,19,20,23,24,25,28],[0,4,6,9,10,12,16,19,20,24,25,26,27,28],[0,1,2,3,7,9,10,13,16,19,20,23,24,25,29],[0,3,5,6,9,11,12,13,16,19,20,22,23,24,25,26,27,29],[1,7,8,10,14,16,19,20,21,22,23,25,26,27,28],[4,5,6,7,9,11,12,14,16,19,20,21,22,23,28],[0,1,2,6,9,13,14,16,19,20,21,22,23,27,29],[1,2,3,4,10,12,13,14,16,19,20,21,25,26,29],[1,2,4,5,6,8,10,15,16,19,20,21,25,27],[0,4,5,7,8,12,15,16,19,20,21,23,24,25,26,27],[2,3,4,6,8,13,15,16,19,20,21,25,26,27,29],[0,2,6,12,13,15,16,19,20,21,22,24,25,27,29],[1,2,3,4,6,7,8,9,10,14,15,16,19,20,22,24,25,26,28,29],[0,3,4,7,8,9,12,14,15,16,19,20,22,28,29],[1,2,4,5,7,13,14,15,16,19,20,22,24,26,28],[0,1,2,3,5,8,12,13,14,15,16,19,20,23,25,28],[1,11,17,19,20,21,26,29],[1,2,3,4,5,9,12,17,19,20,21,22,23,25,27],[1,2,3,4,6,8,13,17,19,20,23,25,26],[0,2,5,6,7,8,10,12,13,17,19,20,23,27,29],[5,6,8,10,14,17,19,20,21,25,26,27,28],[0,1,4,6,8,10,11,12,14,17,19,20,21,22,25,28,29],[0,3,4,6,9,10,13,14,17,19,20,23,25,27,28,29],[0,4,9,10,12,13,14,17,19,20,25,26,28],[1,2,6,8,9,11,15,17,19,20,22,23,24,25,27,28],[0,2,3,5,6,8,11,12,15,17,19,20,26,27,28,29],[0,3,4,6,13,15,17,19,20,21,22,24,26,27,29],[2,3,6,10,12,13,15,17,19,20,21,22,25,27],[0,1,2,5,6,7,9,10,11,14,15,17,19,20,22,23,24,28],[5,6,9,12,14,15,17,19,20,23,26,28,29],[0,2,3,5,7,13,14,15,17,19,20,21,22,24,29],[0,1,4,5,9,12,13,14,15,17,19,20,21,22,23,26],[3,4,5,7,8,9,11,16,17,19,20,21,24,29],[0,4,5,6,10,12,16,17,19,20,21,22,23,24,26,27,29],[0,1,3,4,7,11,13,16,17,19,20,21,23,24,27],[0,1,2,4,5,7,8,12,13,16,17,19,20,21,23,24,26],[0,1,2,3,5,9,11,14,16,17,19,20,21,22,24,25,26,27,28,29],[6,7,8,9,10,12,14,16,17,19,20,21,24,28,29],[0,3,4,6,8,9,10,11,13,14,16,17,19,20,21,22,23,24,28],[0,1,3,5,6,7,8,9,10,12,13,14,16,17,19,20,21,22,24,25,26,27,28],[0,2,4,5,6,9,10,15,16,17,19,20,25,28],[0,1,2,5,10,11,12,15,16,17,19,20,22,23,24,25,26,28],[0,2,3,5,6,8,10,11,13,15,16,17,19,20,23,25,26,27,29],[2,3,4,5,7,9,10,12,13,15,16,17,19,20,23,24,25,27,29],[0,2,3,4,5,6,7,9,10,11,14,15,16,17,19,20,22,26,27,28,29],[0,3,6,10,11,12,14,15,16,17,19,20,24,25,27,28,29],[2,4,8,9,13,14,15,16,17,19,20,22,23,25,26],[12,13,14,15,16,17,19,20,22,24],[1,2,3,4,7,9,10,11,18,19,20,21,22,23,24,25],[1,2,4,7,8,12,18,19,20,21,22,26,28,29],[2,7,8,9,13,18,19,20,22,23,24,25,27,28,29],[1,2,7,10,12,13,18,19,20,23,26,27],[0,1,4,5,6,7,14,18,19,20,21,23,27,29],[0,1,2,3,5,7,8,9,10,12,14,18,19,20,21,23,24,26,27,28],[1,3,7,13,14,18,19,20,23,25,26,28],[2,3,5,9,10,12,13,14,18,19,20,22,24,25,29],[2,5,6,7,8,11,15,18,19,20,22,23,24,25,27],[0,1,2,3,4,7,8,9,10,11,12,15,18,19,20,22,24,26,28,29],[1,4,5,6,7,8,9,10,13,15,18,19,20,21,22,23,24,25,26,29],[1,2,4,11,12,13,15,18,19,20,21,23,24,27,28],[0,1,2,3,7,10,11,14,15,18,19,20,23,28],[2,3,4,5,9,10,11,12,14,15,18,19,20,23,26,27,29],[1,6,10,11,13,14,15,18,19,20,21,23,25,27,28,29],[0,2,3,4,6,8,10,12,13,14,15,18,19,20,21,22,25,26],[4,5,8,16,18,19,20,21,22,26,27,28,29],[0,1,3,5,6,8,12,16,18,19,20,21,22,23,24,27,29],[