{"id":"511.16.5.a","row":1106,"stored":{"file":"master_catalog.json","row":1106,"construction":null,"columns_sha256":null},"parameters":{"n":511,"k":16,"d":5,"N":34,"r":18,"level":3},"gate":{"string":"0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6\u00b7T7\u00b7T8\u00b7T9\u00b7T10\u00b7T11\u00b7T12\u00b7T13\u00b7T14\u00b7T15","monomials":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15]],"sk_key":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15]],"sk_fingerprint":"1a902ca3edc02bc0","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,1,3,4,6,7,9,10,11,12,14,15,16,25],[0,4,7,8,10,13,14,17,28],[4,8,10,12,15,16,17,25,26,27,28],[0,2,3,5,7,9,10,13,18,31],[1,2,3,4,6,9,10,11,15,16,18,25,27,29,31],[0,1,2,3,4,5,7,8,10,11,12,13,17,18,28,29,30,31],[1,2,4,8,9,11,12,13,16,17,18,25,26,28,30,31],[0,3,7,9,10,13,15,19,25,29],[0,3,7,9,10,12,16,19,28,29,31],[1,2,9,10,11,13,14,17,19,25,28,29,30,32],[2,3,4,6,12,13,16,17,19,26,27,29,30,31,32],[0,1,5,10,11,12,14,15,18,19,25,29,31,32,33],[0,1,3,9,11,12,14,15,16,18,19,27,28,32,33],[0,1,2,3,5,9,11,13,14,15,17,18,19,25,28,31,33],[0,2,3,4,6,9,15,16,17,18,19,26,29,33],[2,5,7,9,10,11,15,20,28,32],[0,2,5,6,7,8,9,10,11,12,14,16,20,25,28,29,32,33],[0,4,7,13,17,20,25,29,31,32],[1,3,7,8,9,10,11,12,15,16,17,20,26,27,31,32,33],[1,3,5,7,9,10,18,20,26,28,30,31,32,33],[0,1,6,7,8,13,14,16,18,20,25,26,27,28,30,31,32],[2,3,4,9,10,12,14,15,17,18,20,25,26,32,33],[0,1,2,3,5,8,9,10,11,12,14,15,16,17,18,20,32],[0,1,2,8,11,12,14,19,20,25,26,27,28,29,30,31,32],[0,2,3,4,7,9,10,13,15,16,19,20,26,27,30,32,33],[2,3,5,9,11,12,15,17,19,20,26,27],[2,3,5,6,7,8,9,11,16,17,19,20,25,28,29,31,33],[1,2,3,8,10,11,14,15,18,19,20,25,27,28,29],[2,3,4,5,7,10,14,15,16,18,19,20,29,31,33],[1,2,5,7,12,13,15,17,18,19,20,27,29,31,32],[1,2,3,6,8,9,10,12,16,17,18,19,20,25,26,27,28,29,32,33],[0,1,4,6,10,13,14,21,26,30,31],[1,4,5,8,10,13,14,15,16,21,25,30,31],[2,3,6,9,14,15,17,21,26,27,28,30,32],[0,1,2,4,5,6,8,10,11,13,14,15,16,17,21,25,26,28,30,32],[2,4,6,7,8,9,12,13,15,18,21,25,26,28,29,30,32],[0,2,3,4,7,10,14,16,18,21,27,28,30,32],[3,6,8,9,11,13,17,18,21,25,26,27,31],[0,1,3,4,6,9,12,13,14,15,16,17,18,21,26,27,29,31],[0,1,3,4,7,9,11,12,19,21,25,26,27,30,33],[0,5,8,10,12,13,14,16,19,21,27,28,30,31,33],[1,3,4,7,8,12,15,17,19,21,25,26,28,31,33],[1,3,4,5,6,12,15,16,17,19,21,26,27,33],[0,1,3,4,8,12,14,18,19,21,26,27,28,29,30,31],[0,3,7,11,15,16,18,19,21,25,30],[0,3,4,7,10,13,14,15,17,18,19,21,26,30],[0,4,6,8,9,12,16,17,18,19,21,25,26,28,29,30,31],[0,3,4,5,7,8,12,13,15,20,21,25,26,28,31,32,33],[1,6,8,9,10,11,12,13,14,16,20,21,28,29,31,32],[1,10,11,12,15,17,20,21,26,27,29,31,33],[0,1,5,7,10,11,12,13,14,16,17,20,21,25,26,31],[0,2,3,4,7,11,18,20,21,29,30],[1,2,3,6,12,13,14,15,16,18,20,21,25,26,27,29,30,33],[0,2,5,7,8,9,11,12,14,15,17,18,20,21,25,27,28,29,32],[2,3,5,8,10,11,14,15,16,17,18,20,21,27,28,29,32,33],[0,1,3,4,6,9,10,11,12,13,14,19,20,21,28,30,31,32],[0,1,3,4,5,6,9,10,11,12,14,16,19,20,21,25,26,29,30,32,33],[1,2,3,4,5,6,7,9,10,11,12,13,17,19,20,21,25,27,29,31,32],[2,7,12,13,14,15,16,17,19,20,21,28,32,33],[3,4,5,6,8,9,11,12,14,18,19,20,21,25,26,29,32],[4,5,6,8,10,11,14,15,16,18,19,20,21,27,28,29,31,32,33],[1,2,3,4,6,8,10,13,14,17,18,19,20,21,26,27,28,29,32],[2,3,8,10,11,12,16,17,18,19,20,21,25,26,27,29,31,32,33],[0,1,3,5,6,14,15,22,25,33],[1,2,3,4,5,10,13,14,15,16,22,28,31,32,33],[1,4,5,9,13,14,15,17,22,25