{"id":"511.17.5.a","row":1107,"stored":{"file":"master_catalog.json","row":1107,"construction":null,"columns_sha256":null},"parameters":{"n":511,"k":17,"d":5,"N":35,"r":18,"level":3},"gate":{"string":"0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6\u00b7T7\u00b7T8\u00b7T9\u00b7T10\u00b7T11\u00b7T12\u00b7T13\u00b7T14\u00b7T15\u00b7T16","monomials":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15],[16]],"sk_key":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15],[16]],"sk_fingerprint":"54780f2effb2fd97","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,1,3,4,6,7,9,10,11,12,14,15,16,17,26],[0,4,7,8,10,13,14,18,29],[4,8,10,12,15,17,18,26,27,28,29],[0,2,3,5,7,9,10,13,16,19,32],[1,2,3,4,6,9,10,11,15,17,19,26,28,30,32],[0,1,2,3,4,5,7,8,10,11,12,13,16,18,19,29,30,31,32],[1,2,4,8,9,11,12,13,16,17,18,19,26,27,29,31,32],[0,3,7,9,10,13,15,20,26,30],[0,3,7,9,10,12,16,17,20,29,30,32],[1,2,9,10,11,13,14,18,20,26,29,30,31,33],[2,3,4,6,12,13,16,17,18,20,27,28,30,31,32,33],[0,1,5,10,11,12,14,15,16,19,20,26,30,32,33,34],[0,1,3,9,11,12,14,15,16,17,19,20,28,29,33,34],[0,1,2,3,5,9,11,13,14,15,16,18,19,20,26,29,32,34],[0,2,3,4,6,9,15,17,18,19,20,27,30,34],[2,5,7,9,10,11,15,21,29,33],[0,2,5,6,7,8,9,10,11,12,14,17,21,26,29,30,33,34],[0,4,7,13,16,18,21,26,30,32,33],[1,3,7,8,9,10,11,12,15,17,18,21,27,28,32,33,34],[1,3,5,7,9,10,16,19,21,27,29,31,32,33,34],[0,1,6,7,8,13,14,17,19,21,26,27,28,29,31,32,33],[2,3,4,9,10,12,14,15,16,18,19,21,26,27,33,34],[0,1,2,3,5,8,9,10,11,12,14,15,16,17,18,19,21,33],[0,1,2,8,11,12,14,20,21,26,27,28,29,30,31,32,33],[0,2,3,4,7,9,10,13,15,17,20,21,27,28,31,33,34],[2,3,5,9,11,12,15,18,20,21,27,28],[2,3,5,6,7,8,9,11,16,17,18,20,21,26,29,30,32,34],[1,2,3,8,10,11,14,15,16,19,20,21,26,28,29,30],[2,3,4,5,7,10,14,15,16,17,19,20,21,30,32,34],[1,2,5,7,12,13,15,18,19,20,21,28,30,32,33],[1,2,3,6,8,9,10,12,16,17,18,19,20,21,26,27,28,29,30,33,34],[0,1,4,6,10,13,14,22,27,31,32],[1,4,5,8,10,13,14,15,16,17,22,26,31,32],[2,3,6,9,14,15,16,18,22,27,28,29,31,33],[0,1,2,4,5,6,8,10,11,13,14,15,16,17,18,22,26,27,29,31,33],[2,4,6,7,8,9,12,13,15,19,22,26,27,29,30,31,33],[0,2,3,4,7,10,14,17,19,22,28,29,31,33],[3,6,8,9,11,13,16,18,19,22,26,27,28,32],[0,1,3,4,6,9,12,13,14,15,16,17,18,19,22,27,28,30,32],[0,1,3,4,7,9,11,12,16,20,22,26,27,28,31,34],[0,5,8,10,12,13,14,17,20,22,28,29,31,32,34],[1,3,4,7,8,12,15,18,20,22,26,27,29,32,34],[1,3,4,5,6,12,15,17,18,20,22,27,28,34],[0,1,3,4,8,12,14,19,20,22,27,28,29,30,31,32],[0,3,7,11,15,17,19,20,22,26,31],[0,3,4,7,10,13,14,15,16,18,19,20,22,27,31],[0,4,6,8,9,12,16,17,18,19,20,22,26,27,29,30,31,32],[0,3,4,5,7,8,12,13,15,21,22,26,27,29,32,33,34],[1,6,8,9,10,11,12,13,14,17,21,22,29,30,32,33],[1,10,11,12,15,18,21,22,27,28,30,32,34],[0,1,5,7,10,11,12,13,14,17,18,21,22,26,27,32],[0,2,3,4,7,11,16,19,21,22,30,31],[1,2,3,6,12,13,14,15,16,17,19,21,22,26,27,28,30,31,34],[0,2,5,7,8,9,11,12,14,15,16,18,19,21,22,26,28,29,30,33],[2,3,5,8,10,11,14,15,16,17,18,19,21,22,28,29,30,33,34],[0,1,3,4,6,9,10,11,12,13,14,20,21,22,29,31,32,33],[0,1,3,4,5,6,9,10,11,12,14,17,20,21,22,26,27,30,31,33,34],[1,2,3,4,5,6,7,9,10,11,12,13,16,18,20,21,22,26,28,30,32,33],[2,7,12,13,14,15,16,17,18,20,21,22,29,33,34],[3,4,5,6,8,9,11,12,14,19,20,21,22,26,27,30,33],[4,5,6,8,10,11,14,15,16,17,19,20,21,22,28,29,30,32,33,34],[1,2,3,4,6,8,10,13,14,18,19,20,21,22,27,28,29,30,33],[2,3,8,10,11,12,16,17,18,19,20,21,22,26,27,28,30,32,33,34],