{"id":"210.46.3.a","row":853,"stored":{"file":"master_catalog.json","row":853,"construction":null,"columns_sha256":null},"parameters":{"n":210,"k":46,"d":3,"N":56,"r":10,"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+35+36+37+38+39+40+41+42+43+44+45","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\u00b7T35\u00b7T36\u00b7T37\u00b7T38\u00b7T39\u00b7T40\u00b7T41\u00b7T42\u00b7T43\u00b7T44\u00b7T45","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],[35],[36],[37],[38],[39],[40],[41],[42],[43],[44],[45]],"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],[35],[36],[37],[38],[39],[40],[41],[42],[43],[44],[45]],"sk_fingerprint":"b477c3509325edc9","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[42,46],[18,49,50],[1,3,4,5,6,8,9,10,11,12,15,17,19,20,21,23,25,27,28,29,30,31,32,33,39,40,42,44,45,46,47,49,50,52],[0,2,3,5,9,13,15,17,20,24,25,27,29,32,34,37,38,46,48,49,51,55],[0,1,6,7,8,10,11,12,13,19,21,23,24,28,30,31,33,34,37,38,39,40,42,44,45,46,47,48,50,55],[0,1,2,4,7,9,11,12,15,16,17,18,19,21,23,24,25,27,28,29,30,35,36,37,38,40,45,46,51,54,55],[2,4,7,9,11,13,15,17,18,19,22,23,24,25,27,29,32,33,34,36,37,38,42,46,48,51,52,53,55],[6,11,17,18,22,24,27,29,31,32,33,34,35,36,37,38,44,46,48,50,53,54,55],[1,2,3,4,6,7,11,12,13,16,17,19,20,21,23,24,27,28,29,30,31,33,37,38,40,44,45,46,50,52,53,55],[19,49,50,51,52,53],[2,4,6,7,8,9,10,13,15,16,17,18,22,25,27,29,33,34,35,36,39,42,44,46,48,49,51],[1,2,6,7,14,16,17,18,20,21,23,24,25,27,28,29,30,37,38,40,42,43,45,49,51,55],[44,49,50,51,54],[0,2,7,9,11,12,14,15,18,19,20,31,33,44,45,47,49,50,51],[0,1,6,8,10,11,12,13,19,21,23,24,28,30,31,33,34,37,38,39,40,42,44,46,48,49,50,51,52,54,55],[0,1,2,4,6,7,9,11,12,15,16,17,18,19,21,22,23,24,25,27,28,29,30,35,36,37,38,40,45,46,47,51,54,55],[9,49,53,54],[2,4,5,6,11,12,13,15,17,20,23,24,27,29,31,32,33,34,36,37,38,43,45,46,48,49,51,52,53,54,55],[0,1,2,4,6,7,9,11,12,16,19,21,23,25,28,30,31,32,33,34,40,44,45,46,47,48,49,50,54],[1,2,3,4,6,9,12,13,14,16,17,19,21,24,25,27,28,29,30,31,35,36,37,38,40,42,43,51,52,53,55],[2,4,7,8,9,10,15,16,24,25,32,37,38,39,42,46,51,53,55],[6,14,17,18,22,24,27,29,31,32,33,34,35,36,37,38,44,46,47,48,50,53,54,55],[25,49,51,52,53,54],[1,3,5,8,9,10,11,15,18,19,20,21,22,23,24,25,28,30,34,35,36,37,38,39,40,42,45,46,48,49,50,55],[0,3,7,10,11,12,13,14,15,17,18,19,24,31,33,34,37,39,40,42,43,44,45,48,50,51,53,55],[2,4,6,7,9,11,16,23,25,26,28,29,30,31,33,34,35,36,39,42,43,44,45,46,47,48,49,51,52,53,54],