,28,29,33],[0,2,3,4,5,11,13,14,15,16,17,22,26,27,29,31,32,33],[0,1,5,6,7,10,12,15,18,22,26,29,31,33],[1,2,3,4,7,9,10,15,16,18,22,25,26,27,28,32,33],[0,3,4,5,11,15,17,18,22,26,28,29,30,31,33],[1,2,3,4,10,12,13,14,15,16,17,18,22,25,30,32,33],[0,2,3,4,7,9,11,15,19,22,26,28,29,30,31,32,33],[0,1,4,16,19,22,25,26,28,29,30,31,33],[1,3,4,6,7,8,10,15,17,19,22,26,31,33],[1,2,3,8,12,14,15,16,17,19,22,25,27,31,32,33],[1,4,9,12,13,15,18,19,22,25,28,30],[2,4,5,7,9,10,11,16,18,19,22,27,28,29,30,32],[1,2,4,6,7,8,9,15,17,18,19,22,25,30,32],[1,3,5,8,13,14,16,17,18,19,22,26,29,30],[0,2,4,7,8,11,12,14,20,22,27,28,29,30,31,33],[1,3,4,6,9,14,15,16,20,22,25,27,30,32],[3,5,6,12,13,15,17,20,22,25,27,29,30,33],[0,2,3,4,5,6,7,8,10,16,17,20,22,26,28,30,31,32],[1,2,3,4,5,7,8,9,13,15,18,20,22,25,27,28],[0,3,4,6,9,10,11,12,13,15,16,18,20,22,31,32,33],[6,7,10,12,13,14,15,17,18,20,22,27,29,30,31],[0,2,3,4,5,6,8,9,10,12,13,14,16,17,18,20,22,25,26,27,28,29,30,32,33],[0,3,6,9,12,14,19,20,22,25,30,31,32,33],[0,2,3,4,6,8,9,10,13,16,19,20,22,29,30,31],[1,3,5,7,9,10,12,17,19,20,22,28,33],[2,5,6,7,8,10,11,12,13,15,16,17,19,20,22,25,26,27,28,29,32],[0,2,5,6,10,18,19,20,22,29,33],[0,3,4,6,8,9,10,16,18,19,20,22,25,27,29,32],[0,2,9,10,11,17,18,19,20,22,25,28,31,32,33],[0,1,5,6,8,9,12,14,16,17,18,19,20,22,26,28,31],[0,4,6,8,9,12,13,21,22,25,26,27,28,30],[1,2,3,4,5,7,11,12,13,16,21,22,27,30,31,32],[1,2,7,9,13,14,17,21,22,25,26,29,30,31,32],[0,1,4,5,8,9,10,14,15,16,17,21,22,26,27,28,29,30],[0,1,4,5,6,7,9,10,13,18,21,22,25,27,30,31,32],[2,4,5,8,9,14,15,16,18,21,22,26,28,29,30],[0,1,2,5,7,8,11,15,17,18,21,22,25,28],[1,3,4,5,9,12,13,15,16,17,18,21,22,29,31,32],[1,2,5,6,7,8,13,19,21,22,32,33],[1,4,6,7,10,12,13,14,15,16,19,21,22,25,26,33],[0,1,2,3,5,8,10,12,13,14,15,17,19,21,22,27,28,29,30,31,32,33],[0,6,9,10,13,15,16,17,19,21,22,25,28,29,30,31,33],[0,1,6,14,15,18,19,21,22,26,28,31,32],[0,1,2,3,4,6,8,9,12,14,15,16,18,19,21,22,25,27,28,29,31],[0,3,9,14,17,18,19,21,22,26,27,32],[0,1,2,3,6,8,9,10,11,15,16,17,18,19,21,22,25,26,27,29],[0,5,6,7,8,20,21,22,25,26,29,30,31,33],[2,4,7,8,10,12,13,16,20,21,22,28,30,32],[1,4,7,8,9,12,13,14,15,17,20,21,22,26,27,28,29,30,31,32,33],[0,2,3,4,5,7,8,11,13,14,15,16,17,20,21,22,25,26,30],[5,6,7,9,12,15,18,20,21,22,25,26,28,29,32],[0,2,3,4,5,7,11,12,13,14,16,18,20,21,22,27,29,31,33],[4,9,10,14,15,17,18,20,21,22,26,27,30],[0,1,2,4,9,11,13,15,16,17,18,20,21,22,25,26,27,28,30,31,32,33],[2,3,4,5,6,9,13,14,15,19,20,21,22,26,28,29,30,32],[1,4,6,7,11,12,13,14,15,16,19,20,21,22,25,28,30,33],[0,4,8,10,12,17,19,20,21,22,25,26,27,29,32],[0,2,5,6,7,8,12,14,15,16,17,19,20,21,22,26,33],[1,3,4,5,6,8,10,15,18,19,20,21,22,26,29,31,32],[2,3,4,5,6,7,8,11,13,15,16,18,19,20,21,22,25,27,29,31,33],[2,4,7,10,13,15,17,18,19,20,21,22,25,26,27,28,31,32],[0,1,2,4,5,7,8,11,12,16,17,18,19,20,21,22,26,27,28,31,33],[0,2,3,4,5,6,8,10,11,12,13,14,23,27,28,31],[0,1,2,5,8,9,13,15,16,23,27,28,29,30,31,32],[0,3,4,5,7,8,10,11,12,14,17,23,25,26,27,29,30],[0,3,4,5,7,8,10,14,15,16,17,23,25,32],[0,2,7,8,9,11,13,18,23,27,28,32],[0,1,2,4,5,6,7,8,9,10,11,12,13,15,16,18,23,28,30],[1,6,7,8,12,17,18,23,25,26,27,31,32],[1,3,5,6,7,8,9,11,12,16,17,18,23,25,27,30,31],[0,3,7,10,11,15,19,23,25,27,31,32],[3,12,13,15,16,19,23,25,27,28,29,30],[0,1,4,6,8,10,11,12,13,15,17,19,23,26,27,28,29],[3,7,8,9,10,12,13,16,17,19,23,30,31,32],[1,2,4,5,6,9,13,18,19,23,25,27,32,33],[0,1,2,3,4,6,7,