{"id":"189.35.3.a","row":824,"stored":{"file":"master_catalog.json","row":824,"construction":null,"columns_sha256":null},"parameters":{"n":189,"k":35,"d":3,"N":46,"r":11,"level":3},"gate":{"string":"0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6\u00b7T7\u00b7T8\u00b7T9\u00b7T10\u00b7T11\u00b7T12\u00b7T13\u00b7T14\u00b7T15\u00b7T16\u00b7T17\u00b7T18\u00b7T19\u00b7T20\u00b7T21\u00b7T22\u00b7T23\u00b7T24\u00b7T25\u00b7T26\u00b7T27\u00b7T28\u00b7T29\u00b7T30\u00b7T31\u00b7T32\u00b7T33\u00b7T34","monomials":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15],[16],[17],[18],[19],[20],[21],[22],[23],[24],[25],[26],[27],[28],[29],[30],[31],[32],[33],[34]],"sk_key":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15],[16],[17],[18],[19],[20],[21],[22],[23],[24],[25],[26],[27],[28],[29],[30],[31],[32],[33],[34]],"sk_fingerprint":"7c2e8606aa1e8a26","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,1,2,3,4,9,10,11,13,14,15,21,23,24,27,28,34,35,37,42,44,45],[0,1,2,4,10,11,12,13,14,17,19,21,22,24,26,28,34,37,40,41,44,45],[0,2,3,4,6,8,9,10,11,13,14,15,21,24,26,27,28,32,34,40,44,45],[0,4,6,7,8,10,11,12,13,14,17,19,20,21,22,23,24,28,30,32,34,35,37,39,41,42,43],[0,1,2,5,7,10,12,14,19,22,24,27,28,29,30,31,32,35,36,37,38,39,40,45],[0,1,5,7,9,10,18,19,22,23,24,25,28,29,31,32,34,35,36,37,38,39,41,44,45],[3,7,9,12,14,18,20,23,25,27,34,37,38,41,43,45],[3,38,39,40],[3,6,15,17,19,22,26,35,39,40,41,42],[0,3,5,6,7,8,9,10,13,18,19,22,23,24,25,28,31,32,34,35,36,37,38,39,40,41,42,44,45],[0,2,5,6,8,9,10,13,15,17,18,20,23,24,25,26,28,30,31,32,34,36,38,39,43],[2,4,5,7,11,12,13,14,15,18,21,23,25,26,31,35,36,37,39,42],[1,2,4,6,10,11,12,13,14,17,21,22,23,24,26,27,28,29,34,40,42,44,45],[0,3,4,6,7,8,9,10,11,12,13,14,15,19,20,21,22,23,24,26,28,29,30,32,34,35,39,40,41,42,43],[0,1,2,3,4,5,7,8,9,11,12,13,14,17,18,19,21,23,25,26,27,31,32,36,39,41,42],[0,3,4,5,7,8,11,12,13,15,17,21,22,23,29,30,31,32,34,36,38,39,42,44],[0,1,2,4,6,8,9,10,11,13,14,15,17,19,21,22,24,26,28,32,34,37,38,39,40,44,45],[1,4,6,8,9,10,11,12,15,17,18,19,21,23,24,25,28,29,30,39,40,41,45],[3,4,5,8,11,14,15,17,18,20,21,25,26,30,31,36,41,42,43,44,45],[19,37,41,42],[1,5,6,7,9,10,12,15,17,18,19,22,23,24,25,28,29,31,34,35,36,40,41,42,44,45],[1,2,7,8,13,19,20,26,29,30,32,38,39,40,41,42,43,44,45],[5,6,7,8,9,10,12,13,15,17,18,19,22,23,24,25,26,28,31,32,34,35,36,38,41,42,44,45],[1,2,3,5,6,7,10,14,19,24,26,27,28,29,30,31,32,36,37,39,40,42,45],