[0,3,7,13,15,16,24,29,32,34,39,40,42,43,45,46,47,49,53,55],[1,2,3,4,5,7,11,12,13,16,18,19,20,21,22,23,28,30,32,34,35,36,40,41,45,46,52,54],[1,2,3,4,5,7,8,9,10,12,13,16,18,19,20,21,22,25,26,28,29,32,33,35,40,41,43,46,51,53,54,55],[0,1,2,4,6,7,8,9,14,15,16,18,21,23,24,25,27,28,30,32,38,39,45,46,49,51,52],[0,2,3,4,5,7,8,10,16,17,20,24,27,29,34,39,42,46,47,52,53],[0,1,2,3,5,6,7,10,14,15,16,19,21,27,29,32,34,36,39,40,41,42,43,48,49,51,52,53],[0,1,2,4,6,7,9,11,12,15,16,19,21,23,25,28,30,31,32,33,34,38,40,44,45,46,49,50,55],[6,17,18,22,24,27,29,30,31,32,33,34,35,36,37,38,44,46,50,53,54,55],[1,2,3,4,5,6,7,11,12,13,16,17,19,20,21,23,24,27,28,29,30,31,32,33,37,38,40,44,45,46,48,49,50,51],[3,4,5,8,11,12,13,14,15,16,18,22,23,26,27,28,29,31,41,42,43,44,45,46,47,52,53,55],[10,46,47,48],[1,3,5,6,8,9,10,11,12,15,16,17,19,20,21,23,25,27,28,29,30,31,32,33,39,40,42,44,45,46,48,50,51,52],[1,3,5,6,8,10,11,15,17,18,23,24,25,26,28,30,34,35,36,38,41,43,45,48,49,50,53,54,55],[0,3,5,9,13,15,17,20,24,25,27,29,32,34,37,38,39,46,47,49,51,54],[2,4,5,7,11,12,13,15,16,18,19,21,23,24,25,27,29,30,31,32,33,34,36,37,40,41,45,46,48,50,51,52,53,54,55],[2,3,4,7,8,9,10,12,15,16,19,21,25,26,28,32,33,34,37,38,40,43,44,46,49,51,52,55],[0,2,3,4,5,7,8,10,16,17,20,27,29,39,42,46,52,53],[2,7,8,15,16,19,21,23,25,26,28,29,30,31,32,33,34,36,37,41,43,44,45,47,48,54,55],[0,1,2,4,6,7,9,11,12,15,16,19,21,23,25,27,28,30,31,32,33,34,40,44,45,46,47,50,51,53],[0,1,8,10,11,12,13,17,18,19,22,23,27,28,29,30,32,35,36,39,40,42,45,46,48,49,50,51,55],[2,4,7,8,9,10,13,15,16,17,24,25,32,37,38,39,42,46,48,51,53,55],[0,1,6,7,8,10,11,12,13,19,23,26,28,29,31,32,35,36,37,38,39,40,43,46,47,48,49,50,51,52,53],[1,2,3,4,5,6,7,11,12,13,16,17,19,20,21,23,24,27,28,30,31,33,37,38,40,44,45,46,47,48,49,50,51,54],[0,1,2,6,8,9,11,12,17,18,22,24,27,29,30,32,35,36,37,40,41,44,45,46,48,50,51,52,54],[2,4,6,7,8,9,10,13,15,16,17,22,25,27,29,31,33,34,35,36,39,42,44,46,47,48,49,51,54],[4,49,51],[1,2,3,4,5,7,11,12,13,16,18,19,20,21,22,23,28,30,32,33,34,35,36,40,45,46,48,52,54],[2,49,52],[0,2,3,4,5,6,7,8,10,16,18,20,22,24,31,32,33,35,37,38,39,42,44,46,47,50,52,54,55],[0,2,3,4,5,7,8,10,16,17,27,29,34,39,42,46,47,48,52,53],[0,2,3,4,5,6,7,11,17,19,20,23,24,27,29,31,32,34,35,37,38,42,44,48,50,54,55],[1,2,4,6,7,9,11,12,15,16,19,21,23,25,28,30,31,32,33,34,40,44,45,46,48,50,51,53],[0,1,8,10,11,12,13,17,18,19,21,22,27,28,29,30,32,35,36,39,40,42,45,46,47,53,54],[2,3,4,7,8,9,10,13,15,16,24,25,32,37,38,39,42,46