{"id":"212.42.3.a","row":859,"stored":{"file":"master_catalog.json","row":859,"construction":null,"columns_sha256":null},"parameters":{"n":212,"k":42,"d":3,"N":55,"r":13,"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","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","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]],"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]],"sk_fingerprint":"3bd19ba8e24305b2","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[15,29,33,44,47,52,53,54],[15,27,29,43,44,47,48,50,52,53,54],[8,15,29,47,48,51,52,53,54],[0,1,3,5,12,14,15,16,19,20,21,25,26,29,32,35,37,39,41,42,43,44,45,49,51,53,54],[0,48,49,50,51],[37,48,52],[0,4,6,7,8,9,12,13,14,15,16,19,21,22,26,27,28,29,30,31,35,38,39,40,41,42,44,49,51,54],[1,4,7,9,11,14,15,19,22,25,26,27,28,30,31,32,34,35,36,38,39,40,41,46,52,54],[0,1,3,4,5,6,7,8,11,12,13,15,16,17,21,22,24,25,27,29,31,36,38,39,41,42,43,44,47,49],[2,4,5,8,9,10,12,15,16,17,19,22,26,31,34,45,46,47,51,53],[0,2,4,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,35,38,39,40,41,42,49,51,54],[1,5,10,14,19,20,21,24,25,33,35,38,40,42,44,47,51,52,53],[0,4,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,35,38,39,41,42,43,49,51,54],[0,3,4,5,6,7,11,12,13,14,17,18,21,22,25,27,28,30,31,34,37,38,39,40,41,44,45,46,47,49,53],[12,15,29,42,44,46,47,48,49,52,54],[14,48,49,50,53],[15,22,29,46,47,48,51,52,54],[15,29,31,42,46,47,48,49,51,52,54],[0,1,4,6,8,9,11,12,13,14,16,17,18,20,21,26,28,32,33,34,35,38,40,43,44,46,48,50,51,52,53],[15,29,30,42,43,46,47,52,53,54],[3,4,5,8,9,10,11,15,18,19,25,26,29,33,35,47,51,52,53],[26,48,49,52,53],[0,1,2,5,6,7,10,11,14,15,16,19,21,22,25,26,28,32,35,36,38,39,41,42,44,45,46,48,49,51],[1,2,3,4,8,9,11,13,14,16,19,21,22,24,25,26,27,30,36,38,39,40,41,44,49,51,52,54],[0,4,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,30,31,35,38,39,40,41,46,48,49,52,53,54],[5,48,49,51,52,53],[0,1,3,8,9,11,12,13,14,16,18,19,20,21,24,26,28,30,35,37,39,40,41,42,43,44,46,48,54],[0,4,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,35,38,39,40,41,42,43,46,49,51,54],[4,15,29,44,52,53,54],[0,1,4,5,6,7,8,9,12,13,14,15,16,20,21,23,24,26,27,28,30,32,33,35,37,39,40,42,46,48,49,52,53,54],[23,48,49,50,54],[15,48,51,54],[15,25,29,42,48,49,51,52,53],[13,15,29,43,52,53,54],[0,6,15,24,28,29,30,40,41,42,43,45,46,47,48,49,50,51,52,54],[34,48,52,54],[0,4,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,35,38,40,41,42,44,47,48,51,52],[0,2,3,4,8,9,10,11,13,15,19,21,23,25,26,27,29,30,33,36,37,38,39,44,49,52],[2,5,6,7,11,14,17,23,26,28,35,36,39,40,41,44,45,46,51,53,54],[0,4,6,10,12,13,15,16,17,19,26,29,30,32,34,38,40,42,43,46,47,49,50,51,52,53],[0,4,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,29,30,31,35,38,39,40,41,42,43,47,48,50,52],[16,48,53,54],[0,3,4,6,7,8,9,13,14,16,21,22,27,28,30,31,38,40,41,45,47,49,51],[0,1,3,6,11,12,13,15,16,17,18,19,20,24,25,26,28,30,32,34,35,36,40,43,44,46,47,50,51,52,53,54],[0,3,5,8,11,12,13,15,16,17,18,21,23,25,27,30,31,33,34,36,37,38,39,44,49,51,53,54],[0,4,8,12,13,15,16,19,21,22,23,25,27,29,30,36,38