11,13,14,16,18,19,23,25,28,30,31,33],[0,1,2,3,5,8,11,17,18,19,23,26,27,28,30,31,33],[2,3,4,6,7,8,10,11,13,14,15,16,17,18,19,23,27,32,33],[1,2,4,8,11,20,23,25,26,27,30,32,33],[1,2,4,6,7,11,13,14,15,16,20,23,25,26,27],[1,2,4,5,6,9,13,15,17,20,23,25,27,28,32,33],[2,3,5,6,7,8,11,16,17,20,23,25,26,28,30],[0,2,3,6,8,10,11,14,15,18,20,23,25,27,31],[0,2,5,7,9,11,13,14,16,18,20,23,25,29,30,31,32,33],[1,2,3,5,7,10,12,14,17,18,20,23,25,26,27,28,29,31],[2,3,4,8,10,11,12,16,17,18,20,23,25,27,28,30,31,32,33],[3,6,7,8,12,14,19,20,23,28,31,33],[0,1,4,6,7,9,10,11,13,14,15,16,19,20,23,30,32],[1,2,4,5,7,8,9,10,13,17,19,20,23,26,31,32,33],[0,1,2,4,5,6,7,9,10,14,15,16,17,19,20,23,27,28,30],[2,4,7,8,13,15,18,19,20,23,26,28,30,33],[0,1,2,5,7,10,12,14,15,16,18,19,20,23,26,27,29,31,32],[0,3,5,6,8,10,11,14,17,18,19,20,23,29,32,33],[9,16,17,18,19,20,23,26,28,30,31],[2,3,5,6,7,8,9,11,13,21,23,25,27,29,30,32,33],[2,3,13,16,21,23,25,26,27,33],[1,2,5,7,12,14,17,21,23,26,28,33],[2,3,4,8,12,16,17,21,23,26,27,28,29,30,32,33],[1,2,3,4,5,9,10,11,12,14,15,18,21,23,27,28,30,31,32,33],[1,2,4,5,6,7,8,10,13,16,18,21,23,26,28,31,33],[0,1,2,4,5,6,7,8,12,14,17,18,21,23,25,26,30,31,33],[0,2,5,6,10,11,13,14,15,16,17,18,21,23,25,26,31,32,33],[0,3,4,6,9,10,11,14,15,19,21,23,28,30,31],[1,5,6,8,13,15,16,19,21,23,26,29,32],[0,2,3,9,10,11,12,14,15,17,19,21,23,25,26,27,29,30,31],[2,3,5,6,8,12,13,16,17,19,21,23,25,26,28,32],[2,3,7,8,9,10,13,18,19,21,23,25,29,30,32,33],[0,1,2,3,4,7,11,14,16,18,19,21,23,25,26,27,28,29,31,33],[0,1,3,4,6,8,9,11,12,14,15,17,18,19,21,23,26,27,28,29,32,33],[1,4,9,11,13,16,17,18,19,21,23,26,27,29,30,31,33],[0,3,6,7,9,10,12,20,21,23,25,26,27,28,29,30,31,33],[0,1,4,5,7,9,13,16,20,21,23,25,27,28,29,31,32],[0,1,2,5,11,12,13,14,15,17,20,21,23,25,29,32,33],[0,1,2,9,10,11,12,16,17,20,21,23,25,27,29,30],[3,4,5,7,8,9,10,12,13,18,20,21,23,27],[1,3,5,6,7,8,10,11,13,14,15,16,18,20,21,23,26,29,30,32,33],[0,2,4,6,7,8,9,11,12,14,15,17,18,20,21,23,26,28,29,31,32],[0,2,3,4,6,7,8,10,11,15,16,17,18,20,21,23,26,28,30,31,33],[1,2,4,6,11,12,13,14,15,19,20,21,23,27,31,32],[0,1,2,4,5,6,7,10,11,14,15,16,19,20,21,23,26,27,28,30,33],[1,2,5,7,8,10,11,14,15,17,19,20,21,23,26,28,32],[0,2,3,4,6,14,15,16,17,19,20,21,23,26,27,30,31,33],[5,8,12,15,18,19,20,21,23,25,26,27,28,29,30],[0,3,5,7,9,10,12,14,15,16,18,19,20,21,23,25,31,32,33],[0,1,4,6,8,10,13,17,18,19,20,21,23,25,31],[0,1,2,3,4,5,6,11,13,16,17,18,19,20,21,23,25,28,29,30,32,33],[1,5,9,10,13,14,15,22,23,28,29,30,31,33],[1,2,4,5,6,7,13,16,22,23,33],[1,2,3,5,8,9,11,14,15,17,22,23,25,26,29,33],[5,7,10,11,13,14,15,16,17,22,23,25,27,28,30,31,33],[0,1,2,3,4,5,6,7,9,10,11,18,22,23,25,26,28,30,32,33],[0,1,8,10,11,14,15,16,18,22,23,25,26,27,31,32,33],[4,5,6,8,10,12,13,14,15,17,18,22,23,29,30,31,32,33],[1,2,4,6,7,11,12,14,15,16,17,18,22,23,26,28,29,32,33],[0,3,5,7,13,19,22,23,25,26,28,29,33],[1,2,5,7,10,16,19,22,23,25,26,28,30,33],[0,1,3,4,5,7,9,11,13,14,15,17,19,22,23,29,31,32,33],[1,2,3,5,6,7,9,16,17,19,22,23,26,27,30,31,32,33],[0,1,4,5,6,8,9,14,15,18,19,22,23,28,31],[2,4,6,8,9,10,12,16,18,19,22,23,27,28,30,31],[1,5,6,7,8,11,13,17,18,19,22,23,25,26,29,30,32],[0,1,2,3,4,7,12,16,17,18,19,22,23,25,29,32],[0,1,4,10,12,20,22,23,26,27,30,31],[0,2,3,4,6,14,15,16,20,22,23,26,27,28,33],[0,1,3,4,5,7,8,10,11,12,13,17,20,22,23,27,28,29,31],[0,1,2,3,5,7,8,10,13,14,15,16,17,20,22,23,26,29,30,33],[0,2,3,5,6,10,13,14,15,18,20,22,23