{"id":"511.7.5.a","row":1095,"stored":{"file":"master_catalog.json","row":1095,"construction":null,"columns_sha256":null},"parameters":{"n":511,"k":7,"d":5,"N":25,"r":18,"level":3},"gate":{"string":"0+1+2+3+4+5+6","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6","monomials":[[0],[1],[2],[3],[4],[5],[6]],"sk_key":[[0],[1],[2],[3],[4],[5],[6]],"sk_fingerprint":"4227720e4bdc2b66","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,1,3,4,6,7,16],[0,4,8,19],[4,7,8,16,17,18,19],[0,2,3,5,9,22],[1,2,3,4,6,7,9,16,18,20,22],[0,1,2,3,4,5,8,9,19,20,21,22],[1,2,4,7,8,9,16,17,19,21,22],[0,3,10,16,20],[0,3,7,10,19,20,22],[1,2,8,10,16,19,20,21,23],[2,3,4,6,7,8,10,17,18,20,21,22,23],[0,1,5,9,10,16,20,22,23,24],[0,1,3,7,9,10,18,19,23,24],[0,1,2,3,5,8,9,10,16,19,22,24],[0,2,3,4,6,7,8,9,10,17,20,24],[2,5,11,19,23],[0,2,5,6,7,11,16,19,20,23,24],[0,4,8,11,16,20,22,23],[1,3,7,8,11,17,18,22,23,24],[1,3,5,9,11,17,19,21,22,23,24],[0,1,6,7,9,11,16,17,18,19,21,22,23],[2,3,4,8,9,11,16,17,23,24],[0,1,2,3,5,7,8,9,11,23],[0,1,2,10,11,16,17,18,19,20,21,22,23],[0,2,3,4,7,10,11,17,18,21,23,24],[2,3,5,8,10,11,17,18],[2,3,5,6,7,8,10,11,16,19,20,22,24],[1,2,3,9,10,11,16,18,19,20],[2,3,4,5,7,9,10,11,20,22,24],[1,2,5,8,9,10,11,18,20,22,23],[1,2,3,6,7,8,9,10,11,16,17,18,19,20,23,24],[0,1,4,6,12,17,21,22],[1,4,5,7,12,16,21,22],[2,3,6,8,12,17,18,19,21,23],[0,1,2,4,5,6,7,8,12,16,17,19,21,23],[2,4,6,9,12,16,17,19,20,21,23],[0,2,3,4,7,9,12,18,19,21,23],[3,6,8,9,12,16,17,18,22],[0,1,3,4,6,7,8,9,12,17,18,20,22],[0,1,3,4,10,12,16,17,18,21,24],[0,5,7,10,12,18,19,21,22,24],[1,3,4,8,10,12,16,17,19,22,24],[1,3,4,5,6,7,8,10,12,17,18,24],[0,1,3,4,9,10,12,17,18,19,20,21,22],[0,3,7,9,10,12,16,21],[0,3,4,8,9,10,12,17,21],[0,4,6,7,8,9,10,12,16,17,19,20,21,22],[0,3,4,5,11,12,16,17,19,22,23,24],[1,6,7,11,12,19,20,22,23],[1,8,11,12,17,18,20,22,24],[0,1,5,7,8,11,12,16,17,22],[0,2,3,4,9,11,12,20,21],[1,2,3,6,7,9,11,12,16,17,18,20,21,24],[0,2,5,8,9,11,12,16,18,19,20,23],[2,3,5,7,8,9,11,12,18,19,20,23,24],[0,1,3,4,6,10,11,12,19,21,22,23],[0,1,3,4,5,6,7,10,11,12,16,17,20,21,23,24],[1,2,3,4,5,6,8,10,11,12,16,18,20,22,23],[2,7,8,10,11,12,19,23,24],[3,4,5,6,9,10,11,12,16,17,20,23],[4,5,6,7,9,10,11,12,18,19,20,22,23,24],[1,2,3,4,6,8,9,10,11,12,17,18,19,20,23],[2,3,7,8,9,10,11,12,16,17,18,20,22,23,24],[0,1,3,5,6,13,16,24],[1,2,3,4,5,7,13,19,22,23,24],[1,4,5,8,13,16,19,20,24],[0,2,3,4,5,7,8,13,17,18,20,22,23,24],[0,1,5,6,9,13,17,20,22,24],[1,2,3,4,7,9,13,16,17,18,19,23,24],[0,3,4,5,8,9,13,17,19,20,21,22,24],[1,2,3,4,7,8,9,13,16,21,23,24],[