[26,39,40,42],[1,3,5,6,10,14,19,20,24,27,28,29,31,36,39,43,44],[0,2,5,8,9,10,12,14,15,16,17,24,29,36,38,39,41,45],[0,5,7,8,9,10,12,14,15,16,17,20,24,29,30,31,33,36,37,38,41,43,44],[3,5,7,11,12,15,16,17,18,19,20,22,23,24,25,26,28,31,33,35,36,37,39,42,43,44,45],[5,7,11,14,16,20,24,25,28,31,33,36,38,40,41,43,44,45],[5,14,20,21,24,25,30,31,33,36,37,39,45],[2,3,5,7,12,15,17,18,19,21,22,23,24,25,26,31,33,35,36,37,38,39,40,41,42,43,44],[0,3,5,8,9,10,14,16,19,22,23,25,26,29,30,33,34,35,36,37,38,39,40,42,43,45],[24,38,40,41,43,44],[0,5,6,7,8,9,10,11,12,13,15,17,18,21,23,25,26,28,31,32,34,35,36,44,45],[2,3,6,11,12,13,14,15,16,17,18,19,20,21,22,24,28,29,31,32,33,41,42,43,44,45],[10,36],[0,5,8,9,12,15,16,17,18,24,29,30,33,37,38,41,43,44],[0,5,6,8,9,11,12,13,14,15,16,17,20,21,23,24,25,26,32,33,34,35,38,40,41,43,45],[2,6,7,10,11,13,14,18,21,23,25,26,29,32,34,35,36,39,40,43],[34,37,40,41,43,45],[0,5,8,9,10,11,12,14,15,16,17,20,21,24,25,29,31,36,39,40],[0,2,5,7,8,9,10,11,12,14,15,16,17,21,24,29,30,31,34,36,41,44],[0,2,3,5,8,9,10,18,19,22,23,24,25,26,29,33,34,35,36,41,42,43],[0,3,5,7,8,9,10,16,18,19,20,22,23,24,25,26,28,29,30,33,34,35,36,37,39,41,42,44,45],[2,3,4,5,6,12,13,14,15,16,17,18,19,20,21,22,24,28,29,30,32,33,34,37,40,42,44],[4,5,6,13,14,16,18,20,21,23,24,26,28,29,32,33,34,35,37,38,41,43,45],[0,4,8,9,10,12,14,15,16,17,20,21,25,29,30,31,33,36,38,39,41,43,44],[0,3,4,7,8,9,10,14,16,19,21,22,23,25,26,29,30,31,33,35,36,37,40,42,43,44],[0,1,3,5,7,10,13,18,19,22,23,24,25,26,28,31,34,35,36,38,41,44,45],[0,1,2,3,5,9,10,13,18,19,20,22,23,24,25,26,27,28,30,31,34,35,36,37,38,41,43],[9,39],[1,2,6,7,8,13,17,20,23,29,30,35,37,38,42,43,44,45],[1,2,3,6,8,9,13,14,15,18,19,22,23,25,26,27,29,30,34,38,44],[2,3,9,14,15,18,19,22,25,26,27,30,34,35,39,42,44],[6,35],[2,6,7,12,20,23,30,35,37,39,43,44,45],[1,2,3,5,6,10,12,13,18,19,20,23,24,25,26,27,28,29,30,31,34,36,37,38,39,41,43],[13,37,38,42],[1,3,5,6,7,10,12,18,19,23,24,25,26,27,28,31,34,36,37,41,42,44,45],[1,40,41,42],[5,6,9,10,14,15,17,20,22,24,28,29,31,35,36,40,42,43,44],[8,37,39,40,41,42],[1,2,5,6,7,8,9,10,14,15,17,22,24,28,29,30,31,35,36,40,42,45],[1,2,3,5,6,9,10,18,19,20,22,24,25,26,28,29,30,31,34,36,41,42,43],[0,1,3,5,6,7,9,10,18,19,24,25,26,28,29,31,34,36,37,39,41,42,44,45],[0,1,2,3,8,9,12,13,14,17,18,19,23,25,26,27,29,30,34,35,37,39,40,42,44],[0,2,3,5,6,8,9,10,13,15,18,19,20,22,24,25,26,28,30,31,34,36,37,40,41,42,43],[1,2,5,6,7,10,12,14,17,22,23,24,27