,25,26,27,29,32,33],[0,1,3,12,13,14,15,16,18,20,22,23,25,26,28,30,31,32],[1,2,6,11,12,17,18,20,22,23,25,27,28,29,32,33],[1,3,4,5,6,8,12,16,17,18,20,22,23,25,26,27,30,31,32],[1,4,5,9,10,11,13,14,15,19,20,22,23,25,26,30,31],[0,1,2,5,7,8,9,11,12,14,15,16,19,20,22,23,25,26,31,33],[2,7,8,9,10,11,13,14,15,17,19,20,22,23,25,28,29,30,31,32],[0,1,3,7,8,9,11,14,15,16,17,19,20,22,23,25,26,27,28,29,31,32,33],[0,1,3,6,7,9,12,18,19,20,22,23,26,29],[1,2,4,5,6,9,13,14,15,16,18,19,20,22,23,26,27,30,33],[1,8,9,10,11,17,18,19,20,22,23,28,29,30,32],[1,3,4,6,7,9,10,11,12,16,17,18,19,20,22,23,26,28,32,33],[1,3,4,6,7,9,10,11,12,21,22,23,25,27,28,31,32,33],[2,4,5,7,8,11,13,14,15,16,21,22,23,25,26,27,29,30,32,33],[3,4,6,7,8,10,13,14,15,17,21,22,23,26,30,31,33],[2,3,5,6,7,8,11,12,13,14,15,16,17,21,22,23,26,27,28,29,33],[0,2,3,5,9,11,13,14,15,18,21,22,23,25,26,27,32,33],[0,1,3,5,6,7,9,10,11,16,18,21,22,23,25,28,30,31,32,33],[2,3,5,8,11,17,18,21,22,23,28,29,33],[4,5,7,10,13,16,17,18,21,22,23,29,30,31,33],[4,7,8,11,12,14,15,19,21,22,23,26,28,29,30,31,32],[0,2,5,8,10,12,13,14,15,16,19,21,22,23,28,31,32],[2,3,8,12,13,17,19,21,22,23,25,27,29,30,31,32],[5,8,9,10,11,12,13,16,17,19,21,22,23,25,31,32],[5,6,10,11,13,18,19,21,22,23,29,30,33],[0,2,3,4,5,7,8,9,10,11,13,14,15,16,18,19,21,22,23,26,27,29,33],[0,1,2,3,10,11,12,17,18,19,21,22,23,25,26,27,28,33],[2,4,5,7,10,12,13,14,15,16,17,18,19,21,22,23,25,26,27,28,30,33],[0,2,6,8,9,11,12,14,15,20,21,22,23,26,29,30,31,32,33],[0,3,4,10,11,16,20,21,22,23,28,29,32],[0,1,7,8,13,14,15,17,20,21,22,23,27,28,33],[1,2,4,5,7,16,17,20,21,22,23,30,31],[0,1,2,3,4,5,6,8,13,14,15,18,20,21,22,23,26,28,29,32],[0,1,2,7,9,11,13,14,15,16,18,20,21,22,23,27,30,31,32,33],[0,2,7,11,13,14,15,17,18,20,21,22,23,27,29,31],[0,1,3,5,6,7,12,14,15,16,17,18,20,21,22,23,27,28,30,33],[0,2,6,9,13,14,15,19,20,21,22,23,25,26,30,32],[1,4,5,6,7,8,9,10,11,14,15,16,19,20,21,22,23,25,32,33],[0,2,3,4,6,7,8,10,12,17,19,20,21,22,23,25,27,28,29,30,31,32],[0,1,2,3,4,5,6,7,8,10,12,14,15,16,17,19,20,21,22,23,25,28,29,31,32,33],[3,4,5,9,12,14,15,18,19,20,21,22,23,25,26,28,31],[2,4,8,10,11,12,13,14,15,16,18,19,20,21,22,23,25,27,28,29,30,31,33],[0,1,2,3,5,6,8,10,11,14,15,17,18,19,20,21,22,23,25,27,30],[1,2,4,6,7,8,12,14,15,16,17,18,19,20,21,22,23,25,27,29,33],[2,3,4,5,6,7,9,12,24,25,29,30,31],[0,1,3,4,5,6,7,13,16,24,27,29,30,32,33],[0,1,3,4,5,6,8,9,12,13,17,24,25,26,29,31,32,33],[1,2,5,9,10,13,16,17,24,29],[0,5,6,7,9,10,18,24,28,29,30,32,33],[1,2,3,6,7,8,9,10,11,12,16,18,24,25,28,30,31],[0,2,5,7,8,9,10,13,14,15,17,18,24,26,28,30],[4,9,10,13,16,17,18,24,25,27,28,29,30,31,32,33],[2,6,7,8,9,10,11,12,19,24,26,31],[3,4,7,8,11,12,16,19,24,25,26,27,28,31,32,33],[0,2,3,4,6,7,9,10,11,13,17,19,24,31,33],[0,1,3,4,7,10,11,12,16,17,19,24,25,26,28,31,32],[1,2,3,4,6,11,12,13,14,15,18,19,24,25,26,28],[1,3,5,8,9,10,12,13,14,15,16,18,19,24,26,29,32,33],[2,7,10,13,17,18,19,24,25,28,29,30,33],[1,3,5,7,11,12,14,15,16,17,18,19,24,26,27,30,32],[0,1,2,6,8,12,20,24,25,26,28,29],[1,3,4,6,8,10,11,13,16,20,24,26,27,28,31,32],[2,5,8,13,17,20,24,28,30,31,32,33],[0,1,5,6,7,8,10,11,12,13,14,15,16,17,20,24,25,26,28,29,30,33],[0,3,4,5,7,11,12,13,14,15,18,20,24,29,30,31,32],[2,3,6,9,11,13,16,18,20,24,25,29,30],[0,3,4,6,7,8,17,18,20,24,25,26,29,30,33],[1,2,4,5,9,10,11,13,16,17,18,20,24,27,29,30,31,32,33],[0,2,4,7,11,13,14,15,19,20,24,26,27,28,31],[0,1,4,9,11,13,14,15,16,19,20,24,25