[0,1,3,5,6,14,15,23,26,34],[1,2,3,4,5,10,13,14,15,17,23,29,32,33,34],[1,4,5,9,13,14,15,18,23,26,29,30,34],[0,2,3,4,5,11,13,14,15,17,18,23,27,28,30,32,33,34],[0,1,5,6,7,10,12,15,16,19,23,27,30,32,34],[1,2,3,4,7,9,10,15,16,17,19,23,26,27,28,29,33,34],[0,3,4,5,11,15,16,18,19,23,27,29,30,31,32,34],[1,2,3,4,10,12,13,14,15,17,18,19,23,26,31,33,34],[0,2,3,4,7,9,11,15,16,20,23,27,29,30,31,32,33,34],[0,1,4,17,20,23,26,27,29,30,31,32,34],[1,3,4,6,7,8,10,15,16,18,20,23,27,32,34],[1,2,3,8,12,14,15,17,18,20,23,26,28,32,33,34],[1,4,9,12,13,15,16,19,20,23,26,29,31],[2,4,5,7,9,10,11,17,19,20,23,28,29,30,31,33],[1,2,4,6,7,8,9,15,16,18,19,20,23,26,31,33],[1,3,5,8,13,14,16,17,18,19,20,23,27,30,31],[0,2,4,7,8,11,12,14,16,21,23,28,29,30,31,32,34],[1,3,4,6,9,14,15,17,21,23,26,28,31,33],[3,5,6,12,13,15,16,18,21,23,26,28,30,31,34],[0,2,3,4,5,6,7,8,10,17,18,21,23,27,29,31,32,33],[1,2,3,4,5,7,8,9,13,15,16,19,21,23,26,28,29],[0,3,4,6,9,10,11,12,13,15,16,17,19,21,23,32,33,34],[6,7,10,12,13,14,15,18,19,21,23,28,30,31,32],[0,2,3,4,5,6,8,9,10,12,13,14,16,17,18,19,21,23,26,27,28,29,30,31,33,34],[0,3,6,9,12,14,16,20,21,23,26,31,32,33,34],[0,2,3,4,6,8,9,10,13,17,20,21,23,30,31,32],[1,3,5,7,9,10,12,18,20,21,23,29,34],[2,5,6,7,8,10,11,12,13,15,16,17,18,20,21,23,26,27,28,29,30,33],[0,2,5,6,10,19,20,21,23,30,34],[0,3,4,6,8,9,10,17,19,20,21,23,26,28,30,33],[0,2,9,10,11,18,19,20,21,23,26,29,32,33,34],[0,1,5,6,8,9,12,14,16,17,18,19,20,21,23,27,29,32],[0,4,6,8,9,12,13,22,23,26,27,28,29,31],[1,2,3,4,5,7,11,12,13,17,22,23,28,31,32,33],[1,2,7,9,13,14,16,18,22,23,26,27,30,31,32,33],[0,1,4,5,8,9,10,14,15,17,18,22,23,27,28,29,30,31],[0,1,4,5,6,7,9,10,13,19,22,23,26,28,31,32,33],[2,4,5,8,9,14,15,17,19,22,23,27,29,30,31],[0,1,2,5,7,8,11,15,16,18,19,22,23,26,29],[1,3,4,5,9,12,13,15,16,17,18,19,22,23,30,32,33],[1,2,5,6,7,8,13,20,22,23,33,34],[1,4,6,7,10,12,13,14,15,17,20,22,23,26,27,34],[0,1,2,3,5,8,10,12,13,14,15,18,20,22,23,28,29,30,31,32,33,34],[0,6,9,10,13,15,16,17,18,20,22,23,26,29,30,31,32,34],[0,1,6,14,15,19,20,22,23,27,29,32,33],[0,1,2,3,4,6,8,9,12,14,15,17,19,20,22,23,26,28,29,30,32],[0,3,9,14,16,18,19,20,22,23,27,28,33],[0,1,2,3,6,8,9,10,11,15,16,17,18,19,20,22,23,26,27,28,30],[0,5,6,7,8,21,22,23,26,27,30,31,32,34],[2,4,7,8,10,12,13,17,21,22,23,29,31,33],[1,4,7,8,9,12,13,14,15,18,21,22,23,27,28,29,30,31,32,33,34],[0,2,3,4,5,7,8,11,13,14,15,17,18,21,22,23,26,27,31],[5,6,7,9,12,15,16,19,21,22,23,26,27,29,30,33],[0,2,3,4,5,7,11,12,13,14,16,17,19,21,22,23,28,30,32,34],[4,9,10,14,15,18,19,21,22,23,27,28,31],[0,1,2,4,9,11,13,15,16,17,18,19,21,22,23,26,27,28,29,31,32,33,34],[2,3,4,5,6,9,13,14,15,20,21,22,23,27,29,30,31,33],[1,4,6,7,11,12,13,14,15,17,20,21,22,23,26,29,31,34],[0,4,8,10,12,18,20,21,22,23,26,27,28,30,33],[0,2,5,6,7,8,12,14,15,17,18,20,21,22,23,27,34],[1,3,4,5,6,8,10,15,16,19,20,21,22,23,27,30,32,33],[2,3,4,5,6,7,8,11,13,15,16,17,19,20,21,22,23,26,28,30,32,34],[2,4,7,10,13,15,16,18,19,20,21,22,23,26,27,28,29,32,33],[0,1,2,4,5,7,8,11,12,17,18,19,20,21,22,23,27,28,29,32,34],[0,2,3,4,5,6,8,10,11,12,13,14,16,24,28,29,32],[0,1,2,5,8,9,13,15,16,17,24,28,29,30,31,32,33],[0,3,4,5,7,8,10,11,12,14,16,18,24,26,27,28,30,31],[0,3,4,5,7,8,10,14,15,17,18,24,26,33],[0,2,7,8,9,11,13,19,24,28,29,33],[0,1,2,4,5,6,7,8,9,10,11,12,13,15,16,17,19,24,29,31],[1,6,7,8,12,18,19,24,26,27,28,32,33],[1,3,5,6,7,8,9,11,12,17,18,19,24,26,28,31,32],[0,3,7,10,11,15,16,20,24,26,28,32,33],[3,12,13