,42,44,47,48,51,52,53,54],[15,29,38,43,46,48,50,51,52],[0,4,6,7,8,9,10,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,35,38,39,40,41,44,46,47,48,49,51,52,53],[0,4,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,38,39,40,41,42,44,46,47,48,51,52,53],[0,2,3,6,7,8,10,11,14,15,16,17,18,19,20,21,23,25,27,29,30,31,33,36,37,39,40,44,48,53],[0,1,2,5,6,9,12,15,17,19,23,26,29,30,31,36,40,42,43,45,47,51,52,53],[0,4,6,7,8,9,12,13,14,15,16,17,18,19,21,22,26,27,28,29,30,31,35,38,39,40,41,46,47,49,51,54],[32,48,50,51,52,53,54],[0,4,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,35,38,39,40,42,43,46,47,48,50,52,53],[15,19,29,42,44,47,52,53,54],[27,48,50],[7,15,29,42,43,44,47,52,53,54],[8,48,51],[9,15,29,42,47,52,53,54],[0,1,3,5,12,14,16,19,20,21,25,26,32,35,37,39,41,42,44,45,47,49,51,52],[0,15,29,42,43,47,48,49,50,51,52,53,54],[0,4,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,35,37,38,39,40,41,44,48,49,51,52,54],[0,1,6,8,11,12,13,16,17,21,25,29,32,34,36,43,44,46,49,51,52],[1,3,5,9,11,14,19,24,25,26,28,30,35,36,40,47,51,54],[0,2,5,6,7,10,13,14,21,27,28,29,30,34,35,38,39,40,41,45,46,47,49,53,54],[0,1,4,5,6,7,8,9,10,12,13,15,16,17,20,22,24,25,26,27,28,29,30,31,33,39,41,42,43,44,47,49,52,53,54],[0,3,4,5,6,7,11,12,13,14,15,17,18,21,22,25,27,28,29,30,31,34,37,38,39,40,41,45,49,52,54],[12,48,49,53],[15,21,29,43,44,46,47,52,53,54],[14,15,29,42,43,44,46,47,48,49,50,52,54],[22,48,51,53],[31,48,49,51,53],[0,1,4,6,8,9,11,12,13,14,15,16,17,18,20,21,26,28,29,32,33,34,35,38,40,44,47,48,50,51,54],[0,3,5,6,7,10,11,12,13,14,16,17,18,21,22,25,27,28,30,31,33,38,39,40,41,44,46,47,49,52,53,54],[0,4,6,7,8,9,12,13,14,15,16,17,19,21,22,27,28,29,30,31,35,38,39,40,41,42,44,46,48,51,52,53,54],[1,2,4,5,8,9,10,11,12,13,17,25,27,29,30,31,32,36,40,42,43,45,48,54],[0,1,2,3,6,7,11,12,15,17,24,25,28,29,31,35,36,42,43,46,52],[0,4,5,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,35,38,39,40,41,42,46,48,52,53,54],[1,3,4,6,7,11,15,17,18,20,22,24,27,29,31,37,38,42,44,48,49,51],[3,15,29,42,44,52,53,54],[0,1,4,5,6,7,8,9,12,13,14,16,20,21,23,24,26,27,28,29,30,32,33,35,37,39,40,42,43,44,46,48,49],[15,23,29,42,43,44,48,49,50,52,53],[25,48,49,51,54],[0,6,24,28,30,40,41,45,46,47,48,49,50,51,53],[0,4,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,34,35,38,39,40,41,44,47,48,49,51,52],[39,48,49,52,54],[0,4,6,7,8,9,12,13,14,15,16,17,19,20,21,22,26,27,28,29,30,31,35,38,39,40,41,43,44,47,49,51,54],[0,1,4,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,35,38,39,40,41,42,43,44,47,49,51,54],[2,3,6,7,10,11,12,14,16,17,22,23,25,28,31,33,35,36,37,40,41,44,47,51,52,54],[0,2,4,5,8,9,11,12,13,15,16,19,21,22,23,27,29,30,31,36,38,42,44,45,46,47,49,53],[7,8,9,10,14,21,22,27,28,31,32,34,35,39,41,42,46,50,52,53,54],[28,48,49,50,51,52,54],[15,16,29,44,46,48,52],[0,3,4,6,7,8,9,13,14,15,16,21,22,27,28,29,30,31,38,40,41,42,44,45,46,47,49,51,52,53,54],[0,1,3,6,11,12,13,16,17,18,19,20,24,25,26,28,29,30,32,34,35,36,40,47,50,51],[15,29,36,42,43,44,46,52,53,54],[0,3,5,8,11,12,13,16,17,18,21,23,25,27,29,30,31,33,34,36,37,38,39,44,46,49,51,52],