{"id":"427.85.3.a","row":1046,"stored":{"file":"master_catalog.json","row":1046,"construction":null,"columns_sha256":null},"parameters":{"n":427,"k":85,"d":3,"N":115,"r":30,"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+46+47+48+49+50+51+52+53+54+55+56+57+58+59+60+61+62+63+64+65+66+67+68+69+70+71+72+73+74+75+76+77+78+79+80+81+82+83+84","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\u00b7T46\u00b7T47\u00b7T48\u00b7T49\u00b7T50\u00b7T51\u00b7T52\u00b7T53\u00b7T54\u00b7T55\u00b7T56\u00b7T57\u00b7T58\u00b7T59\u00b7T60\u00b7T61\u00b7T62\u00b7T63\u00b7T64\u00b7T65\u00b7T66\u00b7T67\u00b7T68\u00b7T69\u00b7T70\u00b7T71\u00b7T72\u00b7T73\u00b7T74\u00b7T75\u00b7T76\u00b7T77\u00b7T78\u00b7T79\u00b7T80\u00b7T81\u00b7T82\u00b7T83\u00b7T84","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],[46],[47],[48],[49],[50],[51],[52],[53],[54],[55],[56],[57],[58],[59],[60],[61],[62],[63],[64],[65],[66],[67],[68],[69],[70],[71],[72],[73],[74],[75],[76],[77],[78],[79],[80],[81],[82],[83],[84]],"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],[46],[47],[48],[49],[50],[51],[52],[53],[54],[55],[56],[57],[58],[59],[60],[61],[62],[63],[64],[65],[66],[67],[68],[69],[70],[71],[72],[73],[74],[75],[76],[77],[78],[79],[80],[81],[82],[83],[84]],"sk_fingerprint":"6d09b803779ffe5e","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,110],[0,1,2,3,4,5,6,7,15,16,17,18,19,20,21,109],[0,1,2,3,4,5,6,7,22,23,24,25,26,27,28,109,110],[0,1,2,3,8,9,10,11,29,30,31,32,37,38,39,86],[0,1,2,3,8,9,10,11,33,34,35,36,40,41,42,86,110],[0,1,4,5,15,16,19,20,29,30,33,34,43,44,47,90],[0,1,4,5,15,16,19,20,31,32,35,36,45,46,48,90,109],[0,2,8,10,15,17,22,24,29,31,37,39,43,45,49,93],[0,2,8,10,16,18,23,25,29,31,37,39,44,46,50,86,93],[0,4,8,12,15,19,22,26,29,33,37,40,43,47,49,94],[0,4,9,13,15,19,23,27,29,33,38,41,43,47,50,90,94],[0,6,8,14,15,21,22,28,29,35,37,42,43,48,49,93,94],[0,6,9,12,13,14,16,17,18,21,22,24,25,26,27,28,30,31,32,33,34,36,38,40,41,42,44,45,46,48,50,86,90,93,94,109,110],[0,2,4,6,8,10,12,14,51,53,55,57,59,61,63,98],[0,2,4,6,8,10,12,14,52,54,56,58,60,62,64,98,110],[0,1,2,3,15,16,17,18,51,52,53,54,65,66,67,99],[0,1,2,3,15,16,17,18,55,56,57,58,68,69,70,99,109],[0,1,8,9,15,16,22,23,51,52,59,60,65,66,71,102],[0,1,10,11,15,16,24,25,51,52,61,62,65,66,72,99,102],[0,4,8,12,15,19,22,26,51,55,59,63,65,68,71,104],[0,5,8,13,15,20,22,27,51,56,59,64,65,69,71,102,104],[0,4,8,12,17,21,24,28,51,55,59,63,67,70,72,98,104],[0,5,9,10,11,13,17,19,20,21,22,23,25,26,27,28,52