,28,29,30,31,35,36,38,39,40,41,42,45],[15,37,38,39,40,42],[4,43],[0,3,4,5,7,8,9,10,14,16,19,20,22,23,24,26,29,30,33,35,36,37,38,39,40,42,44],[0,2,3,4,5,6,8,9,10,13,18,19,20,22,24,25,28,30,32,33,34,36,38,40,41,42],[4,6,13,14,16,18,20,23,25,26,28,29,30,32,34,35,41,45],[0,5,6,8,9,10,11,12,13,15,16,17,21,23,24,25,26,30,31,32,34,35,36,38,40,41,43,44,45],[0,2,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,21,23,24,25,26,31,32,34,35,36,39,40,41],[14,37,39,44],[18,38,39,44],[11,37,40,41,43,44],[0,2,5,7,8,9,10,11,12,14,15,16,17,20,24,25,29,33,34,36,37,39,41,44],[0,5,8,9,10,12,14,15,16,17,21,24,25,29,30,33,34,36,37,40,44,45],[0,2,3,5,7,8,9,16,18,19,20,22,23,24,26,29,33,35,36,38,40,42,45],[3,7,10,11,12,14,15,16,17,18,19,20,21,22,23,26,28,31,33,35,37,39,42,43,44],[0,5,7,8,9,11,12,14,15,17,20,21,24,28,29,30,31,36,38,40],[5,6,7,11,13,14,16,18,20,21,23,25,26,28,29,32,34,35,41,43,44],[2,3,5,6,11,12,13,14,15,16,17,18,19,21,22,28,29,30,32,41,42,43],[3,5,12,15,17,19,22,23,25,26,34,35,38,40,41,42],[5,37,38,39,40,41,43,45],[0,4,5,8,9,10,11,12,15,17,18,29,30,41,44],[4,7,11,16,20,24,25,33,34,36,37,40,41,45],[0,2,4,5,6,7,8,9,10,11,12,13,15,17,18,23,26,30,31,32,33,35,37,38,39,40,41,43,45],[4,6,7,11,13,16,23,24,25,26,29,30,31,32,34,35,36,37,38,41,45],[7,43,44,45],[20,37,38,43,44,45],[30,38,39,43,44,45],[0,1,2,3,4,9,10,11,13,14,15,21,23,24,27,28,34,35,42,44,45],[0,1,2,4,10,11,12,13,14,17,19,21,22,24,26,28,34,37,38,40,41,44,45],[0,2,3,4,6,8,9,10,11,13,14,15,21,24,26,27,28,32,34,39,40,44,45],[0,4,6,7,8,10,11,12,13,14,17,19,20,21,22,23,24,28,30,32,34,35,38,41,42,43],[0,1,2,5,7,10,12,14,19,22,24,27,28,29,30,31,32,35,36,37,38,39,45],[0,1,5,7,9,10,18,19,22,23,24,25,28,29,31,32,34,35,36,39,40,41,44,45],[3,7,9,12,14,18,20,23,25,27,34,38,39,40,41,43,45],[6,41],[3,6,15,17,19,22,26,35,37,38,39,40,42],[0,3,5,6,7,8,9,10,13,18,19,22,23,24,25,28,31,32,34,35,36,38,40,42,44,45],[0,2,5,6,8,9,10,13,15,17,18,20,23,24,25,26,28,30,31,32,34,36,41,43],[2,4,5,7,11,12,13,14,15,18,21,23,25,26,31,35,36,37,39],[1,2,4,6,10,11,12,13,14,17,21,22,23,24,26,27,28,29,34,37,38,40,44,45],[0,3,4,6,7,8,9,10,11,12,13,14,15,19,20,21,22,23,24,26,28,29,30,32,34,35,37,40,41,43],[0,1,2,3,4,5,7,8,9,11,12,13,14,17,18,19,21,23,25,26,27,31,32,36,38,41],[0,3,4,5,7,8,11,12,13,15,17,21,22,23,29,30,31,32,34,36,38,39,40,41,44],[0,1,2,4,6,8,9,10,11,13,14,15,17,19,21,22,24,26,28,32,34,39,41,42,44,45],[1,4,6,8,9,10,11,12,15,17,18,19,21,23,24,25,28,29,30,37