0,2,3,4,10,13,17,19,20,21,22,23,24],[0,1,4,7,10,13,16,17,19,20,21,22,24],[1,3,4,6,8,10,13,17,22,24],[1,2,3,7,8,10,13,16,18,22,23,24],[1,4,9,10,13,16,19,21],[2,4,5,7,9,10,13,18,19,20,21,23],[1,2,4,6,8,9,10,13,16,21,23],[1,3,5,7,8,9,10,13,17,20,21],[0,2,4,11,13,18,19,20,21,22,24],[1,3,4,6,7,11,13,16,18,21,23],[3,5,6,8,11,13,16,18,20,21,24],[0,2,3,4,5,6,7,8,11,13,17,19,21,22,23],[1,2,3,4,5,9,11,13,16,18,19],[0,3,4,6,7,9,11,13,22,23,24],[6,8,9,11,13,18,20,21,22],[0,2,3,4,5,6,7,8,9,11,13,16,17,18,19,20,21,23,24],[0,3,6,10,11,13,16,21,22,23,24],[0,2,3,4,6,7,10,11,13,20,21,22],[1,3,5,8,10,11,13,19,24],[2,5,6,7,8,10,11,13,16,17,18,19,20,23],[0,2,5,6,9,10,11,13,20,24],[0,3,4,6,7,9,10,11,13,16,18,20,23],[0,2,8,9,10,11,13,16,19,22,23,24],[0,1,5,6,7,8,9,10,11,13,17,19,22],[0,4,6,12,13,16,17,18,19,21],[1,2,3,4,5,7,12,13,18,21,22,23],[1,2,8,12,13,16,17,20,21,22,23],[0,1,4,5,7,8,12,13,17,18,19,20,21],[0,1,4,5,6,9,12,13,16,18,21,22,23],[2,4,5,7,9,12,13,17,19,20,21],[0,1,2,5,8,9,12,13,16,19],[1,3,4,5,7,8,9,12,13,20,22,23],[1,2,5,6,10,12,13,23,24],[1,4,6,7,10,12,13,16,17,24],[0,1,2,3,5,8,10,12,13,18,19,20,21,22,23,24],[0,6,7,8,10,12,13,16,19,20,21,22,24],[0,1,6,9,10,12,13,17,19,22,23],[0,1,2,3,4,6,7,9,10,12,13,16,18,19,20,22],[0,3,8,9,10,12,13,17,18,23],[0,1,2,3,6,7,8,9,10,12,13,16,17,18,20],[0,5,6,11,12,13,16,17,20,21,22,24],[2,4,7,11,12,13,19,21,23],[1,4,8,11,12,13,17,18,19,20,21,22,23,24],[0,2,3,4,5,7,8,11,12,13,16,17,21],[5,6,9,11,12,13,16,17,19,20,23],[0,2,3,4,5,7,9,11,12,13,18,20,22,24],[4,8,9,11,12,13,17,18,21],[0,1,2,4,7,8,9,11,12,13,16,17,18,19,21,22,23,24],[2,3,4,5,6,10,11,12,13,17,19,20,21,23],[1,4,6,7,10,11,12,13,16,19,21,24],[0,4,8,10,11,12,13,16,17,18,20,23],[0,2,5,6,7,8,10,11,12,13,17,24],[1,3,4,5,6,9,10,11,12,13,17,20,22,23],[2,3,4,5,6,7,9,10,11,12,13,16,18,20,22,24],[2,4,8,9,10,11,12,13,16,17,18,19,22,23],[0,1,2,4,5,7,8,9,10,11,12,13,17,18,19,22,24],[0,2,3,4,5,6,14,18,19,22],[0,1,2,5,7,14,18,19,20,21,22,23],[0,3,4,5,8,14,16,17,18,20,21],[0,3,4,5,7,8,14,16,23],[0,2,9,14,18,19,23],[0,1,2,4,5,6,7,9,14,19,21],[1,6,8,9,14,16,17,18,22,23],[1,3,5,6,7,8,9,14,16,18,21,22],[0,3,10,14,16,18,22,23],[3,7,10,14,16,18,19,20,21],[0,1,4,6,8,10,14,17,18,19,20],[3,7,8,10,14,21,22,23],[1,2,4,5,6,9,10,14,16,18,23,24],[0,1,2,3,4,6,7,9,10,14,16,19,21,22,24],[0,1,2,3,5,8,9,10,14,17,18,19,21,22,24],[2,3,4,6,7,8,9,10,14,18,23,24],[1,2,4,11,14,16,17,18,21,23,24],[1,2,4,6,7,11,14,16,17,18],[1,2,4,5,6,8,11,14,16,18,19,23,24],[2,3,5,6,7,8,11,14,16,17,19,21],[0,2,3,6,9,11,14,16,18,22],[0,2,5,7,9,11,14,16,20,21