,26,29,31,32],[3,5,7,9,12,13,17,19,20,24,25,27,28,29,33],[2,4,5,6,9,10,16,17,19,20,24,26,27,32,33],[2,3,5,6,8,12,14,15,18,19,20,24,25,27,30,33],[1,6,9,11,12,13,14,15,16,18,19,20,24,27,28,30,32,33],[1,4,7,8,9,10,12,13,14,15,17,18,19,20,24,26,27,31],[1,2,5,6,7,9,12,13,16,17,18,19,20,24,25,28,31,32],[0,4,5,6,7,9,10,12,14,15,21,24,26,27,28,29,31,33],[2,3,7,8,10,11,12,13,14,15,16,21,24,25,28,29,32],[3,4,5,8,17,21,24,28,29,30],[0,1,2,3,4,7,9,12,16,17,21,24,25,28,29,30,31,32,33],[1,2,5,6,18,21,24,26,27,28],[0,1,4,5,6,8,9,10,14,15,16,18,21,24,25,27,28,29,31,32,33],[2,3,7,8,9,11,14,15,17,18,21,24,28,29,31,33],[0,1,6,8,10,11,14,15,16,17,18,21,24,25,27,28,32],[3,5,14,15,19,21,24,25,28,29,30],[1,2,3,5,8,11,12,13,14,15,16,19,21,24,26,27,29,30,32,33],[0,1,2,3,4,7,8,9,10,13,14,15,17,19,21,24,25,26,27,28,29,30,31,32,33],[0,1,5,6,7,13,16,17,19,21,24,26,27,29,30,31],[3,4,5,7,10,11,12,13,14,15,18,19,21,24,25,28,30,31,32],[1,2,4,6,9,13,14,15,16,18,19,21,24,26,29,30,31,33],[2,3,5,6,7,8,9,10,12,13,17,18,19,21,24,25,26,27,28,29,33],[3,4,6,7,8,9,11,13,14,15,16,17,18,19,21,24,26,32],[2,5,6,7,9,12,14,15,20,21,24,25,27,29],[0,1,5,6,11,13,14,15,16,20,21,24,26,31,32],[0,3,5,7,9,10,11,13,14,15,17,20,21,24,26,30,33],[2,5,9,10,12,13,16,17,20,21,24,25,26,29,30,31,32,33],[5,6,7,8,10,11,12,13,14,15,18,20,21,24,25,26,27,30,31],[0,1,2,3,4,6,7,8,9,10,11,13,16,18,20,21,24,27,30,32],[1,2,3,7,9,11,12,13,14,15,17,18,20,21,24,30,31,33],[0,1,3,4,5,6,7,8,9,10,14,15,16,17,18,20,21,24,25,27,30,32,33],[0,1,2,5,6,7,8,9,10,11,12,13,14,15,19,20,21,24,27,29,33],[0,1,3,4,5,10,11,12,16,19,20,21,24,25,26,28,32,33],[2,6,7,8,10,11,14,15,17,19,20,21,24,25,26,32],[1,6,7,10,11,13,14,15,16,17,19,20,21,24,26,28,29],[2,4,6,7,8,9,11,12,14,15,18,19,20,21,24,26,27,30,31,32],[5,6,9,11,12,13,14,15,16,18,19,20,21,24,25,27,28,30,31],[2,5,7,9,11,13,17,18,19,20,21,24,25,31,33],[0,2,4,7,8,9,14,15,16,17,18,19,20,21,24,27,28,31,32,33],[0,1,3,4,5,7,8,9,12,13,22,24,26,27,28,31,32,33],[1,4,6,7,9,10,12,13,16,22,24,25,26,31,32],[2,5,7,9,11,12,17,22,24,27,28,29,30,31],[0,1,2,4,5,6,7,9,12,13,16,17,22,24,25,26,27,29,30,31,33],[0,1,4,7,8,10,12,13,14,15,18,22,24,27,29],[1,4,7,8,9,10,14,15,16,18,22,24,25,27,28,33],[0,1,2,3,4,5,8,9,11,12,14,15,17,18,22,24,26,27,29,32,33],[2,5,6,7,8,9,11,13,14,15,16,17,18,22,24,25,28,32],[2,3,6,8,9,10,12,13,14,15,19,22,24,25,26,27,29,33],[1,2,3,8,9,13,16,19,22,24,26,29,31],[0,2,4,5,6,7,11,12,14,15,17,19,22,24,25,27],[0,2,4,5,6,10,12,13,16,17,19,22,24,26,27,31,33],[0,1,3,4,5,6,9,12,14,15,18,19,22,24,25,27,28,31,33],[0,4,7,10,12,13,14,15,16,18,19,22,24,27,28,29],[0,5,9,11,14,15,17,18,19,22,24,25,26,27,28,30,31],[0,4,6,8,9,10,16,17,18,19,22,24,28,29,30,33],[1,4,7,9,11,12,14,15,20,22,24,25,29,31,33],[0,4,5,6,9,10,11,12,14,15,16,20,22,24,27,28,31,33],[0,3,5,6,10,12,17,20,22,24,26,29,30,32],[10,13,14,15,16,17,20,22,24,25,28,30,32],[0,4,5,7,9,10,12,13,18,20,22,24,25,28,30,32,33],[1,3,11,12,14,15,16,18,20,22,24,30,32,33],[0,8,9,10,17,18,20,22,24,26,28,29,30,31],[4,7,9,12,16,17,18,20,22,24,25,27,29,30,31],[0,1,2,3,5,7,8,13,14,15,19,20,22,24,26,27,28,30,31,32,33],[0,1,2,6,8,11,12,13,16,19,20,22,24,25,26,28,29,30,32,33],[1,3,6,7,8,9,17,19,20,22,24,25,27,28,30,32],[3,9,11,13,14,15,16,17,19,20,22,24,26,27,28,29,30,31,32],[0,1,4,5,7,9,10,11,12,13,14,15,18,19,20,22,24,26,27,29,32],[0,1,2,7,8,10,16,18,19,20,22,24,25,26,27,29,31,32],[0,4,5,9,11,12,14,15,17,18,19,20,22,24,