,15,16,17,20,24,26,28,29,30,31],[0,1,4,6,8,10,11,12,13,15,16,18,20,24,27,28,29,30],[3,7,8,9,10,12,13,17,18,20,24,31,32,33],[1,2,4,5,6,9,13,19,20,24,26,28,33,34],[0,1,2,3,4,6,7,11,13,14,16,17,19,20,24,26,29,31,32,34],[0,1,2,3,5,8,11,18,19,20,24,27,28,29,31,32,34],[2,3,4,6,7,8,10,11,13,14,15,17,18,19,20,24,28,33,34],[1,2,4,8,11,21,24,26,27,28,31,33,34],[1,2,4,6,7,11,13,14,15,17,21,24,26,27,28],[1,2,4,5,6,9,13,15,16,18,21,24,26,28,29,33,34],[2,3,5,6,7,8,11,17,18,21,24,26,27,29,31],[0,2,3,6,8,10,11,14,15,19,21,24,26,28,32],[0,2,5,7,9,11,13,14,16,17,19,21,24,26,30,31,32,33,34],[1,2,3,5,7,10,12,14,16,18,19,21,24,26,27,28,29,30,32],[2,3,4,8,10,11,12,17,18,19,21,24,26,28,29,31,32,33,34],[3,6,7,8,12,14,16,20,21,24,29,32,34],[0,1,4,6,7,9,10,11,13,14,15,17,20,21,24,31,33],[1,2,4,5,7,8,9,10,13,18,20,21,24,27,32,33,34],[0,1,2,4,5,6,7,9,10,14,15,17,18,20,21,24,28,29,31],[2,4,7,8,13,15,16,19,20,21,24,27,29,31,34],[0,1,2,5,7,10,12,14,15,17,19,20,21,24,27,28,30,32,33],[0,3,5,6,8,10,11,14,16,18,19,20,21,24,30,33,34],[9,17,18,19,20,21,24,27,29,31,32],[2,3,5,6,7,8,9,11,13,22,24,26,28,30,31,33,34],[2,3,13,17,22,24,26,27,28,34],[1,2,5,7,12,14,16,18,22,24,27,29,34],[2,3,4,8,12,17,18,22,24,27,28,29,30,31,33,34],[1,2,3,4,5,9,10,11,12,14,15,19,22,24,28,29,31,32,33,34],[1,2,4,5,6,7,8,10,13,17,19,22,24,27,29,32,34],[0,1,2,4,5,6,7,8,12,14,16,18,19,22,24,26,27,31,32,34],[0,2,5,6,10,11,13,14,15,17,18,19,22,24,26,27,32,33,34],[0,3,4,6,9,10,11,14,15,20,22,24,29,31,32],[1,5,6,8,13,15,16,17,20,22,24,27,30,33],[0,2,3,9,10,11,12,14,15,18,20,22,24,26,27,28,30,31,32],[2,3,5,6,8,12,13,17,18,20,22,24,26,27,29,33],[2,3,7,8,9,10,13,19,20,22,24,26,30,31,33,34],[0,1,2,3,4,7,11,14,16,17,19,20,22,24,26,27,28,29,30,32,34],[0,1,3,4,6,8,9,11,12,14,15,18,19,20,22,24,27,28,29,30,33,34],[1,4,9,11,13,17,18,19,20,22,24,27,28,30,31,32,34],[0,3,6,7,9,10,12,21,22,24,26,27,28,29,30,31,32,34],[0,1,4,5,7,9,13,17,21,22,24,26,28,29,30,32,33],[0,1,2,5,11,12,13,14,15,18,21,22,24,26,30,33,34],[0,1,2,9,10,11,12,17,18,21,22,24,26,28,30,31],[3,4,5,7,8,9,10,12,13,19,21,22,24,28],[1,3,5,6,7,8,10,11,13,14,15,17,19,21,22,24,27,30,31,33,34],[0,2,4,6,7,8,9,11,12,14,15,18,19,21,22,24,27,29,30,32,33],[0,2,3,4,6,7,8,10,11,15,16,17,18,19,21,22,24,27,29,31,32,34],[1,2,4,6,11,12,13,14,15,20,21,22,24,28,32,33],[0,1,2,4,5,6,7,10,11,14,15,17,20,21,22,24,27,28,29,31,34],[1,2,5,7,8,10,11,14,15,18,20,21,22,24,27,29,33],[0,2,3,4,6,14,15,17,18,20,21,22,24,27,28,31,32,34],[5,8,12,15,16,19,20,21,22,24,26,27,28,29,30,31],[0,3,5,7,9,10,12,14,15,17,19,20,21,22,24,26,32,33,34],[0,1,4,6,8,10,13,18,19,20,21,22,24,26,32],[0,1,2,3,4,5,6,11,13,17,18,19,20,21,22,24,26,29,30,31,33,34],[1,5,9,10,13,14,15,23,24,29,30,31,32,34],[1,2,4,5,6,7,13,17,23,24,34],[1,2,3,5,8,9,11,14,15,18,23,24,26,27,30,34],[5,7,10,11,13,14,15,17,18,23,24,26,28,29,31,32,34],[0,1,2,3,4,5,6,7,9,10,11,19,23,24,26,27,29,31,33,34],[0,1,8,10,11,14,15,17,19,23,24,26,27,28,32,33,34],[4,5,6,8,10,12,13,14,15,18,19,23,24,30,31,32,33,34],[1,2,4,6,7,11,12,14,15,17,18,19,23,24,27,29,30,33,34],[0,3,5,7,13,20,23,24,26,27,29,30,34],[1,2,5,7,10,17,20,23,24,26,27,29,31,34],[0,1,3,4,5,7,9,11,13,14,15,18,20,23,24,30,32,33,34],[1,2,3,5,6,7,9,17,18,20,23,24,27,28,31,32,33,34],[0,1,4,5,6,8,9,14,15,19,20,23,24,29,32],[2,4,6,8,9,10,12,17,19,20,23,24,28,29,31,32],[1,5,6,7,8,11,13,18,19,20,23,24,26,27,30,31,33],[0,1,2,3,4,7,12,17,18,19,20,23,24,26,30,33],[0,1,4,10,12,21,23,24,27