,53,54,55,57,58,60,61,62,64,67,68,69,70,72,98,99,102,104,109,110],[0,1,4,5,29,30,33,34,51,52,55,56,73,74,77,106],[0,2,4,6,29,31,33,35,51,53,55,57,73,75,77,107],[0,3,4,7,29,32,33,36,51,54,55,58,73,76,77,106,107],[0,1,8,9,29,30,37,38,51,52,59,60,73,74,78,108],[0,1,8,9,29,30,37,38,53,54,61,62,75,76,79,86,108],[0,1,12,13,29,30,40,41,51,52,63,64,73,74,80,106,108],[0,2,4,6,37,39,40,42,51,53,55,57,78,79,80,98,107],[0,3,5,7,12,13,31,32,33,34,35,36,37,39,41,42,52,53,56,58,59,60,61,62,63,64,75,76,78,79,80,86,98,106,107,108,110],[0,2,15,17,29,31,43,45,51,53,65,67,73,75,81,112],[0,2,15,17,30,32,44,46,51,53,65,67,74,76,82,99,112],[0,1,4,5,29,30,33,34,65,66,68,69,81,82,83,90,106],[0,2,19,21,29,31,47,48,51,53,68,70,73,75,83,107,112],[0,3,6,7,19,21,30,31,35,36,43,44,45,46,47,48,52,54,55,56,57,58,65,66,69,70,74,76,81,82,83,90,99,106,107,109,112],[0,1,8,9,43,44,49,50,51,52,59,60,81,82,84,102,108],[0,2,15,17,29,31,43,45,59,61,71,72,78,79,84,93,112],[0,3,10,11,16,18,22,23,24,25,30,32,43,46,49,50,53,54,59,62,71,72,73,74,75,76,78,79,81,82,84,86,93,99,102,108,112],[0,4,8,12,15,19,22,26,73,77,78,80,81,83,84,94,104],[0,5,9,12,16,20,23,27,37,38,40,41,43,44,49,50,55,56,63,64,65,66,68,69,73,77,78,80,82,83,84,90,94,102,104,106,108],[0,6,10,14,17,19,24,28,33,35,37,39,40,42,47,48,59,61,65,67,68,70,71,72,73,77,79,80,81,83,84,93,94,98,104,107,112],[0,7,11,14,18,20,25,26,27,28,34,36,38,39,41,42,45,46,47,48,49,50,57,58,60,62,63,64,66,67,69,70,71,72,74,75,76,77,79,80,82,83,84,86,90,93,94,98,99,102,104,106,107,108,109,110,112],[0,91],[1,91,96],[2,91,113],[3,91,96,113],[4,91,97],[5,91,96,97],[6,91,97,113],[7,91,96,97,113],[8,91,105],[9,91,96,105],[10,91,105,113],[11,91,96,105,113],[12,91,97,105],[13,91,96,97,105],[14,91,97,105,113],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,91,96,97,105,110,113],[15,91,103],[16,91,96,103],[17,91,103,113],[18,91,96,103,113],[19,91,97,103],[20,91,96,97,103],[21,91,97,103,113],[0,1,2,3,4,5,6,7,15,16,17,18,19,20,21,91,96,97,103,109,113],[22,91,103,105],[23,91,96,103,105],[24,91,103,105,113],[25,91,96,103,105,113],[26,91,97,103,105],[27,91,96,97,103,105],[28,91,97,103,105,113],[0,1,2,3,4,5,6,7,22,23,24,25,26,27,28,91,96,97,103,105,109,110,113],[29,85,91],[30,85,91,96],[31,85,91,113],[32,85,91,96,113],[33,85,91,97],[34,85,91,96,97],[35,85,91,97,113],[36,85,91,96,97,113],[37,85,91,105],[38,85,91,96,105],[39,85,91,105,113],[0,1,2,3,8,9,10,11,29,30,31,32,37,38,39,85,86,91,96,105,113],[40,85,91,97,105],[41,85,91,96,97,105],[42,85,91