25,27,30,31,32,33],[3,7,8,12,14,15,16,17,18,19,20,22,24,26,30,32,33],[0,1,3,4,5,7,8,10,12,13,21,22,24,25,27,28,30,32,33],[2,4,5,7,9,10,11,12,16,21,22,24,26,30,32],[1,3,5,6,7,8,11,12,17,21,22,24,25,26,28,29,31,32],[0,1,2,3,7,11,14,15,16,17,21,22,24,26,29,31,32,33],[0,2,3,5,6,7,8,9,11,13,18,21,22,24,26,27,28,30,31,32],[1,3,4,6,8,10,11,12,16,18,21,22,24,25,27,29,30,31,32,33],[0,1,6,8,9,10,11,12,17,18,21,22,24,28,30,32,33],[1,4,5,6,9,10,14,15,16,17,18,21,22,24,25,27,29,30,32],[0,3,4,6,7,9,11,13,14,15,19,21,22,24,30],[0,2,3,5,6,8,9,10,14,15,16,19,21,22,24,25,26,27,30,31,33],[1,2,4,6,7,9,10,11,12,13,17,19,21,22,24,26,27,29,30,31,32,33],[4,5,7,8,9,11,16,17,19,21,22,24,25,26,27,29,30,32],[3,4,8,9,10,13,18,19,21,22,24,25,26,30,31,32],[0,1,3,4,7,8,9,11,14,15,16,18,19,21,22,24,29,30,32,33],[3,4,9,11,12,13,14,15,17,18,19,21,22,24,25,27,33],[1,6,7,8,10,11,14,15,16,17,18,19,21,22,24,29,31],[2,4,5,8,9,10,12,13,14,15,20,21,22,24,25,26,29],[0,2,4,6,9,10,11,12,16,20,21,22,24,27,28],[0,1,2,3,7,10,11,12,14,15,17,20,21,22,24,27,29,30,33],[2,3,4,7,9,10,11,12,14,15,16,17,20,21,22,24,25,27,28,30,33],[0,2,3,4,5,8,9,10,12,13,18,20,21,22,24,26,29,30,31],[4,5,7,8,10,12,14,15,16,18,20,21,22,24,25,28,29,30,31],[1,2,4,6,8,9,14,15,17,18,20,21,22,24,25,27,30,31,33],[1,3,4,5,7,9,10,11,12,13,14,15,16,17,18,20,21,22,24,28,30,31,33],[2,3,4,5,9,10,11,13,19,20,21,22,24,28,29,30,31,32,33],[0,3,4,7,8,13,14,15,16,19,20,21,22,24,25,26,27,28,30,32,33],[0,3,4,5,6,9,10,11,12,13,14,15,17,19,20,21,22,24,25,26,27,28,29,30,31],[0,10,11,13,16,17,19,20,21,22,24,26,27,28,30],[1,4,7,8,10,11,12,13,14,15,18,19,20,21,22,24,25,28,29],[0,1,2,3,4,5,6,7,9,13,14,15,16,18,19,20,21,22,24,26,28,29,31],[2,7,8,10,11,13,14,15,17,18,19,20,21,22,24,26,27,28,30,32,33],[16,17,18,19,20,21,22,24,25,26,28,30,31,32,33],[0,2,5,6,10,11,23,24,25,27,29,32,33],[0,1,2,3,4,6,7,10,11,13,16,23,24,25,30,31,32],[0,2,3,4,5,8,11,12,14,15,17,23,24,27,31],[0,3,4,5,6,8,11,12,16,17,23,24,26,27,29,30,33],[0,1,2,5,6,7,18,23,24,27,28,29,31,32],[0,1,2,3,4,7,8,10,11,13,16,18,23,24,27,28,29,30,32,33],[1,4,5,6,8,9,12,13,17,18,23,24,25,27,28,29,30,33],[2,4,5,7,12,13,16,17,18,23,24,25,26,28,29,31],[4,5,6,7,8,9,10,13,19,23,24,26,27,28,29,30,33],[0,1,2,4,6,8,9,13,16,19,23,24,26],[1,2,5,6,8,9,10,11,12,13,17,19,23,24,25,26,27,28,31],[0,5,6,7,8,10,11,12,16,17,19,23,24,25,27,29,30,31,33],[0,1,6,8,10,13,14,15,18,19,23,24,25,26,27,29,30,31,32,33],[1,2,3,5,9,11,16,18,19,23,24,25,26,27,28,29,31,32],[2,3,5,8,10,13,17,18,19,23,24,26,27,29,30,32],[0,2,5,10,11,13,14,15,16,17,18,19,23,24,28,29,32,33],[0,1,2,5,8,9,10,11,12,13,14,15,20,23,24,27,28,29,32],[0,4,6,9,10,13,14,15,16,20,23,24,28,29,30,31,32],[0,1,2,3,7,9,10,12,14,15,17,20,23,24,27,28,29,33],[0,3,5,6,9,11,14,15,16,17,20,23,24,26,27,28,29,30,31,33],[1,7,8,10,12,13,14,15,18,20,23,24,25,26,27,29,30,31,32],[4,5,6,7,9,11,12,13,16,18,20,23,24,25,26,27,32],[0,1,2,6,9,13,14,15,17,18,20,23,24,25,26,27,31,33],[1,2,3,4,10,12,16,17,18,20,23,24,25,29,30,33],[1,2,4,5,6,8,10,13,14,15,19,20,23,24,25,29,31],[0,4,5,7,8,12,14,15,16,19,20,23,24,25,27,28,29,30,31],[2,3,4,6,8,12,17,19,20,23,24,25,29,30,31,33],[0,2,6,13,16,17,19,20,23,24,25,26,28,29,31,33],[1,2,3,4,6,7,8,9,10,13,14,15,18,19,20,23,24,26,28,29,30,32,33],[0,3,4,7,8,9,16,18,19,20,23,24,26,32,33],[1,2,4,5,7,12,17,18,19,20,23,24,26,28,30,32],[0,1,2,3,5,8,14,15,16,17,18,19,20,23,24,27,29,32],[1,11,21,23,24,25,30,33],[1,2,