,22,23,24],[1,2,3,5,8,9,11,14,16,17,18,19,20,22],[2,3,4,7,8,9,11,14,16,18,19,21,22,23,24],[3,6,10,11,14,19,22,24],[0,1,4,6,7,10,11,14,21,23],[1,2,4,5,8,10,11,14,17,22,23,24],[0,1,2,4,5,6,7,8,10,11,14,18,19,21],[2,4,9,10,11,14,17,19,21,24],[0,1,2,5,7,9,10,11,14,17,18,20,22,23],[0,3,5,6,8,9,10,11,14,20,23,24],[7,8,9,10,11,14,17,19,21,22],[2,3,5,6,12,14,16,18,20,21,23,24],[2,3,7,12,14,16,17,18,24],[1,2,5,8,12,14,17,19,24],[2,3,4,7,8,12,14,17,18,19,20,21,23,24],[1,2,3,4,5,9,12,14,18,19,21,22,23,24],[1,2,4,5,6,7,9,12,14,17,19,22,24],[0,1,2,4,5,6,8,9,12,14,16,17,21,22,24],[0,2,5,6,7,8,9,12,14,16,17,22,23,24],[0,3,4,6,10,12,14,19,21,22],[1,5,6,7,10,12,14,17,20,23],[0,2,3,8,10,12,14,16,17,18,20,21,22],[2,3,5,6,7,8,10,12,14,16,17,19,23],[2,3,9,10,12,14,16,20,21,23,24],[0,1,2,3,4,7,9,10,12,14,16,17,18,19,20,22,24],[0,1,3,4,6,8,9,10,12,14,17,18,19,20,23,24],[1,4,7,8,9,10,12,14,17,18,20,21,22,24],[0,3,6,11,12,14,16,17,18,19,20,21,22,24],[0,1,4,5,7,11,12,14,16,18,19,20,22,23],[0,1,2,5,8,11,12,14,16,20,23,24],[0,1,2,7,8,11,12,14,16,18,20,21],[3,4,5,9,11,12,14,18],[1,3,5,6,7,9,11,12,14,17,20,21,23,24],[0,2,4,6,8,9,11,12,14,17,19,20,22,23],[0,2,3,4,6,7,8,9,11,12,14,17,19,21,22,24],[1,2,4,6,10,11,12,14,18,22,23],[0,1,2,4,5,6,7,10,11,12,14,17,18,19,21,24],[1,2,5,8,10,11,12,14,17,19,23],[0,2,3,4,6,7,8,10,11,12,14,17,18,21,22,24],[5,9,10,11,12,14,16,17,18,19,20,21],[0,3,5,7,9,10,11,12,14,16,22,23,24],[0,1,4,6,8,9,10,11,12,14,16,22],[0,1,2,3,4,5,6,7,8,9,10,11,12,14,16,19,20,21,23,24],[1,5,13,14,19,20,21,22,24],[1,2,4,5,6,7,13,14,24],[1,2,3,5,8,13,14,16,17,20,24],[5,7,8,13,14,16,18,19,21,22,24],[0,1,2,3,4,5,6,9,13,14,16,17,19,21,23,24],[0,1,7,9,13,14,16,17,18,22,23,24],[4,5,6,8,9,13,14,20,21,22,23,24],[1,2,4,6,7,8,9,13,14,17,19,20,23,24],[0,3,5,10,13,14,16,17,19,20,24],[1,2,5,7,10,13,14,16,17,19,21,24],[0,1,3,4,5,8,10,13,14,20,22,23,24],[1,2,3,5,6,7,8,10,13,14,17,18,21,22,23,24],[0,1,4,5,6,9,10,13,14,19,22],[2,4,6,7,9,10,13,14,18,19,21,22],[1,5,6,8,9,10,13,14,16,17,20,21,23],[0,1,2,3,4,7,8,9,10,13,14,16,20,23],[0,1,4,11,13,14,17,18,21,22],[0,2,3,4,6,7,11,13,14,17,18,19,24],[0,1,3,4,5,8,11,13,14,18,19,20,22],[0,1,2,3,5,7,8,11,13,14,17,20,21,24],[0,2,3,5,6,9,11,13,14,16,17,18,20,23,24],[0,1,3,7,9,11,13,14,16,17,19,21,22,23],[1,2,6,8,9,11,13,14,16,18,19,20,23,24],[1,3,4,5,6,7,8,9,11,13,14,16,17,18,21,22,23],[1,4,5,10,11,13,14,16,17,21,22],[0,1,2,5,7,10,11,13,14,16,17,22,24],[2,8,10,11,13,14,16,19,20,21,22,23],[0,1,3,7,8,10,11,13,14,16,17,18,19,20,22,23,24],[0,1,3,6,9,10,11,13,14,17,20],[1,2,4,5,6,7,9,10