,47,51,53,55],[1,3,5,8,9,10,11,12,15,18,20,21,22,23,24,25,28,30,34,35,36,37,38,39,40,42,45,46,47,48,49,50,54,55],[43,46,47],[31,49,50,54],[2,3,5,7,8,9,10,11,12,14,15,16,18,19,24,31,32,33,37,38,39,43,44,46,49,50,52,55],[1,2,3,4,5,7,11,12,13,16,18,19,20,21,22,23,28,30,32,34,35,36,40,44,45,46,47,48,49,50,51,52],[2,3,5,7,11,12,13,14,17,18,19,24,25,27,29,31,32,33,34,37,38,44,45,46,48,49,50,52,55],[0,2,3,4,5,6,7,8,10,16,18,20,22,24,31,32,33,36,37,38,39,42,44,46,50,52,54,55],[45,49,51,52,54],[0,2,3,4,5,7,8,9,10,16,17,20,27,29,34,39,42,46,48,49,52,54],[0,2,3,4,9,11,12,17,18,22,23,24,25,27,29,32,34,35,37,38,43,44,45,47,48,49,50,55],[15,49,51,53,54],[0,2,3,4,6,8,9,10,11,14,16,18,22,23,24,25,31,32,37,38,39,43,45,46,51,52,54,55],[1,2,3,4,5,6,7,11,12,13,16,17,19,20,21,23,24,25,27,28,29,30,31,33,37,38,40,44,45,46,47,49,50,51,54,55],[12,49,50,51,52,53,54],[0,3,7,10,11,12,13,14,15,17,18,19,24,31,33,34,37,39,40,42,43,44,45,46,50,51,53,55],[8,10,11,13,15,17,18,22,23,26,27,28,30,43,45,48,49,50,52,53],[0,1,5,6,7,8,9,10,11,12,13,16,17,19,20,21,23,24,25,27,28,30,31,33,34,43,44,48,49,50,51,52,53,55],[0,3,5,9,13,15,17,20,24,25,27,29,32,34,37,38,40,46,51,52,55],[0,1,6,9,12,13,19,21,24,25,26,28,29,31,36,37,38,39,40,41,42,43,44,47,48,50,51,52,53],[2,4,7,9,10,11,12,13,14,15,16,18,19,25,27,31,32,33,34,37,40,42,44,47,49,50,51,52,55],[0,1,2,4,7,9,11,12,15,16,17,18,19,21,22,23,24,25,27,29,30,35,36,37,38,40,45,46,48,51,54,55],[1,2,7,9,10,13,14,16,18,19,20,21,22,25,27,29,31,32,33,34,35,39,40,41,42,43,44,46,49,50,54],[38,49,51,53,55],[0,1,8,10,11,12,13,17,18,19,21,22,23,26,27,28,29,30,32,35,36,39,40,42,45,46,47,48,53,54],[2,4,7,8,9,10,13,15,16,24,25,32,38,39,42,46,47,48,51,53,55],[32,49,51,52,53,55],[1,4,9,10,13,14,16,19,20,21,24,25,26,27,29,30,31,34,35,36,37,38,39,40,41,43,44,51,54],[1,2,4,6,7,8,9,10,13,15,16,17,18,22,25,27,29,31,33,34,35,36,39,42,44,46,50,51,54],[2,4,6,7,8,10,12,13,15,16,17,19,20,21,22,24,25,26,32,38,40,41,43,46,47,48,49,50,52,53,55],[39,49,52,54,55],[0,3,6,8,10,11,12,13,15,19,20,21,22,23,25,27,29,30,34,35,38,39,40,41,42,44,45,51,53],[0,1,6,10,11,12,13,19,21,23,24,28,30,31,33,34,37,38,39,40,42,44,45,46,50,55],[0,1,3,8,10,11,17,18,22,23,24,26,27,29,30,32,33,34,35,36,43,44,45,47,48,49,52,54],[0,2,3,5,6,7,8,9,13,16,18,19,20,21,22,23,26,28,29,30,32,34,35,37,41,43,45,46,50,51,52,53,55],[21,49,50,51,53,54,55],[0,1,7,8,10,11,12,13,17,18,19,22,23,24,26,27,28,33,34,39,40,43,44,48,49,51,52,54,55],[29,49,51,52,53,54,55],[0,2,3,5,6,10