3,4,5,9,14,15,16,21,23,24,25,26,27,29,31],[1,2,3,4,6,8,12,13,14,15,17,21,23,24,27,29,30],[0,2,5,6,7,8,10,12,16,17,21,23,24,27,31,33],[5,6,8,10,12,13,18,21,23,24,25,29,30,31,32],[0,1,4,6,8,10,11,12,14,15,16,18,21,23,24,25,26,29,32,33],[0,3,4,6,9,10,12,13,14,15,17,18,21,23,24,27,29,31,32,33],[0,4,9,10,14,15,16,17,18,21,23,24,29,30,32],[1,2,6,8,9,11,19,21,23,24,26,27,28,29,31,32],[0,2,3,5,6,8,11,12,14,15,16,19,21,23,24,30,31,32,33],[0,3,4,6,14,15,17,19,21,23,24,25,26,28,30,31,33],[2,3,6,10,12,13,16,17,19,21,23,24,25,26,29,31],[0,1,2,5,6,7,9,10,11,12,18,19,21,23,24,26,27,28,32],[5,6,9,12,16,18,19,21,23,24,27,30,32,33],[0,2,3,5,7,13,14,15,17,18,19,21,23,24,25,26,28,33],[0,1,4,5,9,13,14,15,16,17,18,19,21,23,24,25,26,27,30],[3,4,5,7,8,9,11,13,14,15,20,21,23,24,25,28,33],[0,4,5,6,10,13,14,15,16,20,21,23,24,25,26,27,28,30,31,33],[0,1,3,4,7,11,17,20,21,23,24,25,27,28,31],[0,1,2,4,5,7,8,13,14,15,16,17,20,21,23,24,25,27,28,30],[0,1,2,3,5,9,11,12,14,15,18,20,21,23,24,25,26,28,29,30,31,32,33],[6,7,8,9,10,12,16,18,20,21,23,24,25,28,32,33],[0,3,4,6,8,9,10,11,12,13,17,18,20,21,23,24,25,26,27,28,32],[0,1,3,5,6,7,8,9,10,12,16,17,18,20,21,23,24,25,26,28,29,30,31,32],[0,2,4,5,6,9,10,13,19,20,21,23,24,29,32],[0,1,2,5,10,11,12,13,14,15,16,19,20,21,23,24,26,27,28,29,30,32],[0,2,3,5,6,8,10,11,12,13,14,15,17,19,20,21,23,24,27,29,30,31,33],[2,3,4,5,7,9,10,12,14,15,16,17,19,20,21,23,24,27,28,29,31,33],[0,2,3,4,5,6,7,9,10,11,12,13,14,15,18,19,20,21,23,24,26,30,31,32,33],[0,3,6,10,11,12,16,18,19,20,21,23,24,28,29,31,32,33],[2,4,8,9,12,13,17,18,19,20,21,23,24,26,27,29,30],[16,17,18,19,20,21,23,24,26,28],[1,2,3,4,7,9,10,11,12,13,14,15,22,23,24,25,26,27,28,29],[1,2,4,7,8,12,16,22,23,24,25,26,30,32,33],[2,7,8,9,17,22,23,24,26,27,28,29,31,32,33],[1,2,7,10,12,13,16,17,22,23,24,27,30,31],[0,1,4,5,6,7,18,22,23,24,25,27,31,33],[0,1,2,3,5,7,8,9,10,12,14,15,16,18,22,23,24,25,27,28,30,31,32],[1,3,7,12,17,18,22,23,24,27,29,30,32],[2,3,5,9,10,12,14,15,16,17,18,22,23,24,26,28,29,33],[2,5,6,7,8,11,12,13,14,15,19,22,23,24,26,27,28,29,31],[0,1,2,3,4,7,8,9,10,11,16,19,22,23,24,26,28,30,32,33],[1,4,5,6,7,8,9,10,12,13,14,15,17,19,22,23,24,25,26,27,28,29,30,33],[1,2,4,11,14,15,16,17,19,22,23,24,25,27,28,31,32],[0,1,2,3,7,10,11,13,18,19,22,23,24,27,32],[2,3,4,5,9,10,11,13,14,15,16,18,19,22,23,24,27,30,31,33],[1,6,10,11,17,18,19,22,23,24,25,27,29,31,32,33],[0,2,3,4,6,8,10,12,16,17,18,19,22,23,24,25,26,29,30],[4,5,8,12,14,15,20,22,23,24,25,26,30,31,32,33],[0,1,3,5,6,8,14,15,16,20,22,23,24,25,26,27,28,31,33],[1,5,9,10,11,13,17,20,22,23,24,25,26,29,30,31],[1,2,8,13,16,17,20,22,23,24,25,28,29,31,32],[0,1,3,4,5,6,8,11,18,20,22,23,24,25,26,28,29,32,33],[0,2,4,10,12,13,14,15,16,18,20,22,23,24,25,26,30,33],[1,4,5,13,14,15,17,18,20,22,23,24,25,26,28,29,30],[0,1,2,4,7,9,10,12,16,17,18,20,22,23,24,25,27,32],[0,1,2,3,6,7,9,10,11,13,14,15,19,20,22,23,24,27,31,32,33],[0,1,2,3,4,6,8,10,11,12,14,15,16,19,20,22,23,24,30,33],[0,3,4,5,8,9,11,13,17,19,20,22,23,24,27,29,30,31,32],[2,4,5,6,9,10,11,13,16,17,19,20,22,23,24,26,27,29],[0,2,4,7,9,11,12,13,18,19,20,22,23,24,27,28,29,30],[0,1,3,4,6,7,9,10,11,13,16,18,19,20,22,23,24,27,28,31,32],[2,5,7,13,14,15,17,18,19,20,22,23,24,27,28,29,30,33],[16,17,18,19,20,22,23,24,26,28,31,32,33],[3,4,6,9,10,12,14,15,21,22,23,24,25,26,27,30,31,32,33],[0,1,7,9,10,12,14,15,16,21,22,23,24,25,28,29,31],[2,3,4,5,7,8,9,11,12,13,17,21,22,23,24,26,30,