,11,13,14,17,18,21,24],[1,8,9,10,11,13,14,19,20,21,23],[1,3,4,6,7,8,9,10,11,13,14,17,19,23,24],[1,3,4,6,12,13,14,16,18,19,22,23,24],[2,4,5,7,12,13,14,16,17,18,20,21,23,24],[3,4,6,8,12,13,14,17,21,22,24],[2,3,5,6,7,8,12,13,14,17,18,19,20,24],[0,2,3,5,9,12,13,14,16,17,18,23,24],[0,1,3,5,6,7,9,12,13,14,16,19,21,22,23,24],[2,3,5,8,9,12,13,14,19,20,24],[4,5,7,8,9,12,13,14,20,21,22,24],[4,10,12,13,14,17,19,20,21,22,23],[0,2,5,7,10,12,13,14,19,22,23],[2,3,8,10,12,13,14,16,18,20,21,22,23],[5,7,8,10,12,13,14,16,22,23],[5,6,9,10,12,13,14,20,21,24],[0,2,3,4,5,7,9,10,12,13,14,17,18,20,24],[0,1,2,3,8,9,10,12,13,14,16,17,18,19,24],[2,4,5,7,8,9,10,12,13,14,16,17,18,19,21,24],[0,2,6,11,12,13,14,17,20,21,22,23,24],[0,3,4,7,11,12,13,14,19,20,23],[0,1,8,11,12,13,14,18,19,24],[1,2,4,5,7,8,11,12,13,14,21,22],[0,1,2,3,4,5,6,9,11,12,13,14,17,19,20,23],[0,1,2,7,9,11,12,13,14,18,21,22,23,24],[0,2,8,9,11,12,13,14,18,20,22],[0,1,3,5,6,7,8,9,11,12,13,14,18,19,21,24],[0,2,6,10,11,12,13,14,16,17,21,23],[1,4,5,6,7,10,11,12,13,14,16,23,24],[0,2,3,4,6,8,10,11,12,13,14,16,18,19,20,21,22,23],[0,1,2,3,4,5,6,7,8,10,11,12,13,14,16,19,20,22,23,24],[3,4,5,9,10,11,12,13,14,16,17,19,22],[2,4,7,9,10,11,12,13,14,16,18,19,20,21,22,24],[0,1,2,3,5,6,8,9,10,11,12,13,14,16,18,21],[1,2,4,6,7,8,9,10,11,12,13,14,16,18,20,24],[2,3,4,5,6,15,16,20,21,22],[0,1,3,4,5,6,7,15,18,20,21,23,24],[0,1,3,4,5,6,8,15,16,17,20,22,23,24],[1,2,5,7,8,15,20],[0,5,6,9,15,19,20,21,23,24],[1,2,3,6,7,9,15,16,19,21,22],[0,2,5,8,9,15,17,19,21],[4,7,8,9,15,16,18,19,20,21,22,23,24],[2,6,10,15,17,22],[3,4,7,10,15,16,17,18,19,22,23,24],[0,2,3,4,6,8,10,15,22,24],[0,1,3,4,7,8,10,15,16,17,19,22,23],[1,2,3,4,6,9,10,15,16,17,19],[1,3,5,7,9,10,15,17,20,23,24],[2,8,9,10,15,16,19,20,21,24],[1,3,5,7,8,9,10,15,17,18,21,23],[0,1,2,6,11,15,16,17,19,20],[1,3,4,6,7,11,15,17,18,19,22,23],[2,5,8,11,15,19,21,22,23,24],[0,1,5,6,7,8,11,15,16,17,19,20,21,24],[0,3,4,5,9,11,15,20,21,22,23],[2,3,6,7,9,11,15,16,20,21],[0,3,4,6,8,9,11,15,16,17,20,21,24],[1,2,4,5,7,8,9,11,15,18,20,21,22,23,24],[0,2,4,10,11,15,17,18,19,22],[0,1,4,7,10,11,15,16,17,20,22,23],[3,5,8,10,11,15,16,18,19,20,24],[2,4,5,6,7,8,10,11,15,17,18,23,24],[2,3,5,6,9,10,11,15,16,18,21,24],[1,6,7,9,10,11,15,18,19,21,23,24],[1,4,8,9,10,11,15,17,18,22],[1,2,5,6,7,8,9,10,11,15,16,19,22,23],[0,4,5,6,12,15,17,18,19,20,22,24],[2,3,7,12,15,16,19,20,23],[3,4,5,8,12,15,19,20,21],[0,1,2,3,4,7,8,12,15,16,19,20,21,22,23,24],[1,2,5,6,9,12,15,17,18,19],[0,1,4,5,6,7,9,12,15,16,18,19,20,22,23,24],[2,3,8,9,12,15,19,20,22,24],[0,1,6,7,8