,15,17,19,20,21,23,25,27,28,29,32,34,38,39,41,42,44,48,50,53,55],[42,46,49],[1,3,4,5,6,8,9,10,11,12,15,17,19,20,21,23,25,27,28,29,30,31,32,33,39,40,42,44,45,46,47,50,51,52],[33,49,50,51],[0,2,3,5,9,13,15,17,20,24,25,27,29,32,34,37,38,46,48,51,52,55],[36,49,50,52],[0,1,6,7,8,10,11,12,13,19,21,23,24,28,30,31,33,34,37,38,39,40,42,44,45,46,47,48,49,50,51,52,55],[0,1,2,4,7,9,11,12,15,16,17,18,19,21,23,24,25,27,28,29,30,35,36,37,38,40,45,46,49,50,52,54,55],[20,49,53],[2,4,7,9,11,13,15,17,18,19,22,23,24,25,27,29,32,33,34,36,37,38,42,46,48,49,50,51,52,55],[0,49,51,53],[23,49,50,51,53],[3,49,52,53],[6,11,17,18,22,24,27,29,31,32,33,34,35,36,37,38,44,46,48,49,52,54,55],[1,2,3,4,6,7,11,12,13,16,17,19,20,21,23,24,27,28,29,30,31,33,37,38,40,44,45,46,49,50,51,55],[43,49,54],[2,4,6,7,8,9,10,13,15,16,17,18,22,25,27,29,33,34,35,36,39,42,44,46,48,50,51,54],[1,2,6,7,14,16,17,18,20,21,23,24,25,27,28,29,30,37,38,40,42,43,45,54,55],[0,2,7,9,11,12,14,15,18,19,20,31,33,44,45,47,50,51,52,54],[35,49,50,52,54],[0,1,6,8,10,11,12,13,19,21,23,24,28,30,31,33,34,37,38,39,40,42,44,46,48,50,55],[0,1,2,4,6,7,9,11,12,15,16,17,18,19,21,22,23,24,25,27,28,29,30,35,36,37,38,40,45,46,47,49,50,52,55],[2,4,5,6,11,12,13,15,17,20,23,24,27,29,31,32,33,34,36,37,38,43,45,46,48,50,51,52,55],[0,1,2,4,6,7,9,11,12,16,19,21,23,25,28,30,31,32,33,34,40,44,45,46,47,48,50,51,53],[1,2,3,4,6,9,12,13,14,16,17,19,21,24,25,27,28,29,30,31,35,36,37,38,40,42,43,49,50,52,54,55],[2,4,7,8,9,10,15,16,24,25,32,37,38,39,42,46,49,51,52,54,55],[6,14,17,18,22,24,27,29,31,32,33,34,35,36,37,38,44,46,47,48,49,52,55],[1,3,5,8,9,10,11,15,18,19,20,21,22,23,24,25,28,30,34,35,36,37,38,39,40,42,45,46,48,51,52,53,54,55],[0,3,7,10,11,12,13,14,15,17,18,19,24,31,33,34,37,39,40,42,43,44,45,48,49,50,51,53],[2,4,6,7,9,11,16,23,25,26,28,29,30,31,33,34,35,36,39,42,43,44,45,46,47,48,50,51,52,53,54,55],[0,3,7,13,15,16,24,29,32,34,39,40,42,43,45,46,47,51,53],[1,2,3,4,5,7,11,12,13,16,18,19,20,21,22,23,28,30,32,34,35,36,40,41,45,46,49,50,51,52,54,55],[40,49,52,55],[1,2,3,4,5,7,8,9,10,12,13,16,18,19,20,21,22,25,26,28,29,32,33,35,40,41,43,46,49,50,51,52,53,54],[0,1,2,4,6,7,8,9,14,15,16,18,21,23,24,25,27,28,30,32,38,39,45,46,55],[28,49,50,51,52,55],[0,2,3,4,5,7,8,10,16,17,20,24,27,29,34,39,42,46,47,49,52,55],[0,1,2,3,5,6,7,10,14,15,16,19,21,27,29,32,34,36,39,40,41,42,43,48,50,51,52,55],[0,1,2,4,6,7,9,11,12,15,16,19,21,23,25,28,30,31,32,33,34,38,40,44,45,46,50,51,53],[26,49,50,51,53,55],[37,49,52,53,55],[6,