31,32],[2,5,6,7,8,10,16,17,21,22,23,24,26,28,29,31,33],[1,4,7,8,11,12,14,15,18,21,22,23,24,27,30],[0,1,2,6,7,8,11,12,16,18,21,22,23,24,26,27,28,32,33],[0,3,5,7,8,10,17,18,21,22,23,24,25,29,33],[16,17,18,21,22,23,24,25,27,28,29,30,32],[1,2,4,5,7,8,12,13,19,21,22,23,24,26,29,30,31,32],[4,7,8,13,16,19,21,22,23,24,27,33],[0,1,3,6,7,9,11,13,17,19,21,22,23,24,25,26,27,29,31,33],[16,17,19,21,22,23,24,25,26,27,30,32],[0,1,2,3,5,6,10,13,18,19,21,22,23,24,25,29,30,32],[16,18,19,21,22,23,24,25,26,29,31,33],[1,2,3,4,8,11,12,13,14,15,17,18,19,21,22,23,24,27,30,33],[16,17,18,19,21,22,23,24,31,32],[0,3,5,6,7,8,9,10,12,13,14,15,20,21,22,23,24,26,28,29,30,33],[0,1,3,4,6,7,11,12,16,20,21,22,23,24,27,29,32,33],[2,3,4,5,6,7,8,10,12,13,14,15,17,20,21,22,23,24,26,27,28,30,31],[16,17,20,21,22,23,24,26,27,31,32],[0,2,4,5,7,10,11,13,18,20,21,22,23,24,25,26,28,29,31,32,33],[16,18,20,21,22,23,24,25,30,31,33],[17,18,20,21,22,23,24,25,26,27,28,29,30,32],[16,17,18,20,21,22,23,24,25,26],[0,1,2,5,11,12,19,20,21,22,23,24,25,28,31],[16,19,20,21,22,23,24,25,26,27,28,30,32],[17,19,20,21,22,23,24,25,27,28,29,30,32,33],[16,17,19,20,21,22,23,24,25,27,28,29,31,33],[18,19,20,21,22,23,24,28,30,33],[16,18,19,20,21,22,23,24,26,28,29,31,32,33],[17,18,19,20,21,22,23,24,27,28,30,31,32],[16,17,18,19,20,21,22,23,24,28,29]]},"distance":{"d":5,"is_exact":true,"upper":5,"witness":[28,194,199,448,470],"A_d":1093845,"certified":null},"clifford":{"kind":"required","correction":{"S":[[1,2],[3,1],[5,3],[7,2],[8,2],[9,1],[11,1],[12,3],[15,2]],"CZ":[[0,1],[0,2],[0,6],[0,9],[0,10],[0,11],[0,12],[0,13],[0,14],[0,17],[0,18],[0,21],[0,23],[0,25],[0,27],[0,29],[0,33],[1,4],[1,7],[1,8],[1,12],[1,18],[1,24],[1,29],[1,33],[2,3],[2,4],[2,5],[2,11],[2,13],[2,15],[2,16],[2,17],[2,18],[2,19],[2,20],[2,21],[2,22],[2,23],[2,26],[2,27],[2,28],[2,30],[2,31],[2,32],[2,33],[3,4],[3,5],[3,9],[3,10],[3,12],[3,14],[3,19],[3,20],[3,21],[3,22],[3,27],[3,28],[3,29],[3,31],[4,8],[4,12],[4,13],[4,14],[4,19],[4,21],[4,22],[4,26],[4,27],[4,31],[5,8],[5,10],[5,11],[5,12],[5,16],[5,22],[5,23],[5,25],[5,26],[5,28],[5,29],[5,31],[5,33],[6,8],[6,9],[6,10],[6,11],[6,13],[6,16],[6,18],[6,23],[6,27],[6,28],[6,30],[6,32],[6,33],[7,8],[7,10],[7,11],[7,13],[7,16],[7,17],[7,20],[7,23],[7,24],[7,27],[7,30],[7,31],[7,33],[8,10],[8,13],[8,15],[8,18],[8,20],[8,21],[8,22],[8,24],[8,25],[8,26],[8,27],[8,28],[8,29],[8,31],[8,33],[9,10],[9,13],[9,15],[9,18],[9,20],[9,21],[9,23],[9,24],[9,25],[9,27],[9,30],[10,12],[10,14],[10,15],[10,16],[10,20],[10,22],[10,25],[10,32],[11,14],[11,16],[11,17],[11,18],[11,19],[11,22],[11,24],[11,26],[11,31],[11,33],[12,13],[12,14],[12,15],[12,17],[12,19],[12,20],[12,24],[12,26],[12,27],[12,28],[12,32],[13,15],[13,17],[13,18],[13,19],[13,20],[13,22],[13,25],[13,27],[13,29],[13,31],[14,22],[14,23],[14,25],[14,27],[14,30],[14,31],[14,33],[15,16],[15,20],[15,21],[15,22],[15,23],[15,25],[15,27],[15,31]]},"rotation_powers":null},"metrics":{"gamma":2.1521680589252,"gamma_t":null,"gamma_rho":2.1521680589252,"gamma_claim":2.1521680589252,"gamma_t_claim":null,"gamma_rho_claim":2.1521680589252,"v_ex":16,"rate":0.03131115459882583,"t_count":null,"poly_degree":null,"effective_width":16},"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.T12.T13.T14.T15","N":34,"d":5,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:372"}]},"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"}]}