,9,12,15,16,18,19,23],[3,5,10,12,15,16,19,20,21],[1,2,3,5,7,10,12,15,17,18,20,21,23,24],[0,1,2,3,4,8,10,12,15,16,17,18,19,20,21,22,23,24],[0,1,5,6,7,8,10,12,15,17,18,20,21,22],[3,4,5,9,10,12,15,16,19,21,22,23],[1,2,4,6,7,9,10,12,15,17,20,21,22,24],[2,3,5,6,8,9,10,12,15,16,17,18,19,20,24],[3,4,6,7,8,9,10,12,15,17,23],[2,5,6,11,12,15,16,18,20],[0,1,5,6,7,11,12,15,17,22,23],[0,3,5,8,11,12,15,17,21,24],[2,5,7,8,11,12,15,16,17,20,21,22,23,24],[5,6,9,11,12,15,16,17,18,21,22],[0,1,2,3,4,6,7,9,11,12,15,18,21,23],[1,2,3,8,9,11,12,15,21,22,24],[0,1,3,4,5,6,7,8,9,11,12,15,16,18,21,23,24],[0,1,2,5,6,10,11,12,15,18,20,24],[0,1,3,4,5,7,10,11,12,15,16,17,19,23,24],[2,6,8,10,11,12,15,16,17,23],[1,6,7,8,10,11,12,15,17,19,20],[2,4,6,9,10,11,12,15,17,18,21,22,23],[5,6,7,9,10,11,12,15,16,18,19,21,22],[2,5,8,9,10,11,12,15,16,22,24],[0,2,4,7,8,9,10,11,12,15,18,19,22,23,24],[0,1,3,4,5,13,15,17,18,19,22,23,24],[1,4,6,7,13,15,16,17,22,23],[2,5,8,13,15,18,19,20,21,22],[0,1,2,4,5,6,7,8,13,15,16,17,18,20,21,22,24],[0,1,4,9,13,15,18,20],[1,4,7,9,13,15,16,18,19,24],[0,1,2,3,4,5,8,9,13,15,17,18,20,23,24],[2,5,6,7,8,9,13,15,16,19,23],[2,3,6,10,13,15,16,17,18,20,24],[1,2,3,7,10,13,15,17,20,22],[0,2,4,5,6,8,10,13,15,16,18],[0,2,4,5,6,7,8,10,13,15,17,18,22,24],[0,1,3,4,5,6,9,10,13,15,16,18,19,22,24],[0,4,7,9,10,13,15,18,19,20],[0,5,8,9,10,13,15,16,17,18,19,21,22],[0,4,6,7,8,9,10,13,15,19,20,21,24],[1,4,11,13,15,16,20,22,24],[0,4,5,6,7,11,13,15,18,19,22,24],[0,3,5,6,8,11,13,15,17,20,21,23],[7,8,11,13,15,16,19,21,23],[0,4,5,9,11,13,15,16,19,21,23,24],[1,3,7,9,11,13,15,21,23,24],[0,8,9,11,13,15,17,19,20,21,22],[4,7,8,9,11,13,15,16,18,20,21,22],[0,1,2,3,5,10,11,13,15,17,18,19,21,22,23,24],[0,1,2,6,7,10,11,13,15,16,17,19,20,21,23,24],[1,3,6,8,10,11,13,15,16,18,19,21,23],[3,7,8,10,11,13,15,17,18,19,20,21,22,23],[0,1,4,5,9,10,11,13,15,17,18,20,23],[0,1,2,7,9,10,11,13,15,16,17,18,20,22,23],[0,4,5,8,9,10,11,13,15,16,18,21,22,23,24],[3,7,8,9,10,11,13,15,17,21,23,24],[0,1,3,4,5,12,13,15,16,18,19,21,23,24],[2,4,5,7,12,13,15,17,21,23],[1,3,5,6,8,12,13,15,16,17,19,20,22,23],[0,1,2,3,7,8,12,13,15,17,20,22,23,24],[0,2,3,5,6,9,12,13,15,17,18,19,21,22,23],[1,3,4,6,7,9,12,13,15,16,18,20,21,22,23,24],[0,1,6,8,9,12,13,15,19,21,23,24],[1,4,5,6,7,8,9,12,13,15,16,18,20,21,23],[0,3,4,6,10,12,13,15,21],[0,2,3,5,6,7,10,12,13,15,16,17,18,21,22,24],[1,2,4,6,8,10,12,13,15,17,18,20,21,22,23,24],[4,5,7,8,10,12,13,15,16,17,18,20,21,23],[3,4,9,10,12,13,15,16,17,21,22,23],[0,1,3,4,7,9,10,12,13,15,20,21,23,24],[3,4,8,9,10,12,13,15,16,18,24],[1,6,7,