[0,4,8,12,13,16,19,21,22,23,25,27,30,36,38,44,46,47,48,51],[38,48,50,51,53,54],[15,24,29,42,43,46,52,53,54],[10,48,52,53,54],[35,48,49,52,53,54],[2,3,4,9,10,11,12,13,18,20,22,23,25,26,28,33,35,36,37,38,41,43,46,47,48,49,51,53,54],[1,2,4,5,7,8,13,14,16,21,22,23,27,28,35,36,38,39,41,44,45,46,49,52,53,54],[0,4,6,7,8,9,11,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,35,38,39,40,41,42,46,47,49,51,54],[0,4,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,32,35,38,39,40,41,43,46,47,48,49,50,52,53],[41,48,49,50,51,52,53,54],[15,29,33,44,47,48,52,53,54],[19,48,49],[15,27,29,43,44,47,52,53,54],[7,48,49,50],[8,15,29,47,52,53,54],[9,48,49,51],[0,1,3,5,12,14,15,16,19,20,21,25,26,29,32,35,37,39,41,42,43,44,45,48,49,50,53,54],[0,4,6,7,8,9,12,13,14,15,16,19,21,22,26,27,28,29,30,31,35,38,39,40,41,42,44,48,51,52,54],[1,4,7,9,11,14,15,19,22,25,26,27,28,30,31,32,34,35,36,38,39,40,41,46,48,50,54],[0,1,3,4,5,6,7,8,11,12,13,15,16,17,21,22,24,25,27,29,31,36,38,39,41,42,43,44,47,48,50,52],[2,4,5,8,9,10,12,15,16,17,19,22,26,31,34,45,46,47,48,52,53],[0,2,4,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,35,38,39,40,41,42,48,52,54],[1,5,10,14,19,20,21,24,25,33,35,38,40,42,44,47,48,50,53],[0,4,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,35,38,39,41,42,43,48,50,52,54],[0,3,4,5,6,7,11,12,13,14,17,18,21,22,25,27,28,30,31,34,37,38,39,40,41,44,45,46,47,48,49],[12,15,29,42,44,46,47,52,53,54],[21,48,50,53],[15,22,29,46,47,52,53,54],[15,29,31,42,46,47,52,53,54],[0,1,4,6,8,9,11,12,13,14,16,17,18,20,21,26,28,32,33,34,35,38,40,43,44,46,52],[15,29,30,42,43,46,47,48,49,50,51,52,54],[3,4,5,8,9,10,11,15,18,19,25,26,29,33,35,47,48,51],[0,1,2,5,6,7,10,11,14,15,16,19,21,22,25,26,28,32,35,36,38,39,41,42,44,45,46,49,50,51,52,53],[1,2,3,4,8,9,11,13,14,16,19,21,22,24,25,26,27,30,36,38,39,40,41,44,48,50,51,53,54],[0,4,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,30,31,35,38,39,40,41,46,49,51,54],[0,1,3,8,9,11,12,13,14,16,18,19,20,21,24,26,28,30,35,37,39,40,41,42,43,44,46,50,51,52,53,54],[0,4,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,35,38,39,40,41,42,43,46,48,50,52,53,54],[4,15,29,44,48,52,53],[3,48,49,54],[0,1,4,5,6,7,8,9,12,13,14,15,16,20,21,23,24,26,27,28,30,32,33,35,37,39,40,42,46,49,50,52,53],[15,25,29,42,52,53,54],[13,15,29,43,48,50,51,52,53],[0,6,15,24,28,29,30,40,41,42,43,45,46,47,52],[0,4,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,35,38,40,41,42,44,47,49,51,54],[20,48,50,52,54],[1,48,49,50,52,54],[0,2,3,4,8,9,10,11,13,15,19,21,23,25,26,27,29,30,33,36,37,38,39,44,48,49,51,54],[2,5,6,7,11,14,17,23,26,28,35,36,39,40,41,44,45,46,48,49,52,53],[0,4,6,10,12,13,15,16,17,19,26,29,30,32,34,38,40,42,43,46,47,48,49,53,54],[0,4,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,29,30,31,35,38,39,40,41,42,43,47,49,51,54],[0,3,4,6,7,8,9,13,14,16,21,22,27,28,30,31,38,40,41,45,47,48,51,53,54],[0,1,3,6,11,12,13,15,16,17,18,19,20,24,25,26,28,30,32,34,35,36,40,43,44,46,47,48,51,52],[36,48,49,50,53,54],[0,3,5,8,11,12,13,15,16,17,18,21,23,25,27,30,31,33,34,36,37,38,39,44,48,49],[0,4,8,12,13,15,16,19