,42,45],[3,4,5,8,11,14,15,17,18,20,21,25,26,30,31,36,38,39,40,43,44,45],[1,5,6,7,9,10,12,15,17,18,19,22,23,24,25,28,29,31,34,35,36,38,40,44,45],[1,2,7,8,13,19,20,26,29,30,32,38,40,43,44,45],[5,6,7,8,9,10,12,13,15,17,18,19,22,23,24,25,26,28,31,32,34,35,36,37,39,44,45],[32,37,40,42],[1,2,3,5,6,7,10,14,19,24,26,27,28,29,30,31,32,36,37,38,39,45],[1,3,5,6,10,14,19,20,24,27,28,29,31,36,37,38,40,42,43,44],[0,2,5,8,9,10,12,14,15,16,17,24,29,36,38,39,41,43,45],[33,37,38,43],[0,5,7,8,9,10,12,14,15,16,17,20,24,29,30,31,33,36,38,39,41,44],[31,38,39,43],[3,5,7,11,12,15,16,17,18,19,20,22,23,24,25,26,28,31,33,35,36,37,39,42,43,45],[5,7,11,14,16,20,24,25,28,31,33,36,37,40,41,43,45],[5,14,20,21,24,25,30,31,33,36,44,45],[2,3,5,7,12,15,17,18,19,21,22,23,24,25,26,31,33,35,36,37,40,41,42,43],[0,3,5,8,9,10,14,16,19,22,23,25,26,29,30,33,34,35,36,38,39,41,42,44,45],[0,5,6,7,8,9,10,11,12,13,15,17,18,21,23,25,26,28,31,32,34,35,36,39,40,41,43,45],[2,3,6,11,12,13,14,15,16,17,18,19,20,21,22,24,28,29,31,32,33,37,38,39,40,42,45],[10,36,45],[0,5,8,9,12,15,16,17,18,24,29,30,33,41,43,44,45],[0,5,6,8,9,11,12,13,14,15,16,17,20,21,23,24,25,26,32,33,34,35,37,38,39,40,41,43],[2,6,7,10,11,13,14,18,21,23,25,26,29,32,34,35,36,38,40,43,45],[25,38,40,41,43,45],[0,5,8,9,10,11,12,14,15,16,17,20,21,24,25,29,31,36,41,43,45],[0,2,5,7,8,9,10,11,12,14,15,16,17,21,24,29,30,31,34,36,37,38,39,40,43,44,45],[0,2,3,5,8,9,10,18,19,22,23,24,25,26,29,33,34,35,36,37,40,42,43,44,45],[16,38,40,41,44,45],[28,39,40,41,44,45],[0,3,5,7,8,9,10,16,18,19,20,22,23,24,25,26,28,29,30,33,34,35,36,38,40,42],[2,3,4,5,6,12,13,14,15,16,17,18,19,20,21,22,24,28,29,30,32,33,34,37,40,42,43,45],[4,5,6,13,14,16,18,20,21,23,24,26,28,29,32,33,34,35,41,44],[0,4,8,9,10,12,14,15,16,17,20,21,25,29,30,31,33,36,37,38,41,45],[0,3,4,7,8,9,10,14,16,19,21,22,23,25,26,29,30,31,33,35,36,37,38,39,40,42,45],[0,1,3,5,7,10,13,18,19,22,23,24,25,26,28,31,34,35,36,37,38,41,44,45],[0,1,2,3,5,9,10,13,18,19,20,22,23,24,25,26,27,28,30,31,34,35,36,37,41,43],[27,37,38,39],[1,2,6,7,8,13,17,20,23,29,30,35,37,38,40,42,43,44,45],[1,2,3,6,8,9,13,14,15,18,19,22,23,25,26,27,29,30,34,37,40,44],[17,37,39,40],[2,3,9,14,15,18,19,22,25,26,27,30,34,35,38,40,42,44],[6,35,41],[2,6,7,12,20,23,30,35,38,39,41,43,44,45],[23,37,39,41],[12,38,39,41],[1,2,3,5,6,10,12,13,18,19,20,23,24,25,26,27,28,29,30,31,34,36,37,38,39,41,42,43],[1,3,5,6,7,10,12,18,19,23,24,25,26,27,28,31,34,36,39,41,44,45],[29,38,39,42],[5,