,28,31,32],[0,2,3,4,6,14,15,17,21,23,24,27,28,29,34],[0,1,3,4,5,7,8,10,11,12,13,18,21,23,24,28,29,30,32],[0,1,2,3,5,7,8,10,13,14,15,17,18,21,23,24,27,30,31,34],[0,2,3,5,6,10,13,14,15,19,21,23,24,26,27,28,30,33,34],[0,1,3,12,13,14,15,17,19,21,23,24,26,27,29,31,32,33],[1,2,6,11,12,18,19,21,23,24,26,28,29,30,33,34],[1,3,4,5,6,8,12,17,18,19,21,23,24,26,27,28,31,32,33],[1,4,5,9,10,11,13,14,15,20,21,23,24,26,27,31,32],[0,1,2,5,7,8,9,11,12,14,15,17,20,21,23,24,26,27,32,34],[2,7,8,9,10,11,13,14,15,18,20,21,23,24,26,29,30,31,32,33],[0,1,3,7,8,9,11,14,15,17,18,20,21,23,24,26,27,28,29,30,32,33,34],[0,1,3,6,7,9,12,19,20,21,23,24,27,30],[1,2,4,5,6,9,13,14,15,17,19,20,21,23,24,27,28,31,34],[1,8,9,10,11,18,19,20,21,23,24,29,30,31,33],[1,3,4,6,7,9,10,11,12,17,18,19,20,21,23,24,27,29,33,34],[1,3,4,6,7,9,10,11,12,22,23,24,26,28,29,32,33,34],[2,4,5,7,8,11,13,14,15,17,22,23,24,26,27,28,30,31,33,34],[3,4,6,7,8,10,13,14,15,18,22,23,24,27,31,32,34],[2,3,5,6,7,8,11,12,13,14,15,17,18,22,23,24,27,28,29,30,34],[0,2,3,5,9,11,13,14,15,19,22,23,24,26,27,28,33,34],[0,1,3,5,6,7,9,10,11,17,19,22,23,24,26,29,31,32,33,34],[2,3,5,8,11,18,19,22,23,24,29,30,34],[4,5,7,10,13,17,18,19,22,23,24,30,31,32,34],[4,7,8,11,12,14,15,20,22,23,24,27,29,30,31,32,33],[0,2,5,8,10,12,13,14,15,17,20,22,23,24,29,32,33],[2,3,8,12,13,18,20,22,23,24,26,28,30,31,32,33],[5,8,9,10,11,12,13,17,18,20,22,23,24,26,32,33],[5,6,10,11,13,19,20,22,23,24,30,31,34],[0,2,3,4,5,7,8,9,10,11,13,14,15,17,19,20,22,23,24,27,28,30,34],[0,1,2,3,10,11,12,18,19,20,22,23,24,26,27,28,29,34],[2,4,5,7,10,12,13,14,15,17,18,19,20,22,23,24,26,27,28,29,31,34],[0,2,6,8,9,11,12,14,15,21,22,23,24,27,30,31,32,33,34],[0,3,4,10,11,17,21,22,23,24,29,30,33],[0,1,7,8,13,14,15,18,21,22,23,24,28,29,34],[1,2,4,5,7,17,18,21,22,23,24,31,32],[0,1,2,3,4,5,6,8,13,14,15,19,21,22,23,24,27,29,30,33],[0,1,2,7,9,11,13,14,15,17,19,21,22,23,24,28,31,32,33,34],[0,2,7,11,13,14,15,18,19,21,22,23,24,28,30,32],[0,1,3,5,6,7,12,14,15,17,18,19,21,22,23,24,28,29,31,34],[0,2,6,9,13,14,15,20,21,22,23,24,26,27,31,33],[1,4,5,6,7,8,9,10,11,14,15,17,20,21,22,23,24,26,33,34],[0,2,3,4,6,7,8,10,12,18,20,21,22,23,24,26,28,29,30,31,32,33],[0,1,2,3,4,5,6,7,8,10,12,14,15,17,18,20,21,22,23,24,26,29,30,32,33,34],[3,4,5,9,12,14,15,19,20,21,22,23,24,26,27,29,32],[2,4,8,10,11,12,13,14,15,17,19,20,21,22,23,24,26,28,29,30,31,32,34],[0,1,2,3,5,6,8,10,11,14,15,18,19,20,21,22,23,24,26,28,31],[1,2,4,6,7,8,12,14,15,17,18,19,20,21,22,23,24,26,28,30,34],[2,3,4,5,6,7,9,12,25,26,30,31,32],[0,1,3,4,5,6,7,13,17,25,28,30,31,33,34],[0,1,3,4,5,6,8,9,12,13,18,25,26,27,30,32,33,34],[1,2,5,9,10,13,17,18,25,30],[0,5,6,7,9,10,19,25,29,30,31,33,34],[1,2,3,6,7,8,9,10,11,12,17,19,25,26,29,31,32],[0,2,5,7,8,9,10,13,14,15,18,19,25,27,29,31],[4,9,10,13,17,18,19,25,26,28,29,30,31,32,33,34],[2,6,7,8,9,10,11,12,20,25,27,32],[3,4,7,8,11,12,17,20,25,26,27,28,29,32,33,34],[0,2,3,4,6,7,9,10,11,13,18,20,25,32,34],[0,1,3,4,7,10,11,12,17,18,20,25,26,27,29,32,33],[1,2,3,4,6,11,12,13,14,15,19,20,25,26,27,29],[1,3,5,8,9,10,12,13,14,15,17,19,20,25,27,30,33,34],[2,7,10,13,18,19,20,25,26,29,30,31,34],[1,3,5,7,11,12,14,15,17,18,19,20,25,27,28,31,33],[0,1,2,6,8,12,21,25,26,27,29,30],[1,3,4,6,8,10,11,13,17,21,25,27,28,29,32,33],[2,5,8,13,18,21,25,29,31,32,33,34],[0,1,5,6,7,8,10,11,12,13,14,15,17,18,21,25,26,27,29,30,31,34],[0,3,4,5,7,11,12,13,14,15,19,21,25,30,31,32,33],[2,3,6,9,11,13,17,19,21,25,26,30,31],[0