17,18,22,24,27,29,30,31,32,33,34,35,36,37,38,44,46,49,52,54],[1,2,3,4,5,6,7,11,12,13,16,17,19,20,21,23,24,27,28,29,30,31,32,33,37,38,40,44,45,46,48,50,52,53,55],[3,4,5,8,11,12,13,14,15,16,18,22,23,26,27,28,29,31,41,42,43,44,45,46,47,49,50,51],[10,46,47,48,49,54,55],[1,49,50,54,55],[1,3,5,6,8,9,10,11,12,15,16,17,19,20,21,23,25,27,28,29,30,31,32,33,39,40,42,44,45,46,48,49,50,52,54,55],[1,3,5,6,8,10,11,15,17,18,23,24,25,26,28,30,34,35,36,38,41,43,45,48,51,53],[0,3,5,9,13,15,17,20,24,25,27,29,32,34,37,38,39,46,47,51,52,55],[2,4,5,7,11,12,13,15,16,18,19,21,23,24,25,27,29,30,31,32,33,34,36,37,40,41,45,46,48,49,51,53],[8,49,51,52,54,55],[2,3,4,7,8,9,10,12,15,16,19,21,25,26,28,32,33,34,37,38,40,43,44,46,50,54],[0,2,3,4,5,7,8,10,16,17,20,27,29,39,42,46,49,52,54,55],[2,7,8,15,16,19,21,23,25,26,28,29,30,31,32,33,34,36,37,41,43,44,45,47,48,49,50,53],[0,1,2,4,6,7,9,11,12,15,16,19,21,23,25,27,28,30,31,32,33,34,40,44,45,46,47,49,50,54,55],[0,1,8,10,11,12,13,17,18,19,22,23,27,28,29,30,32,35,36,39,40,42,45,46,48,53,54],[2,4,7,8,9,10,13,15,16,17,24,25,32,37,38,39,42,46,48,49,51,52,54],[0,1,6,7,8,10,11,12,13,19,23,26,28,29,31,32,35,36,37,38,39,40,43,46,47,48,51,54,55],[1,2,3,4,5,6,7,11,12,13,16,17,19,20,21,23,24,27,28,30,31,33,37,38,40,44,45,46,47,48,50,52,53,55],[0,1,2,6,8,9,11,12,17,18,22,24,27,29,30,32,35,36,37,40,41,44,45,46,48,49,53,55],[42,49],[2,4,6,7,8,9,10,13,15,16,17,22,25,27,29,31,33,34,35,36,39,42,44,46,47,48,50,51,54],[1,2,3,4,5,7,11,12,13,16,18,19,20,21,22,23,28,30,32,33,34,35,36,40,45,46,48,49,50,51,52,54],[0,2,3,4,5,6,7,8,10,16,18,20,22,24,31,32,33,35,37,38,39,42,44,46,47,49,54,55],[7,49,51,52],[22,49,50,51,52],[0,2,3,4,5,7,8,10,16,17,27,29,34,39,42,46,47,48,49,52],[0,2,3,4,5,6,7,11,17,19,20,23,24,27,29,31,32,34,35,37,38,42,44,48,49,53,54,55],[1,2,4,6,7,9,11,12,15,16,19,21,23,25,28,30,31,32,33,34,40,44,45,46,48,49,50],[0,1,8,10,11,12,13,17,18,19,21,22,27,28,29,30,32,35,36,39,40,42,45,46,47,49,50,51,54],[2,3,4,7,8,9,10,13,15,16,24,25,32,37,38,39,42,46,47,49,51,52,55],[11,49,50,52,53],[5,49,51,52,53],[1,3,5,8,9,10,11,12,15,18,20,21,22,23,24,25,28,30,34,35,36,37,38,39,40,42,45,46,47,48,51,52,53,54,55],[43,46,47,49,54],[2,3,5,7,8,9,10,11,12,14,15,16,18,19,24,31,32,33,37,38,39,43,44,46,50,51,52,54,55],[1,2,3,4,5,7,11,12,13,16,18,19,20,21,22,23,28,30,32,34,35,36,40,44,45,46,47,48,52,54],[2,3,5,7,11,12,13,14,17,18,19,24,25,27,29,31,32,33,34,37,38,44,45,46,48,50,54,55],[0,2,3,4,5,6,7,8,10,16,18,20,22,24,31,32,33,36,37