1,5,9,10,11,13,16,18,19,20,21,22,25,26,27],[1,2,8,12,13,16,18,19,20,21,24,25,27,28],[0,1,3,4,5,6,8,11,14,16,18,19,20,21,22,24,25,28,29],[0,2,4,10,12,14,16,18,19,20,21,22,26,29],[1,4,5,13,14,16,18,19,20,21,22,24,25,26],[0,1,2,4,7,9,10,12,13,14,16,18,19,20,21,23,28],[0,1,2,3,6,7,9,10,11,15,16,18,19,20,23,27,28,29],[0,1,2,3,4,6,8,10,11,12,15,16,18,19,20,26,29],[0,3,4,5,8,9,11,13,15,16,18,19,20,23,25,26,27,28],[2,4,5,6,9,10,11,12,13,15,16,18,19,20,22,23,25],[0,2,4,7,9,11,14,15,16,18,19,20,23,24,25,26],[0,1,3,4,6,7,9,10,11,12,14,15,16,18,19,20,23,24,27,28],[2,5,7,13,14,15,16,18,19,20,23,24,25,26,29],[12,13,14,15,16,18,19,20,22,24,27,28,29],[3,4,6,9,10,17,18,19,20,21,22,23,26,27,28,29],[0,1,7,9,10,12,17,18,19,20,21,24,25,27],[2,3,4,5,7,8,9,11,13,17,18,19,20,22,26,27,28],[2,5,6,7,8,10,12,13,17,18,19,20,22,24,25,27,29],[1,4,7,8,11,14,17,18,19,20,23,26],[0,1,2,6,7,8,11,12,14,17,18,19,20,22,23,24,28,29],[0,3,5,7,8,10,13,14,17,18,19,20,21,25,29],[12,13,14,17,18,19,20,21,23,24,25,26,28],[1,2,4,5,7,8,15,17,18,19,20,22,25,26,27,28],[4,7,8,12,15,17,18,19,20,23,29],[0,1,3,6,7,9,11,13,15,17,18,19,20,21,22,23,25,27,29],[12,13,15,17,18,19,20,21,22,23,26,28],[0,1,2,3,5,6,10,14,15,17,18,19,20,21,25,26,28],[12,14,15,17,18,19,20,21,22,25,27,29],[1,2,3,4,8,11,13,14,15,17,18,19,20,23,26,29],[12,13,14,15,17,18,19,20,27,28],[0,3,5,6,7,8,9,10,16,17,18,19,20,22,24,25,26,29],[0,1,3,4,6,7,11,12,16,17,18,19,20,23,25,28,29],[2,3,4,5,6,7,8,10,13,16,17,18,19,20,22,23,24,26,27],[12,13,16,17,18,19,20,22,23,27,28],[0,2,4,5,7,10,11,14,16,17,18,19,20,21,22,24,25,27,28,29],[12,14,16,17,18,19,20,21,26,27,29],[13,14,16,17,18,19,20,21,22,23,24,25,26,28],[12,13,14,16,17,18,19,20,21,22],[0,1,2,5,11,15,16,17,18,19,20,21,24,27],[12,15,16,17,18,19,20,21,22,23,24,26,28],[13,15,16,17,18,19,20,21,23,24,25,26,28,29],[12,13,15,16,17,18,19,20,21,23,24,25,27,29],[14,15,16,17,18,19,20,24,26,29],[12,14,15,16,17,18,19,20,22,24,25,27,28,29],[13,14,15,16,17,18,19,20,23,24,26,27,28],[12,13,14,15,16,17,18,19,20,24,25]]},"distance":{"d":5,"is_exact":true,"upper":5,"witness":[28,194,199,448,470],"A_d":1087842,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[1,2],[3,1],[5,3],[7,2],[8,2],[9,1],[11,1]],"CZ":[[0,1],[0,2],[0,6],[0,9],[0,10],[0,11],[0,13],[0,14],[0,17],[0,19],[0,21],[0,23],[0,25],[0,29],[1,4],[1,7],[1,8],[1,14],[1,20],[1,25],[1,29],[2,3],[2,4],[2,5],[2,11],[2,12],[2,13],[2,14],[2,15],[2,16],[2,17],[2,18],[2,19],[2,22],[2,23],[2,24],[2,26],[2,27],[2,28],[2,29],[3,4],[3,5],[3,9],[3,10],[3,15],[3,16],[3,17],[3,18],[3,23],[3,24],[3,25],[3,27],[4,8],[4,15],[4,17],[4,18],[4,22],[4,23],[4,27],[5,8],[5,10],[5,11],[5,12],[5,18],[5,19],[5,21],[5,22],[5,24],[5,25],[5,27],[5,29],[6,8],[6,9],[6,10],[6,11],[6,12],[6,14],[6,19],[6,23],[6,24],[6,26],[6,28],[6,29],[7,8],[7,10],[7,11],[7,12],[7,13],[7,16],[7,19],[7,20],[7,23],[7,26],[7,27],[7,29],[8,10],[8,14],[8,16],[8,17],[8,18],[8,20],[8,21],[8,22],[8,23],