,3,4,6,7,8,18,19,21,25,26,27,30,31,34],[1,2,4,5,9,10,11,13,17,18,19,21,25,28,30,31,32,33,34],[0,2,4,7,11,13,14,15,20,21,25,27,28,29,32],[0,1,4,9,11,13,14,15,17,20,21,25,26,27,30,32,33],[3,5,7,9,12,13,18,20,21,25,26,28,29,30,34],[2,4,5,6,9,10,17,18,20,21,25,27,28,33,34],[2,3,5,6,8,12,14,15,19,20,21,25,26,28,31,34],[1,6,9,11,12,13,14,15,17,19,20,21,25,28,29,31,33,34],[1,4,7,8,9,10,12,13,14,15,18,19,20,21,25,27,28,32],[1,2,5,6,7,9,12,13,17,18,19,20,21,25,26,29,32,33],[0,4,5,6,7,9,10,12,14,15,22,25,27,28,29,30,32,34],[2,3,7,8,10,11,12,13,14,15,17,22,25,26,29,30,33],[3,4,5,8,18,22,25,29,30,31],[0,1,2,3,4,7,9,12,17,18,22,25,26,29,30,31,32,33,34],[1,2,5,6,19,22,25,27,28,29],[0,1,4,5,6,8,9,10,14,15,17,19,22,25,26,28,29,30,32,33,34],[2,3,7,8,9,11,14,15,18,19,22,25,29,30,32,34],[0,1,6,8,10,11,14,15,17,18,19,22,25,26,28,29,33],[3,5,14,15,20,22,25,26,29,30,31],[1,2,3,5,8,11,12,13,14,15,17,20,22,25,27,28,30,31,33,34],[0,1,2,3,4,7,8,9,10,13,14,15,18,20,22,25,26,27,28,29,30,31,32,33,34],[0,1,5,6,7,13,17,18,20,22,25,27,28,30,31,32],[3,4,5,7,10,11,12,13,14,15,19,20,22,25,26,29,31,32,33],[1,2,4,6,9,13,14,15,17,19,20,22,25,27,30,31,32,34],[2,3,5,6,7,8,9,10,12,13,18,19,20,22,25,26,27,28,29,30,34],[3,4,6,7,8,9,11,13,14,15,17,18,19,20,22,25,27,33],[2,5,6,7,9,12,14,15,21,22,25,26,28,30],[0,1,5,6,11,13,14,15,17,21,22,25,27,32,33],[0,3,5,7,9,10,11,13,14,15,18,21,22,25,27,31,34],[2,5,9,10,12,13,17,18,21,22,25,26,27,30,31,32,33,34],[5,6,7,8,10,11,12,13,14,15,19,21,22,25,26,27,28,31,32],[0,1,2,3,4,6,7,8,9,10,11,13,17,19,21,22,25,28,31,33],[1,2,3,7,9,11,12,13,14,15,18,19,21,22,25,31,32,34],[0,1,3,4,5,6,7,8,9,10,14,15,17,18,19,21,22,25,26,28,31,33,34],[0,1,2,5,6,7,8,9,10,11,12,13,14,15,20,21,22,25,28,30,34],[0,1,3,4,5,10,11,12,17,20,21,22,25,26,27,29,33,34],[2,6,7,8,10,11,14,15,18,20,21,22,25,26,27,33],[1,6,7,10,11,13,14,15,17,18,20,21,22,25,27,29,30],[2,4,6,7,8,9,11,12,14,15,19,20,21,22,25,27,28,31,32,33],[5,6,9,11,12,13,14,15,17,19,20,21,22,25,26,28,29,31,32],[2,5,7,9,11,13,18,19,20,21,22,25,26,32,34],[0,2,4,7,8,9,14,15,17,18,19,20,21,22,25,28,29,32,33,34],[0,1,3,4,5,7,8,9,12,13,23,25,27,28,29,32,33,34],[1,4,6,7,9,10,12,13,17,23,25,26,27,32,33],[2,5,7,9,11,12,18,23,25,28,29,30,31,32],[0,1,2,4,5,6,7,9,12,13,17,18,23,25,26,27,28,30,31,32,34],[0,1,4,7,8,10,12,13,14,15,19,23,25,28,30],[1,4,7,8,9,10,14,15,17,19,23,25,26,28,29,34],[0,1,2,3,4,5,8,9,11,12,14,15,18,19,23,25,27,28,30,33,34],[2,5,6,7,8,9,11,13,14,15,17,18,19,23,25,26,29,33],[2,3,6,8,9,10,12,13,14,15,20,23,25,26,27,28,30,34],[1,2,3,8,9,13,17,20,23,25,27,30,32],[0,2,4,5,6,7,11,12,14,15,18,20,23,25,26,28],[0,2,4,5,6,10,12,13,17,18,20,23,25,27,28,32,34],[0,1,3,4,5,6,9,12,14,15,19,20,23,25,26,28,29,32,34],[0,4,7,10,12,13,14,15,17,19,20,23,25,28,29,30],[0,5,9,11,14,15,18,19,20,23,25,26,27,28,29,31,32],[0,4,6,8,9,10,17,18,19,20,23,25,29,30,31,34],[1,4,7,9,11,12,14,15,21,23,25,26,30,32,34],[0,4,5,6,9,10,11,12,14,15,17,21,23,25,28,29,32,34],[0,3,5,6,10,12,18,21,23,25,27,30,31,33],[10,13,14,15,17,18,21,23,25,26,29,31,33],[0,4,5,7,9,10,12,13,19,21,23,25,26,29,31,33,34],[1,3,11,12,14,15,17,19,21,23,25,31,33,34],[0,8,9,10,18,19,21,23,25,27,29,30,31,32],[4,7,9,12,17,18,19,21,23,25,26,28,30,31,32],[0,1,2,3,5,7,8,13,14,15,20,21,23,25,27,28,29,31,32,33,34],[0,1,2,6,8,11,12,13,17,20,21,23,25,26,27,29,30,31,33,34],[1,3,6,7,8,9,18,20,21,23,25,26,28,29,31,33],[3,9,11,13,14,15,17,18,20,21,23,25,27,28,29,30,31,32,33],[0