8,9,10,12,13,15,20,22],[2,4,5,11,12,13,15,16,17,20],[0,2,4,6,7,11,12,13,15,18,19],[0,1,2,3,8,11,12,13,15,18,20,21,24],[2,3,4,7,8,11,12,13,15,16,18,19,21,24],[0,2,3,4,5,9,11,12,13,15,17,20,21,22],[4,5,7,9,11,12,13,15,16,19,20,21,22],[1,2,4,6,8,9,11,12,13,15,16,18,21,22,24],[1,3,4,5,7,8,9,11,12,13,15,19,21,22,24],[2,3,4,5,10,11,12,13,15,19,20,21,22,23,24],[0,3,4,7,10,11,12,13,15,16,17,18,19,21,23,24],[0,3,4,5,6,8,10,11,12,13,15,16,17,18,19,20,21,22],[0,7,8,10,11,12,13,15,17,18,19,21],[1,4,9,10,11,12,13,15,16,19,20],[0,1,2,3,4,5,6,7,9,10,11,12,13,15,17,19,20,22],[2,8,9,10,11,12,13,15,17,18,19,21,23,24],[7,8,9,10,11,12,13,15,16,17,19,21,22,23,24],[0,2,5,6,14,15,16,18,20,23,24],[0,1,2,3,4,6,7,14,15,16,21,22,23],[0,2,3,4,5,8,14,15,18,22],[0,3,4,5,6,7,8,14,15,17,18,20,21,24],[0,1,2,5,6,9,14,15,18,19,20,22,23],[0,1,2,3,4,7,9,14,15,18,19,20,21,23,24],[1,4,5,6,8,9,14,15,16,18,19,20,21,24],[2,4,5,7,8,9,14,15,16,17,19,20,22],[4,5,6,10,14,15,17,18,19,20,21,24],[0,1,2,4,6,7,10,14,15,17],[1,2,5,6,8,10,14,15,16,17,18,19,22],[0,5,6,7,8,10,14,15,16,18,20,21,22,24],[0,1,6,9,10,14,15,16,17,18,20,21,22,23,24],[1,2,3,5,7,9,10,14,15,16,17,18,19,20,22,23],[2,3,5,8,9,10,14,15,17,18,20,21,23],[0,2,5,7,8,9,10,14,15,19,20,23,24],[0,1,2,5,11,14,15,18,19,20,23],[0,4,6,7,11,14,15,19,20,21,22,23],[0,1,2,3,8,11,14,15,18,19,20,24],[0,3,5,6,7,8,11,14,15,17,18,19,20,21,22,24],[1,9,11,14,15,16,17,18,20,21,22,23],[4,5,6,7,9,11,14,15,16,17,18,23],[0,1,2,6,8,9,11,14,15,16,17,18,22,24],[1,2,3,4,7,8,9,11,14,15,16,20,21,24],[1,2,4,5,6,10,11,14,15,16,20,22],[0,4,5,7,10,11,14,15,16,18,19,20,21,22],[2,3,4,6,8,10,11,14,15,16,20,21,22,24],[0,2,6,7,8,10,11,14,15,16,17,19,20,22,24],[1,2,3,4,6,9,10,11,14,15,17,19,20,21,23,24],[0,3,4,7,9,10,11,14,15,17,23,24],[1,2,4,5,8,9,10,11,14,15,17,19,21,23],[0,1,2,3,5,7,8,9,10,11,14,15,18,20,23],[1,12,14,15,16,21,24],[1,2,3,4,5,7,12,14,15,16,17,18,20,22],[1,2,3,4,6,8,12,14,15,18,20,21],[0,2,5,6,7,8,12,14,15,18,22,24],[5,6,9,12,14,15,16,20,21,22,23],[0,1,4,6,7,9,12,14,15,16,17,20,23,24],[0,3,4,6,8,9,12,14,15,18,20,22,23,24],[0,4,7,8,9,12,14,15,20,21,23],[1,2,6,10,12,14,15,17,18,19,20,22,23],[0,2,3,5,6,7,10,12,14,15,21,22,23,24],[0,3,4,6,8,10,12,14,15,16,17,19,21,22,24],[2,3,6,7,8,10,12,14,15,16,17,20,22],[0,1,2,5,6,9,10,12,14,15,17,18,19,23],[5,6,7,9,10,12,14,15,18,21,23,24],[0,2,3,5,8,9,10,12,14,15,16,17,19,24],[0,1,4,5,7,8,9,10,12,14,15,16,17,18,21],[3,4,5,11,12,14,15,16,19,24],[0,4,5,6,7,11,12,14,15,16,17,18,19,21,22,24],[0,1,3,4,8,11,12,14,15,16,18,19,22],[0,1,2,4,5,7,8,11,12,14,15,16,18