,97,105,113],[0,1,2,3,8,9,10,11,33,34,35,36,40,41,42,85,86,91,96,97,105,110,113],[43,85,91,103],[44,85,91,96,103],[45,85,91,103,113],[46,85,91,96,103,113],[47,85,91,97,103],[0,1,4,5,15,16,19,20,29,30,33,34,43,44,47,85,90,91,96,97,103],[48,85,91,97,103,113],[0,1,4,5,15,16,19,20,31,32,35,36,45,46,48,85,90,91,96,97,103,109,113],[49,85,91,103,105],[50,85,91,96,103,105],[0,2,8,10,15,17,22,24,29,31,37,39,43,45,49,85,91,93,103,105,113],[0,2,8,10,16,18,23,25,29,31,37,39,44,46,50,85,86,91,93,96,103,105,113],[0,4,8,12,15,19,22,26,29,33,37,40,43,47,49,85,91,94,97,103,105],[0,4,9,13,15,19,23,27,29,33,38,41,43,47,50,85,90,91,94,96,97,103,105],[0,6,8,14,15,21,22,28,29,35,37,42,43,48,49,85,91,93,94,97,103,105,113],[0,6,9,12,13,14,16,17,18,21,22,24,25,26,27,28,30,31,32,33,34,36,38,40,41,42,44,45,46,48,50,85,86,90,91,93,94,96,97,103,105,109,110,113],[51,91,111],[52,91,96,111],[53,91,111,113],[54,91,96,111,113],[55,91,97,111],[56,91,96,97,111],[57,91,97,111,113],[58,91,96,97,111,113],[59,91,105,111],[60,91,96,105,111],[61,91,105,111,113],[62,91,96,105,111,113],[63,91,97,105,111],[64,91,96,97,105,111],[0,2,4,6,8,10,12,14,51,53,55,57,59,61,63,91,97,98,105,111,113],[0,2,4,6,8,10,12,14,52,54,56,58,60,62,64,91,96,97,98,105,110,111,113],[65,91,103,111],[66,91,96,103,111],[67,91,103,111,113],[0,1,2,3,15,16,17,18,51,52,53,54,65,66,67,91,96,99,103,111,113],[68,91,97,103,111],[69,91,96,97,103,111],[70,91,97,103,111,113],[0,1,2,3,15,16,17,18,55,56,57,58,68,69,70,91,96,97,99,103,109,111,113],[71,91,103,105,111],[0,1,8,9,15,16,22,23,51,52,59,60,65,66,71,91,96,102,103,105,111],[72,91,103,105,111,113],[0,1,10,11,15,16,24,25,51,52,61,62,65,66,72,91,96,99,102,103,105,111,113],[0,4,8,12,15,19,22,26,51,55,59,63,65,68,71,91,97,103,104,105,111],[0,5,8,13,15,20,22,27,51,56,59,64,65,69,71,91,96,97,102,103,104,105,111],[0,4,8,12,17,21,24,28,51,55,59,63,67,70,72,91,97,98,103,104,105,111,113],[0,5,9,10,11,13,17,19,20,21,22,23,25,26,27,28,52,53,54,55,57,58,60,61,62,64,67,68,69,70,72,91,96,97,98,99,102,103,104,105,109,110,111,113],[73,85,91,111],[74,85,91,96,111],[75,85,91,111,113],[76,85,91,96,111,113],[77,85,91,97,111],[0,1,4,5,29,30,33,34,51,52,55,56,73,74,77,85,91,96,97,106,111],[0,2,4,6,29,31,33,35,51,53,55,57,73,75,77,85,91,97,107,111,113],[0,3,4,7,29,32,33,36,51,54,55,58,73,76,77,85,91,96,97,106,107,111,113],[78,85,91,105,111],[0,1,8,9,29,30,37,38,51,52,59,60,73,74,78,85,91,96,105,108,111],[79,85,91,105,111,113],[0,1,8,9,29,30,37,38,53,54,61,62,75,76,79,85,86,91,96,105,