,1,4,5,7,9,10,11,12,13,14,15,19,20,21,23,25,27,28,30,33],[0,1,2,7,8,10,17,19,20,21,23,25,26,27,28,30,32,33],[0,4,5,9,11,12,14,15,18,19,20,21,23,25,26,28,31,32,33,34],[3,7,8,12,14,15,17,18,19,20,21,23,25,27,31,33,34],[0,1,3,4,5,7,8,10,12,13,22,23,25,26,28,29,31,33,34],[2,4,5,7,9,10,11,12,17,22,23,25,27,31,33],[1,3,5,6,7,8,11,12,18,22,23,25,26,27,29,30,32,33],[0,1,2,3,7,11,14,15,17,18,22,23,25,27,30,32,33,34],[0,2,3,5,6,7,8,9,11,13,19,22,23,25,27,28,29,31,32,33],[1,3,4,6,8,10,11,12,17,19,22,23,25,26,28,30,31,32,33,34],[0,1,6,8,9,10,11,12,18,19,22,23,25,29,31,33,34],[1,4,5,6,9,10,14,15,17,18,19,22,23,25,26,28,30,31,33],[0,3,4,6,7,9,11,13,14,15,20,22,23,25,31],[0,2,3,5,6,8,9,10,14,15,17,20,22,23,25,26,27,28,31,32,34],[1,2,4,6,7,9,10,11,12,13,18,20,22,23,25,27,28,30,31,32,33,34],[4,5,7,8,9,11,17,18,20,22,23,25,26,27,28,30,31,33],[3,4,8,9,10,13,19,20,22,23,25,26,27,31,32,33],[0,1,3,4,7,8,9,11,14,15,17,19,20,22,23,25,30,31,33,34],[3,4,9,11,12,13,14,15,18,19,20,22,23,25,26,28,34],[1,6,7,8,10,11,14,15,17,18,19,20,22,23,25,30,32],[2,4,5,8,9,10,12,13,14,15,21,22,23,25,26,27,30],[0,2,4,6,9,10,11,12,17,21,22,23,25,28,29],[0,1,2,3,7,10,11,12,14,15,18,21,22,23,25,28,30,31,34],[2,3,4,7,9,10,11,12,14,15,17,18,21,22,23,25,26,28,29,31,34],[0,2,3,4,5,8,9,10,12,13,19,21,22,23,25,27,30,31,32],[4,5,7,8,10,12,14,15,17,19,21,22,23,25,26,29,30,31,32],[1,2,4,6,8,9,14,15,18,19,21,22,23,25,26,28,31,32,34],[1,3,4,5,7,9,10,11,12,13,14,15,17,18,19,21,22,23,25,29,31,32,34],[2,3,4,5,9,10,11,13,20,21,22,23,25,29,30,31,32,33,34],[0,3,4,7,8,13,14,15,17,20,21,22,23,25,26,27,28,29,31,33,34],[0,3,4,5,6,9,10,11,12,13,14,15,18,20,21,22,23,25,26,27,28,29,30,31,32],[0,10,11,13,17,18,20,21,22,23,25,27,28,29,31],[1,4,7,8,10,11,12,13,14,15,19,20,21,22,23,25,26,29,30],[0,1,2,3,4,5,6,7,9,13,14,15,17,19,20,21,22,23,25,27,29,30,32],[2,7,8,10,11,13,14,15,18,19,20,21,22,23,25,27,28,29,31,33,34],[17,18,19,20,21,22,23,25,26,27,29,31,32,33,34],[0,2,5,6,10,11,24,25,26,28,30,33,34],[0,1,2,3,4,6,7,10,11,13,17,24,25,26,31,32,33],[0,2,3,4,5,8,11,12,14,15,18,24,25,28,32],[0,3,4,5,6,8,11,12,17,18,24,25,27,28,30,31,34],[0,1,2,5,6,7,19,24,25,28,29,30,32,33],[0,1,2,3,4,7,8,10,11,13,17,19,24,25,28,29,30,31,33,34],[1,4,5,6,8,9,12,13,18,19,24,25,26,28,29,30,31,34],[2,4,5,7,12,13,17,18,19,24,25,26,27,29,30,32],[4,5,6,7,8,9,10,13,20,24,25,27,28,29,30,31,34],[0,1,2,4,6,8,9,13,17,20,24,25,27],[1,2,5,6,8,9,10,11,12,13,18,20,24,25,26,27,28,29,32],[0,5,6,7,8,10,11,12,17,18,20,24,25,26,28,30,31,32,34],[0,1,6,8,10,13,14,15,19,20,24,25,26,27,28,30,31,32,33,34],[1,2,3,5,9,11,17,19,20,24,25,26,27,28,29,30,32,33],[2,3,5,8,10,13,18,19,20,24,25,27,28,30,31,33],[0,2,5,10,11,13,14,15,17,18,19,20,24,25,29,30,33,34],[0,1,2,5,8,9,10,11,12,13,14,15,21,24,25,28,29,30,33],[0,4,6,9,10,13,14,15,17,21,24,25,29,30,31,32,33],[0,1,2,3,7,9,10,12,14,15,18,21,24,25,28,29,30,34],[0,3,5,6,9,11,14,15,17,18,21,24,25,27,28,29,30,31,32,34],[1,7,8,10,12,13,14,15,19,21,24,25,26,27,28,30,31,32,33],[4,5,6,7,9,11,12,13,17,19,21,24,25,26,27,28,33],[0,1,2,6,9,13,14,15,18,19,21,24,25,26,27,28,32,34],[1,2,3,4,10,12,17,18,19,21,24,25,26,30,31,34],[1,2,4,5,6,8,10,13,14,15,20,21,24,25,26,30,32],[0,4,5,7,8,12,14,15,17,20,21,24,25,26,28,29,30,31,32],[2,3,4,6,8,12,18,20,21,24,25,26,30,31,32,34],[0,2,6,13,17,18,20,21,24,25,26,27,29,30,32,34],[1,2,3,4,6,7,8,9,10,13,14,15,19,20,21,24,25,27,29,30,31,33,34],[0,3,4,7,8,9,17,19,20,21,24,25,27,33,34],[