,19,21],[0,1,2,3,5,9,11,12,14,15,16,17,19,20,21,22,23,24],[6,7,9,11,12,14,15,16,19,23,24],[0,3,4,6,8,9,11,12,14,15,16,17,18,19,23],[0,1,3,5,6,7,8,9,11,12,14,15,16,17,19,20,21,22,23],[0,2,4,5,6,10,11,12,14,15,20,23],[0,1,2,5,7,10,11,12,14,15,17,18,19,20,21,23],[0,2,3,5,6,8,10,11,12,14,15,18,20,21,22,24],[2,3,4,5,7,8,10,11,12,14,15,18,19,20,22,24],[0,2,3,4,5,6,9,10,11,12,14,15,17,21,22,23,24],[0,3,6,7,9,10,11,12,14,15,19,20,22,23,24],[2,4,8,9,10,11,12,14,15,17,18,20,21],[7,8,9,10,11,12,14,15,17,19],[1,2,3,4,13,14,15,16,17,18,19,20],[1,2,4,7,13,14,15,16,17,21,23,24],[2,8,13,14,15,17,18,19,20,22,23,24],[1,2,7,8,13,14,15,18,21,22],[0,1,4,5,6,9,13,14,15,16,18,22,24],[0,1,2,3,5,7,9,13,14,15,16,18,19,21,22,23],[1,3,8,9,13,14,15,18,20,21,23],[2,3,5,7,8,9,13,14,15,17,19,20,24],[2,5,6,10,13,14,15,17,18,19,20,22],[0,1,2,3,4,7,10,13,14,15,17,19,21,23,24],[1,4,5,6,8,10,13,14,15,16,17,18,19,20,21,24],[1,2,4,7,8,10,13,14,15,16,18,19,22,23],[0,1,2,3,9,10,13,14,15,18,23],[2,3,4,5,7,9,10,13,14,15,18,21,22,24],[1,6,8,9,10,13,14,15,16,18,20,22,23,24],[0,2,3,4,6,7,8,9,10,13,14,15,16,17,20,21],[4,5,11,13,14,15,16,17,21,22,23,24],[0,1,3,5,6,7,11,13,14,15,16,17,18,19,22,24],[1,5,8,11,13,14,15,16,17,20,21,22],[1,2,7,8,11,13,14,15,16,19,20,22,23],[0,1,3,4,5,6,9,11,13,14,15,16,17,19,20,23,24],[0,2,4,7,9,11,13,14,15,16,17,21,24],[1,4,5,8,9,11,13,14,15,16,17,19,20,21],[0,1,2,4,7,8,9,11,13,14,15,16,18,23],[0,1,2,3,6,10,11,13,14,15,18,22,23,24],[0,1,2,3,4,6,7,10,11,13,14,15,21,24],[0,3,4,5,8,10,11,13,14,15,18,20,21,22,23],[2,4,5,6,7,8,10,11,13,14,15,17,18,20],[0,2,4,9,10,11,13,14,15,18,19,20,21],[0,1,3,4,6,7,9,10,11,13,14,15,18,19,22,23],[2,5,8,9,10,11,13,14,15,18,19,20,21,24],[7,8,9,10,11,13,14,15,17,19,22,23,24],[3,4,6,12,13,14,15,16,17,18,21,22,23,24],[0,1,7,12,13,14,15,16,19,20,22],[2,3,4,5,8,12,13,14,15,17,21,22,23],[2,5,6,7,8,12,13,14,15,17,19,20,22,24],[1,4,9,12,13,14,15,18,21],[0,1,2,6,7,9,12,13,14,15,17,18,19,23,24],[0,3,5,8,9,12,13,14,15,16,20,24],[7,8,9,12,13,14,15,16,18,19,20,21,23],[1,2,4,5,10,12,13,14,15,17,20,21,22,23],[4,7,10,12,13,14,15,18,24],[0,1,3,6,8,10,12,13,14,15,16,17,18,20,22,24],[7,8,10,12,13,14,15,16,17,18,21,23],[0,1,2,3,5,6,9,10,12,13,14,15,16,20,21,23],[7,9,10,12,13,14,15,16,17,20,22,24],[1,2,3,4,8,9,10,12,13,14,15,18,21,24],[7,8,9,10,12,13,14,15,22,23],[0,3,5,6,11,12,13,14,15,17,19,20,21,24],[0,1,3,4,6,7,11,12,13,14,15,18,20,23,24],[2,3,4,5,6,8,11,12,13,14,15,17,18,19,21,22],[7,8,11,12,13,14,15,17,18,22,23],[0,2,4,5,9,11,12,13,14,15,16,17,19,20,22,23,24],[7,9,11,12,13,14,15,16,21