6,9,10,14,15,17,20,22,24,28,29,31,35,36,37,38,41,43,44],[1,2,5,6,7,8,9,10,14,15,17,22,24,28,29,30,31,35,36,38,39,41,45],[1,2,3,5,6,9,10,18,19,20,22,24,25,26,28,29,30,31,34,36,37,43],[22,38,41,42],[0,39,41,42],[0,1,3,5,6,7,9,10,18,19,24,25,26,28,29,31,34,36,38,44,45],[0,1,2,3,8,9,12,13,14,17,18,19,23,25,26,27,29,30,34,35,39,44],[0,2,3,5,6,8,9,10,13,15,18,19,20,22,24,25,26,28,30,31,34,36,37,38,41,43],[1,2,5,6,7,10,12,14,17,22,23,24,27,28,29,30,31,35,36,38,41,45],[0,3,4,5,7,8,9,10,14,16,19,20,22,23,24,26,29,30,33,35,36,39,40,42,43,44],[0,2,3,4,5,6,8,9,10,13,18,19,20,22,24,25,28,30,32,33,34,36,37,38,39,40,41,42,43],[4,6,13,14,16,18,20,23,25,26,28,29,30,32,34,35,38,39,41,43,45],[0,5,6,8,9,10,11,12,13,15,16,17,21,23,24,25,26,30,31,32,34,35,36,38,40,41,43,45],[0,2,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,21,23,24,25,26,31,32,34,35,36,37,38,39,40,41,44],[0,2,5,7,8,9,10,11,12,14,15,16,17,20,24,25,29,33,34,36,37,38,39,40,43],[0,5,8,9,10,12,14,15,16,17,21,24,25,29,30,33,34,36,37,39,41,43,45],[21,37,38,39,40,41,43,44],[10,45],[0,2,3,5,7,8,9,16,18,19,20,22,23,24,26,29,33,35,36,37,40,42],[3,7,10,11,12,14,15,16,17,18,19,20,21,22,23,26,28,31,33,35,42,43,44,45],[0,5,7,8,9,11,12,14,15,17,20,21,24,28,29,30,31,36,39,40,45],[5,6,7,11,13,14,16,18,20,21,23,25,26,28,29,32,34,35,37,40,44,45],[2,3,5,6,11,12,13,14,15,16,17,18,19,21,22,28,29,30,32,38,40,42,45],[3,5,12,15,17,19,22,23,25,26,34,35,38,39,42,43,45],[0,4,5,8,9,10,11,12,15,17,18,29,30,37,40,45],[4,7,11,16,20,24,25,33,34,36,37,38,44],[0,2,4,5,6,7,8,9,10,11,12,13,15,17,18,23,26,30,31,32,33,35,37,38,43,44],[4,6,7,11,13,16,23,24,25,26,29,30,31,32,34,35,36,39,40,44],[2,37,39,43,44,45]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,15,99],"A_d":722,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,1],[1,1],[2,1],[3,1],[4,1],[5,1],[6,1],[7,1],[8,1],[9,1],[10,1],[11,1],[12,1],[13,1],[14,1],[15,1],[16,1],[17,1],[18,1],[19,1],[20,1],[21,1],[22,1],[23,1],[24,1],[25,1],[26,1],[27,1],[28,1],[29,1],[30,1],[31,1],[32,1],[33,1],[34,1],[38,2]],"CZ":[[0,37],[0,38],[2,37],[2,39],[3,38],[3,39],[5,37],[5,38],[6,37],[6,38],[7,38],[7,39],[8,37],[8,38],[9,37],[9,38],[10,37],[10,38],[12,37],[12,39],[13,37],[13,38],[15,37],[15,39],[17,37],[17,39],[18,37],[18,38],[19,38],[19,39],[20,37],[20,39],[22,38],[22,39],[23,37],[23,39],[24,37],[24,38],[25,37],[25,38],[26,37],[26,39],[28,37],[28,38],[30,37],[30,39],[31,37],[31,38],[32,37],[32,38],[34,37],[34,38],