1,2,4,5,7,12,18,19,20,21,24,25,27,29,31,33],[0,1,2,3,5,8,14,15,17,18,19,20,21,24,25,28,30,33],[1,11,22,24,25,26,31,34],[1,2,3,4,5,9,14,15,17,22,24,25,26,27,28,30,32],[1,2,3,4,6,8,12,13,14,15,18,22,24,25,28,30,31],[0,2,5,6,7,8,10,12,17,18,22,24,25,28,32,34],[5,6,8,10,12,13,19,22,24,25,26,30,31,32,33],[0,1,4,6,8,10,11,12,14,15,17,19,22,24,25,26,27,30,33,34],[0,3,4,6,9,10,12,13,14,15,18,19,22,24,25,28,30,32,33,34],[0,4,9,10,14,15,17,18,19,22,24,25,30,31,33],[1,2,6,8,9,11,20,22,24,25,27,28,29,30,32,33],[0,2,3,5,6,8,11,12,14,15,17,20,22,24,25,31,32,33,34],[0,3,4,6,14,15,18,20,22,24,25,26,27,29,31,32,34],[2,3,6,10,12,13,17,18,20,22,24,25,26,27,30,32],[0,1,2,5,6,7,9,10,11,12,19,20,22,24,25,27,28,29,33],[5,6,9,12,17,19,20,22,24,25,28,31,33,34],[0,2,3,5,7,13,14,15,18,19,20,22,24,25,26,27,29,34],[0,1,4,5,9,13,14,15,17,18,19,20,22,24,25,26,27,28,31],[3,4,5,7,8,9,11,13,14,15,21,22,24,25,26,29,34],[0,4,5,6,10,13,14,15,17,21,22,24,25,26,27,28,29,31,32,34],[0,1,3,4,7,11,18,21,22,24,25,26,28,29,32],[0,1,2,4,5,7,8,13,14,15,17,18,21,22,24,25,26,28,29,31],[0,1,2,3,5,9,11,12,14,15,19,21,22,24,25,26,27,29,30,31,32,33,34],[6,7,8,9,10,12,17,19,21,22,24,25,26,29,33,34],[0,3,4,6,8,9,10,11,12,13,18,19,21,22,24,25,26,27,28,29,33],[0,1,3,5,6,7,8,9,10,12,17,18,19,21,22,24,25,26,27,29,30,31,32,33],[0,2,4,5,6,9,10,13,20,21,22,24,25,30,33],[0,1,2,5,10,11,12,13,14,15,17,20,21,22,24,25,27,28,29,30,31,33],[0,2,3,5,6,8,10,11,12,13,14,15,18,20,21,22,24,25,28,30,31,32,34],[2,3,4,5,7,9,10,12,14,15,17,18,20,21,22,24,25,28,29,30,32,34],[0,2,3,4,5,6,7,9,10,11,12,13,14,15,19,20,21,22,24,25,27,31,32,33,34],[0,3,6,10,11,12,17,19,20,21,22,24,25,29,30,32,33,34],[2,4,8,9,12,13,18,19,20,21,22,24,25,27,28,30,31],[17,18,19,20,21,22,24,25,27,29],[1,2,3,4,7,9,10,11,12,13,14,15,23,24,25,26,27,28,29,30],[1,2,4,7,8,12,17,23,24,25,26,27,31,33,34],[2,7,8,9,18,23,24,25,27,28,29,30,32,33,34],[1,2,7,10,12,13,17,18,23,24,25,28,31,32],[0,1,4,5,6,7,19,23,24,25,26,28,32,34],[0,1,2,3,5,7,8,9,10,12,14,15,17,19,23,24,25,26,28,29,31,32,33],[1,3,7,12,18,19,23,24,25,28,30,31,33],[2,3,5,9,10,12,14,15,17,18,19,23,24,25,27,29,30,34],[2,5,6,7,8,11,12,13,14,15,20,23,24,25,27,28,29,30,32],[0,1,2,3,4,7,8,9,10,11,17,20,23,24,25,27,29,31,33,34],[1,4,5,6,7,8,9,10,12,13,14,15,18,20,23,24,25,26,27,28,29,30,31,34],[1,2,4,11,14,15,17,18,20,23,24,25,26,28,29,32,33],[0,1,2,3,7,10,11,13,19,20,23,24,25,28,33],[2,3,4,5,9,10,11,13,14,15,17,19,20,23,24,25,28,31,32,34],[1,6,10,11,18,19,20,23,24,25,26,28,30,32,33,34],[0,2,3,4,6,8,10,12,17,18,19,20,23,24,25,26,27,30,31],[4,5,8,12,14,15,21,23,24,25,26,27,31,32,33,34],[0,1,3,5,6,8,14,15,17,21,23,24,25,26,27,28,29,32,34],[1,5,9,10,11,13,18,21,23,24,25,26,27,30,31,32],[1,2,8,13,17,18,21,23,24,25,26,29,30,32,33],[0,1,3,4,5,6,8,11,19,21,23,24,25,26,27,29,30,33,34],[0,2,4,10,12,13,14,15,17,19,21,23,24,25,26,27,31,34],[1,4,5,13,14,15,18,19,21,23,24,25,26,27,29,30,31],[0,1,2,4,7,9,10,12,17,18,19,21,23,24,25,26,28,33],[0,1,2,3,6,7,9,10,11,13,14,15,20,21,23,24,25,28,32,33,34],[0,1,2,3,4,6,8,10,11,12,14,15,17,20,21,23,24,25,31,34],[0,3,4,5,8,9,11,13,18,20,21,23,24,25,28,30,31,32,33],[2,4,5,6,9,10,11,13,17,18,20,21,23,24,25,27,28,30],[0,2,4,7,9,11,12,13,19,20,21,23,24,25,28,29,30,31],[0,1,3,4,6,7,9,10,11,13,17,19,20,21,23,24,25,28,29,32,33],[2,5,7,13,14,15,18,19,20,21,23,24,25,28,29,30,31,34],[17,18,19,20,21,23,24,25,27,29,32,33,34],[3,4,6,9,10,12,14,15,22,23,24,25,26,27,28,31,32,