[8,24],[8,25],[8,27],[8,29],[9,10],[9,14],[9,16],[9,17],[9,19],[9,20],[9,21],[9,23],[9,26],[10,12],[10,16],[10,18],[10,21],[10,28],[11,12],[11,13],[11,14],[11,15],[11,18],[11,20],[11,22],[11,27],[11,29]]},"rotation_powers":[[0,7],[1,7],[2,5],[3,3],[4,7],[5,5],[7,7],[8,7],[9,7],[11,7],[17,7],[23,3],[31,5],[63,5],[99,3],[104,3],[107,3],[109,3],[113,3],[115,3],[117,3],[121,3],[122,3],[124,3],[127,5],[134,3],[135,3],[137,3],[140,3],[141,3],[143,3],[146,3],[147,3],[148,3],[152,3],[153,3],[155,3],[157,3],[160,5],[161,3],[162,3],[164,3],[168,3],[171,3],[172,3],[174,3],[176,3],[180,3],[182,3],[183,3],[185,3],[186,3],[191,3],[192,3],[195,3],[196,3],[197,3],[199,3],[200,3],[202,3],[204,3],[206,3],[210,3],[211,3],[212,3],[213,3],[214,3],[215,3],[218,3],[219,3],[221,7],[224,3],[225,3],[230,3],[233,3],[234,3],[236,3],[237,3],[238,3],[239,7],[240,5],[241,3],[246,3],[247,3],[250,3],[252,3],[253,3],[255,3],[260,3],[261,3],[262,3],[263,3],[264,3],[267,3],[269,3],[270,3],[271,3],[272,3],[275,3],[276,3],[280,3],[282,3],[284,3],[286,3],[288,3],[290,3],[291,3],[292,3],[293,3],[294,3],[295,3],[296,3],[297,3],[299,3],[305,3],[307,3],[309,3],[310,3],[312,3],[313,3],[315,3],[316,3],[318,3],[319,3],[321,3],[323,3],[324,3],[325,3],[327,3],[329,3],[330,3],[334,3],[336,3],[337,3],[339,3],[345,3],[346,3],[349,3],[353,3],[354,3],[355,3],[357,3],[358,3],[361,3],[363,3],[364,3],[367,3],[368,3],[369,3],[370,3],[371,3],[374,3],[375,3],[376,3],[379,3],[381,3],[382,3],[383,3],[386,3],[387,3],[389,3],[395,3],[396,3],[397,3],[398,3],[399,3],[403,3],[404,3],[405,3],[406,3],[407,3],[408,3],[411,3],[412,3],[413,3],[415,3],[416,3],[417,3],[418,3],[421,3],[424,3],[430,3],[432,3],[433,3],[436,3],[438,3],[439,3],[440,3],[442,3],[443,3],[444,3],[445,3],[446,3],[447,3],[449,3],[451,3],[452,3],[454,3],[455,3],[457,3],[458,3],[460,3],[461,3],[462,3],[466,3],[469,3],[475,3],[476,3],[478,3],[483,3],[484,3],[485,3],[487,3],[488,3],[489,3],[490,3],[493,3],[495,3],[496,3],[499,3],[500,3],[501,3],[503,3],[504,3],[505,3],[506,3],[508,3]]},"metrics":{"gamma":2.3309149805860003,"gamma_t":null,"gamma_rho":2.3309149805860003,"gamma_claim":2.3309149805860003,"gamma_t_claim":null,"gamma_rho_claim":2.3309149805860003,"v_ex":12,"rate":0.023483365949119372,"t_count":null,"poly_degree":null,"effective_width":12},"provenance":{"regimes":["AI search"],"discovery":"AI search","strongest_claim":"found by an AI search campaign; a verified witness, not a maximum","sources":[{"regime":"AI search","file":"master_catalog/catalogue_new","label":"T0.T1.T2.T3.T4.T5.T6.T7.T8.T9.T10.T11","N":30,"d":5,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:377"}]},"references":[{"key":"jain2026symmetry","short":"Jain et al. (2026)","full":"S. P. Jain, A. Wills, and S. Singh, \"Symmetry and AI-assisted discovery of magic-state factories,\" arXiv:2610.06535 (2026).","url":"https://arxiv.org/abs/2610.06535","date":"2026-10-05"}]}