[35,37],[35,39],[36,37],[36,38],[37,43],[38,39],[38,40],[38,41],[38,42],[38,44],[38,45],[39,40],[39,41],[39,42],[39,43],[39,44],[39,45]]},"rotation_powers":[[0,7],[1,5],[2,5],[3,5],[4,3],[8,3],[10,7],[11,5],[12,5],[13,7],[15,3],[19,7],[23,7],[25,3],[26,3],[27,5],[28,7],[32,5],[33,3],[34,3],[35,3],[36,5],[37,7],[40,5],[43,3],[48,3],[50,5],[51,5],[52,7],[53,3],[55,7],[57,7],[59,3],[63,3],[64,3],[66,3],[68,3],[69,3],[71,3],[74,3],[75,3],[76,3],[81,3],[83,3],[84,3],[85,3],[87,3],[88,3],[93,3],[94,3],[95,5],[97,7],[99,7],[100,3],[102,5],[103,3],[104,3],[105,3],[107,3],[108,3],[109,3],[112,3],[114,3],[116,3],[118,3],[119,3],[121,3],[122,3],[123,3],[124,7],[125,3],[127,3],[128,3],[130,3],[131,5],[134,3],[135,3],[136,3],[138,3],[140,3],[141,3],[142,3],[144,3],[145,3],[146,3],[148,3],[149,3],[151,3],[152,3],[156,3],[157,3],[158,3],[161,3],[162,3],[164,3],[165,3],[169,3],[170,3],[172,3],[175,3],[176,3],[177,3],[182,3],[183,3],[184,3],[185,3],[187,3]]},"metrics":{"gamma":1.535026479282073,"gamma_t":null,"gamma_rho":1.535026479282073,"gamma_claim":1.535026479282073,"gamma_t_claim":null,"gamma_rho_claim":1.535026479282073,"v_ex":35,"rate":0.18518518518518517,"t_count":null,"poly_degree":null,"effective_width":35},"provenance":{"regimes":["AI search (gamma frontier): from Wills parent codes"],"discovery":"AI search","strongest_claim":"built from one of Wills's parent codes (weighted Reed-Muller, restricted-light or one-heavy) by searched punctures, paired-column contractions or logical-pair checks, in the pure-T distillation-exponent release (gamma = log(n/k)/log d, n < 1000); a verified witness, not a maximum -- only the release's own frontier points are the lowest gamma it knows","sources":[{"regime":"AI search (gamma frontier): from Wills parent codes","file":"gamma_frontier_release/protocols/restricted_light_189_35_3.json","label":"restricted_light_189_35_3","N":46,"d":3,"d_is_exact":true,"origin":"Wills-derived restricted-light construction","provenance":"gamma frontier release record restricted_light_189_35_3 (source catalogue id restricted_light_189_35_3); construction: Wills-derived restricted-light construction; matrix 7f6444a2df8cf68d...; the release states d=3 (exact), gamma=1.535026479282073 (exact)","notes":"matrix gamma_frontier_release/matrices/7f6444a2df8cf68dd23af1fff9cea4192a69352368528f907524ae6251f8ab10.matrix"}]},"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"}]}