,21,22,23,25,27,29,30,36,38,42,44,47,49,52],[15,29,38,43,46,52,53,54],[24,48,49,50,51,53,54],[0,4,6,7,8,9,10,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,35,38,39,40,41,44,46,47,49,51,54],[0,4,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,38,39,40,41,42,44,46,47,49,51,54],[0,2,3,6,7,8,10,11,14,15,16,17,18,19,20,21,23,25,27,29,30,31,33,36,37,39,40,44,50,52,54],[0,1,2,5,6,9,12,15,17,19,23,26,29,30,31,36,40,42,43,45,47,48,49,50,51,54],[0,4,6,7,8,9,12,13,14,15,16,17,18,19,21,22,26,27,28,29,30,31,35,38,39,40,41,46,47,48,49,52,53],[11,48,49,51,52,53,54],[0,4,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,35,38,39,40,42,43,46,47,49,51,54],[33,48],[15,19,29,42,44,47,48,49,52,53,54],[7,15,29,42,43,44,47,48,49,50,52,53,54],[9,15,29,42,47,48,49,51,52,53,54],[0,1,3,5,12,14,16,19,20,21,25,26,32,35,37,39,41,42,44,45,47,48,49,50,52],[0,15,29,42,43,47,52,53,54],[0,4,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,35,37,38,39,40,41,44,49,51,54],[17,48,49,52],[0,1,6,8,11,12,13,16,17,21,25,29,32,34,36,43,44,46,48,49,50,51],[1,3,5,9,11,14,19,24,25,26,28,30,35,36,40,47,48,49,50,51,52,54],[0,2,5,6,7,10,13,14,21,27,28,29,30,34,35,38,39,40,41,45,46,47,48,49,51,52,53,54],[2,48,49,51,52],[0,1,4,5,6,7,8,9,10,12,13,15,16,17,20,22,24,25,26,27,28,29,30,31,33,39,41,42,43,44,47,48,49,50,51,53,54],[40,48,49,50,51,52],[0,3,4,5,6,7,11,12,13,14,15,17,18,21,22,25,27,28,29,30,31,34,37,38,39,40,41,45,48,49,52,53,54],[15,21,29,43,44,46,47,48,50,52,54],[14,15,29,42,43,44,46,47,52,53,54],[0,1,4,6,8,9,11,12,13,14,15,16,17,18,20,21,26,28,29,32,33,34,35,38,40,44,47,53,54],[30,48,49,50,51,53],[0,3,5,6,7,10,11,12,13,14,16,17,18,21,22,25,27,28,30,31,33,38,39,40,41,44,46,47,48,49,54],[0,4,6,7,8,9,12,13,14,15,16,17,19,21,22,27,28,29,30,31,35,38,39,40,41,42,44,46,49,51,54],[1,2,4,5,8,9,10,11,12,13,17,25,27,29,30,31,32,36,40,42,43,45,50,52,53,54],[0,1,2,3,6,7,11,12,15,17,24,25,28,29,31,35,36,42,43,46,48,49,50,53],[0,4,5,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,35,38,39,40,41,42,46,49,51,54],[1,3,4,6,7,11,15,17,18,20,22,24,27,29,31,37,38,42,44,49,50,52,53],[6,48,49,50,51,52,53],[4,48,54],[3,15,29,42,44,48,49,52,53],[0,1,4,5,6,7,8,9,12,13,14,16,20,21,23,24,26,27,28,29,30,32,33,35,37,39,40,42,43,44,46,49,50,54],[15,23,29,42,43,44,52,53,54],[29,52,53,54],[13,48,50,51,54],[0,6,24,28,30,40,41,45,46,47,53,54],[0,4,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,34,35,38,39,40,41,44,47,49,51,54],[0,4,6,7,8,9,12,13,14,15,16,17,19,20,21,22,26,27,28,29,30,31,35,38,39,40,41,43,44,47,48,49,50,51,52],[0,1,4,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,35,38,39,40,41,42,43,44,47,48,50,51,52],[2,3,6,7,10,11,12,14,16,17,22,23,25,28,31,33,35,36,37,40,41,44,47,48],[0,2,4,5,8,9,11,12,13,15,16,19,21,22,23,27,29,30,31,36,38,42,44,45,46,47,48,51,52,53,54],[7,8,9,10,14,21,22,27,28,31,32,34,35,39,41,42,46,48,51,53],[15,16,29,44,46,52,53,54],[0,3,4,6,7,8,9,13,14,15,16,21,22,27,28,29,30,31,38,40,41,42,44,45,46,47,48,51,52],[0,1,3,6,11,12,13,16,17,18,19,20,24,25,26,28,29,30,32,34,35,36,40,47,48,51,53,54],[15,29,36,42,43,