,38,39,42,44,46,49,55],[6,49,50,51,52,54],[0,2,3,4,5,7,8,9,10,16,17,20,27,29,34,39,42,46,48,52,53],[0,2,3,4,9,11,12,17,18,22,23,24,25,27,29,32,34,35,37,38,43,44,45,47,48,53,54,55],[0,2,3,4,6,8,9,10,11,14,16,18,22,23,24,25,31,32,37,38,39,43,45,46,49,50,52,53,55],[13,49,52,53,54],[14,49,50,52,53,54],[1,2,3,4,5,6,7,11,12,13,16,17,19,20,21,23,24,25,27,28,29,30,31,33,37,38,40,44,45,46,47,50,52,53,55],[0,3,7,10,11,12,13,14,15,17,18,19,24,31,33,34,37,39,40,42,43,44,45,46,49,50,51,53],[8,10,11,13,15,17,18,22,23,26,27,28,30,43,45,48,52,53,55],[0,1,5,6,7,8,9,10,11,12,13,16,17,19,20,21,23,24,25,27,28,30,31,33,34,43,44,48,50,52,53],[41,49,50,51,55],[0,3,5,9,13,15,17,20,24,25,27,29,32,34,37,38,40,46,49,51],[0,1,6,9,12,13,19,21,24,25,26,28,29,31,36,37,38,39,40,41,42,43,44,47,48,49,51,53,55],[2,4,7,9,10,11,12,13,14,15,16,18,19,25,27,31,32,33,34,37,40,42,44,47,50],[0,1,2,4,7,9,11,12,15,16,17,18,19,21,22,23,24,25,27,29,30,35,36,37,38,40,45,46,48,49,50,52,54],[24,49,53,55],[1,2,7,9,10,13,14,16,18,19,20,21,22,25,27,29,31,32,33,34,35,39,40,41,42,43,44,46,53,54,55],[0,1,8,10,11,12,13,17,18,19,21,22,23,26,27,28,29,30,32,35,36,39,40,42,45,46,47,48,49,50,51,54,55],[2,4,7,8,9,10,13,15,16,24,25,32,38,39,42,46,47,48,49,51,52],[30,49,50,52,53,55],[1,4,9,10,13,14,16,19,20,21,24,25,26,27,29,30,31,34,35,36,37,38,39,40,41,43,44,49,50,52,53,54,55],[10,49,54,55],[1,2,4,6,7,8,9,10,13,15,16,17,18,22,25,27,29,31,33,34,35,36,39,42,44,46,49,51,55],[16,49,51,54,55],[2,4,6,7,8,10,12,13,15,16,17,19,20,21,22,24,25,26,32,38,40,41,43,46,47,48,51,52,53,54],[0,3,6,8,10,11,12,13,15,19,20,21,22,23,25,27,29,30,34,35,38,39,40,41,42,44,45,49,50,51,52,53,54,55],[0,1,6,10,11,12,13,19,21,23,24,28,30,31,33,34,37,38,39,40,42,44,45,46,49,50,51,52,54],[0,1,3,8,10,11,17,18,22,23,24,26,27,29,30,32,33,34,35,36,43,44,45,47,48,50,51,55],[34,49,53,54,55],[0,2,3,5,6,7,8,9,13,16,18,19,20,21,22,23,26,28,29,30,32,34,35,37,41,43,45,46,49,51,52,54],[27,49,51,53,54,55],[17,49,52,53,54,55],[0,1,7,8,10,11,12,13,17,18,19,22,23,24,26,27,28,33,34,39,40,43,44,48,50,51,53],[0,2,3,5,6,10,15,17,19,20,21,23,25,27,28,29,32,34,38,39,41,42,44,48,49,51,52,54]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,11,198],"A_d":1382,"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],[35,1],[36,1],[37,1],[38,1],[39,1],[40,1],[41,1],[42,1],[43,1],[44,1],[45,1]],"CZ":[]},"rotation_powers":[[0,7],[1,7],[2,7],[3,7],[4,7],[5,7],[6,7],[7,7],[8,7],[9,7],[10,7],[11,7],[12,7],[13,7],[14,7],[15,7],[16