33,34],[0,1,7,9,10,12,14,15,17,22,23,24,25,26,29,30,32],[2,3,4,5,7,8,9,11,12,13,18,22,23,24,25,27,31,32,33],[2,5,6,7,8,10,17,18,22,23,24,25,27,29,30,32,34],[1,4,7,8,11,12,14,15,19,22,23,24,25,28,31],[0,1,2,6,7,8,11,12,17,19,22,23,24,25,27,28,29,33,34],[0,3,5,7,8,10,18,19,22,23,24,25,26,30,34],[17,18,19,22,23,24,25,26,28,29,30,31,33],[1,2,4,5,7,8,12,13,20,22,23,24,25,27,30,31,32,33],[4,7,8,13,17,20,22,23,24,25,28,34],[0,1,3,6,7,9,11,13,18,20,22,23,24,25,26,27,28,30,32,34],[17,18,20,22,23,24,25,26,27,28,31,33],[0,1,2,3,5,6,10,13,19,20,22,23,24,25,26,30,31,33],[17,19,20,22,23,24,25,26,27,30,32,34],[1,2,3,4,8,11,12,13,14,15,18,19,20,22,23,24,25,28,31,34],[17,18,19,20,22,23,24,25,32,33],[0,3,5,6,7,8,9,10,12,13,14,15,21,22,23,24,25,27,29,30,31,34],[0,1,3,4,6,7,11,12,17,21,22,23,24,25,28,30,33,34],[2,3,4,5,6,7,8,10,12,13,14,15,18,21,22,23,24,25,27,28,29,31,32],[17,18,21,22,23,24,25,27,28,32,33],[0,2,4,5,7,10,11,13,19,21,22,23,24,25,26,27,29,30,32,33,34],[17,19,21,22,23,24,25,26,31,32,34],[18,19,21,22,23,24,25,26,27,28,29,30,31,33],[17,18,19,21,22,23,24,25,26,27],[0,1,2,5,11,12,20,21,22,23,24,25,26,29,32],[17,20,21,22,23,24,25,26,27,28,29,31,33],[18,20,21,22,23,24,25,26,28,29,30,31,33,34],[17,18,20,21,22,23,24,25,26,28,29,30,32,34],[19,20,21,22,23,24,25,29,31,34],[17,19,20,21,22,23,24,25,27,29,30,32,33,34],[18,19,20,21,22,23,24,25,28,29,31,32,33],[17,18,19,20,21,22,23,24,25,29,30]]},"distance":{"d":5,"is_exact":true,"upper":5,"witness":[28,194,199,448,470],"A_d":1094562,"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],[0,16],[0,18],[0,19],[0,22],[0,24],[0,26],[0,28],[0,30],[0,34],[1,4],[1,7],[1,8],[1,12],[1,19],[1,25],[1,30],[1,34],[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],[2,24],[2,27],[2,28],[2,29],[2,31],[2,32],[2,33],[2,34],[3,4],[3,5],[3,9],[3,10],[3,12],[3,14],[3,16],[3,20],[3,21],[3,22],[3,23],[3,28],[3,29],[3,30],[3,32],[4,8],[4,12],[4,13],[4,14],[4,16],[4,20],[4,22],[4,23],[4,27],[4,28],[4,32],[5,8],[5,10],[5,11],[5,12],[5,17],[5,23],[5,24],[5,26],[5,27],[5,29],[5,30],[5,32],[5,34],[6,8],[6,9],[6,10],[6,11],[6,13],[6,17],[6,19],[6,24],[6,28],[6,29],[6,31],[6,33],[6,34],[7,8],[7,10],[7,11],[7,13],[7,17],[7,18],[7,21],[7,24],[7,25],[7,28],[7,31],[7,32],[7,34],[8,10],[8,13],[8,15],[8,16],[8,19],[8,21],[8,22],[8,23],[8,25],[8,26],[8,27],[8,28],[8,29],[8,30],[8,32],[8,34],[9,10],[9,13],[9,15],[9,16],[9,19],[9,21],[9,22],[9,24],[9,25],[9,26],[9,28],[9,31],[10,12],[10,14],[10,15],[10,17],[10,21],[10,23],[10,26],[10,33],[11,14],[11,16],[11,17],[11,18],[11,19],[11,20],[11,23],[11,25],[11,27],[11,32],[11,34],[12,13],[12,14],[12,15],[12,18],[12,20],[12,21],[12,25],[12,27],[12,28],[12,29],[12,33],[13,15],[13,16],[13,18],[13,19],[13,20],[13,21],[13,23],[13,26],[13,28],[13,30],[13,32],[14,23],[14,24],[14,26],[14,28],[14,31],[14,32],[14,34],[15,17],[15,21],[15,22],[15,23],[15,24],[15,26],[15,28],[15,32],[16,17],[16,21],[16,22],[16,31],[16,34]]},"rotation_powers":null},"metrics":{"gamma":2.114499863496184,"gamma_t":null,"gamma_rho":2.114499863496184,"gamma_claim":2.114499863496184,"gamma_t_claim":null,"gamma_rho_claim":2.114499863496184,"v_ex":17,"rate":0.033268101761252444,"t_count":null,"poly_degree":null,"effective_width":17},"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.T16","N":35,"d":5,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:371"}]},"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"}]}