44,46,48,49,50,52],[0,3,5,8,11,12,13,16,17,18,21,23,25,27,29,30,31,33,34,36,37,38,39,44,46,48,49,52,53,54],[0,4,8,12,13,16,19,21,22,23,25,27,30,36,38,44,46,47,49,53,54],[15,24,29,42,43,46,48,49,50,51,52],[2,3,4,9,10,11,12,13,18,20,22,23,25,26,28,33,35,36,37,38,41,43,46,47,49,50,51,52],[1,2,4,5,7,8,13,14,16,21,22,23,27,28,35,36,38,39,41,44,45,46,48,50],[18,48,51,52,53,54],[0,4,6,7,8,9,11,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,35,38,39,40,41,42,46,47,48,52,53],[0,4,6,7,8,9,12,13,14,15,16,17,19,21,22,26,27,28,29,30,31,32,35,38,39,40,41,43,46,47,49,51,54]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,69,183],"A_d":283,"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],[29,2],[30,1],[31,1],[32,1],[33,1],[34,1],[35,1],[36,1],[37,1],[38,1],[39,1],[40,1],[41,1],[48,1],[51,1],[52,1],[53,1]],"CZ":[[29,48],[29,51],[29,52],[29,53],[48,51],[48,52],[48,53],[51,52],[51,53],[52,53]]},"rotation_powers":[[0,3],[1,7],[2,3],[3,3],[5,3],[6,3],[7,7],[8,3],[9,7],[10,7],[11,3],[13,3],[14,5],[15,7],[16,3],[17,7],[18,3],[19,3],[20,7],[21,5],[23,5],[24,3],[25,3],[28,3],[30,7],[31,3],[32,3],[34,5],[35,3],[37,3],[39,7],[42,7],[43,5],[56,3],[57,7],[62,3],[65,3],[66,3],[67,3],[69,3],[70,3],[76,3],[77,3],[80,3],[81,3],[86,3],[90,3],[91,3],[94,3],[95,3],[97,3],[98,3],[99,3],[100,3],[103,3],[104,3],[106,3],[108,7],[110,3],[111,3],[113,3],[114,5],[115,3],[118,3],[121,5],[124,3],[126,3],[128,3],[130,3],[132,3],[135,3],[136,3],[139,3],[140,3],[141,3],[147,3],[148,3],[149,3],[151,3],[155,3],[157,3],[158,3],[159,3],[163,3],[164,3],[166,3],[169,3],[170,3],[171,3],[172,3],[174,3],[176,3],[177,3],[181,3],[184,3],[185,3],[186,3],[190,3],[191,3],[192,3],[193,3],[195,3],[196,3],[197,3],[200,3],[203,3],[210,3],[211,3]]},"metrics":{"gamma":1.4736014452845048,"gamma_t":null,"gamma_rho":1.4736014452845048,"gamma_claim":1.4736014452845048,"gamma_t_claim":null,"gamma_rho_claim":1.4736014452845048,"v_ex":42,"rate":0.19811320754716982,"t_count":null,"poly_degree":null,"effective_width":42},"provenance":{"regimes":["AI search (gamma frontier): contraction of an existing code"],"discovery":"AI search","strongest_claim":"a paired-column contraction of an existing triorthogonal code, 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): contraction of an existing code","file":"gamma_frontier_release/protocols/paired_column_contraction_212_42_3_bfc4e9658e57.json","label":"paired_column_contraction_212_42_3_bfc4e9658e57","N":55,"d":3,"d_is_exact":true,"origin":"Existing triorthogonal code with physical paired-column contraction","provenance":"gamma frontier release record paired_column_contraction_212_42_3_bfc4e9658e57 (source catalogue id paired_column_contraction_212_42_3_bfc4e9658e57); construction: Existing triorthogonal code with physical paired-column contraction; matrix bfc4e9658e57fbeb...; the release states d=3 (exact), gamma=1.4736014452845048 (exact)","notes":"matrix gamma_frontier_release/matrices/bfc4e9658e57fbebf179934b93649c5874abf30cd3357b177bfac8b2c3b609f6.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"}]}