,22,24],[8,9,11,12,13,14,15,16,17,18,19,20,21,23],[7,8,9,11,12,13,14,15,16,17],[0,1,2,5,10,11,12,13,14,15,16,19,22],[7,10,11,12,13,14,15,16,17,18,19,21,23],[8,10,11,12,13,14,15,16,18,19,20,21,23,24],[7,8,10,11,12,13,14,15,16,18,19,20,22,24],[9,10,11,12,13,14,15,19,21,24],[7,9,10,11,12,13,14,15,17,19,20,22,23,24],[8,9,10,11,12,13,14,15,18,19,21,22,23],[7,8,9,10,11,12,13,14,15,19,20]]},"distance":{"d":5,"is_exact":true,"upper":5,"witness":[28,194,199,448,470],"A_d":1026759,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[1,2],[3,1],[5,3]],"CZ":[[0,1],[0,2],[0,6],[0,8],[0,9],[0,12],[0,14],[0,16],[0,18],[0,20],[0,24],[1,4],[1,9],[1,15],[1,20],[1,24],[2,3],[2,4],[2,5],[2,7],[2,8],[2,9],[2,10],[2,11],[2,12],[2,13],[2,14],[2,17],[2,18],[2,19],[2,21],[2,22],[2,23],[2,24],[3,4],[3,5],[3,10],[3,11],[3,12],[3,13],[3,18],[3,19],[3,20],[3,22],[4,10],[4,12],[4,13],[4,17],[4,18],[4,22],[5,7],[5,13],[5,14],[5,16],[5,17],[5,19],[5,20],[5,22],[5,24],[6,7],[6,9],[6,14],[6,18],[6,19],[6,21],[6,23],[6,24]]},"rotation_powers":[[0,7],[2,5],[4,5],[5,5],[7,7],[8,5],[9,5],[11,3],[15,5],[17,3],[19,5],[23,7],[63,3],[126,5],[127,7],[218,5],[221,7],[237,3],[239,5],[240,5],[254,3],[257,3],[258,3],[260,3],[261,3],[264,3],[265,3],[270,3],[271,3],[273,3],[274,3],[276,3],[277,3],[278,3],[280,3],[282,3],[283,3],[284,3],[286,3],[288,3],[290,3],[291,3],[296,3],[302,3],[304,3],[307,3],[309,3],[310,3],[312,3],[313,3],[316,3],[318,3],[319,3],[320,3],[322,3],[323,3],[328,3],[332,3],[333,3],[338,3],[342,3],[343,3],[348,3],[349,3],[352,3],[353,3],[354,3],[360,3],[361,3],[363,3],[366,3],[367,3],[369,3],[370,3],[371,3],[374,3],[375,3],[377,3],[381,3],[383,3],[390,3],[396,3],[397,3],[398,3],[400,3],[401,3],[403,3],[404,3],[405,3],[407,3],[410,3],[411,3],[412,3],[413,3],[414,3],[415,3],[416,3],[417,3],[420,3],[424,3],[431,3],[432,3],[433,3],[436,3],[438,3],[439,3],[441,3],[443,3],[445,3],[446,3],[447,3],[449,3],[451,3],[456,3],[458,3],[459,3],[467,3],[469,3],[476,3],[477,3],[480,3],[482,3],[484,3],[485,3],[487,3],[491,3],[497,3],[499,3],[501,3],[502,3],[503,3],[509,3],[510,3]]},"metrics":{"gamma":2.665812336096604,"gamma_t":null,"gamma_rho":2.665812336096604,"gamma_claim":2.665812336096604,"gamma_t_claim":null,"gamma_rho_claim":2.665812336096604,"v_ex":7,"rate":0.0136986301369863,"t_count":null,"poly_degree":null,"effective_width":7},"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","N":25,"d":5,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:383"}]},"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"}]}