,7],[17,7],[18,7],[19,7],[20,7],[21,7],[22,7],[23,7],[24,7],[25,7],[26,7],[27,7],[28,7],[29,7],[30,7],[31,7],[32,7],[33,7],[34,7],[35,7],[36,7],[37,7],[38,7],[39,7],[40,7],[41,7],[42,7],[43,7],[44,7],[45,7],[46,7],[47,7],[48,7],[49,7],[50,7],[51,7],[52,7],[53,7],[54,7],[55,7],[56,7],[57,7],[58,7],[59,7],[60,7],[61,7],[62,7],[63,7],[64,7],[65,7],[66,7],[67,7],[68,7],[69,7],[70,7],[71,7],[72,7],[73,7],[74,7],[75,7],[76,7],[77,7],[78,7],[79,7],[80,7],[81,7],[82,7],[83,7],[84,7],[85,7],[86,7],[87,7],[88,7],[89,7],[90,7],[91,7],[92,7],[93,7],[94,7],[95,7],[96,7],[97,7],[98,7],[99,7],[100,7],[101,7],[102,7],[103,7],[104,7],[105,7],[106,7],[107,7],[108,7],[109,7],[110,7],[111,7],[112,7],[113,7],[114,7],[115,7],[116,7],[117,7],[118,7],[119,7],[120,7],[121,7],[122,7],[123,7],[124,7],[125,7],[126,7],[127,7],[128,7],[129,7],[130,7],[131,7],[132,7],[133,7],[134,7],[135,7],[136,7],[137,7],[138,7],[139,7],[140,7],[141,7],[142,7],[143,7],[144,7],[145,7],[146,7],[147,7],[148,7],[149,7],[150,7],[151,7],[152,7],[153,7],[154,7],[155,7],[156,7],[157,7],[158,7],[159,7],[160,7],[161,7],[162,7],[163,7],[164,7],[165,7],[166,7],[167,7],[168,7],[169,7],[170,7],[171,7],[172,7],[173,7],[174,7],[175,7],[176,7],[177,7],[178,7],[179,7],[180,7],[181,7],[182,7],[183,7],[184,7],[185,7],[186,7],[187,7],[188,7],[189,7],[190,7],[191,7],[192,7],[193,7],[194,7],[195,7],[196,7],[197,7],[198,7],[199,7],[200,7],[201,7],[202,7],[203,7],[204,7],[205,7],[206,7],[207,7],[208,7],[209,7]]},"metrics":{"gamma":1.3821674396790782,"gamma_t":null,"gamma_rho":1.3821674396790782,"gamma_claim":1.3821674396790782,"gamma_t_claim":null,"gamma_rho_claim":1.3821674396790782,"v_ex":46,"rate":0.21904761904761905,"t_count":null,"poly_degree":null,"effective_width":46},"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/graph_210_46_3.json","label":"graph_210_46_3","N":56,"d":3,"d_is_exact":true,"origin":"Wills weighted Reed\u2013Muller parent (weights 1^6,2^2, cutoff 3), with searched graph punctures","provenance":"gamma frontier release record graph_210_46_3 (source catalogue id graph_210_46_3); construction: Wills weighted Reed\u2013Muller parent (weights 1^6,2^2, cutoff 3), with searched graph punctures; matrix 2665678fd5b2a0b3...; the release states d=3 (exact), gamma=1.3821674396790782 (exact)","notes":"matrix gamma_frontier_release/matrices/2665678fd5b2a0b3e8c7fe99629a92c479bc19c577f1645c745c5129e75e5461.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"}]}