108,111,113],[80,85,91,97,105,111],[0,1,12,13,29,30,40,41,51,52,63,64,73,74,80,85,91,96,97,105,106,108,111],[0,2,4,6,37,39,40,42,51,53,55,57,78,79,80,85,91,97,98,105,107,111,113],[0,3,5,7,12,13,31,32,33,34,35,36,37,39,41,42,52,53,56,58,59,60,61,62,63,64,75,76,78,79,80,85,86,91,96,97,98,105,106,107,108,110,111,113],[81,85,91,103,111],[82,85,91,96,103,111],[0,2,15,17,29,31,43,45,51,53,65,67,73,75,81,85,91,103,111,112,113],[0,2,15,17,30,32,44,46,51,53,65,67,74,76,82,85,91,96,99,103,111,112,113],[83,85,91,97,103,111],[0,1,4,5,29,30,33,34,65,66,68,69,81,82,83,85,90,91,96,97,103,106,111],[0,2,19,21,29,31,47,48,51,53,68,70,73,75,83,85,91,97,103,107,111,112,113],[0,3,6,7,19,21,30,31,35,36,43,44,45,46,47,48,52,54,55,56,57,58,65,66,69,70,74,76,81,82,83,85,90,91,96,97,99,103,106,107,109,111,112,113],[84,85,91,103,105,111],[0,1,8,9,43,44,49,50,51,52,59,60,81,82,84,85,91,96,102,103,105,108,111],[0,2,15,17,29,31,43,45,59,61,71,72,78,79,84,85,91,93,103,105,111,112,113],[0,3,10,11,16,18,22,23,24,25,30,32,43,46,49,50,53,54,59,62,71,72,73,74,75,76,78,79,81,82,84,85,86,91,93,96,99,102,103,105,108,111,112,113],[0,4,8,12,15,19,22,26,73,77,78,80,81,83,84,85,91,94,97,103,104,105,111],[0,5,9,12,16,20,23,27,37,38,40,41,43,44,49,50,55,56,63,64,65,66,68,69,73,77,78,80,82,83,84,85,90,91,94,96,97,102,103,104,105,106,108,111],[0,6,10,14,17,19,24,28,33,35,37,39,40,42,47,48,59,61,65,67,68,70,71,72,73,77,79,80,81,83,84,85,91,93,94,97,98,103,104,105,107,111,112,113],[0,7,11,14,18,20,25,26,27,28,34,36,38,39,41,42,45,46,47,48,49,50,57,58,60,62,63,64,66,67,69,70,71,72,74,75,76,77,79,80,82,83,84,85,86,90,91,93,94,96,97,98,99,102,103,104,105,106,107,108,109,110,111,112,113],[0,101],[1,95,101],[2,101,114],[3,95,101,114],[4,92,101],[5,92,95,101],[6,92,101,114],[7,92,95,101,114],[8,87,101],[9,87,95,101],[10,87,101,114],[11,87,95,101,114],[12,87,92,101],[13,87,92,95,101],[14,87,92,101,114],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,87,92,95,101,110,114],[15,88,101],[16,88,95,101],[17,88,101,114],[18,88,95,101,114],[19,88,92,101],[20,88,92,95,101],[21,88,92,101,114],[0,1,2,3,4,5,6,7,15,16,17,18,19,20,21,88,92,95,101,109,114],[22,87,88,101],[23,87,88,95,101],[24,87,88,101,114],[25,87,88,95,101,114],[26,87,88,92,101],[27,87,88,92,95,101],[28,87,88,92,101,114],[0,1,2,3,4,5,6,7,22,23,24,25,26,27,28,87,88,92,95,101,109,110,114],[29,89,101],[30,89,95,101],[31,89,101,114],[32,89,95,101,114],[33,89,92,101],[34,89,92,95,101],[35,89,92,101,114],[36,89,92,95,101,114],[37,87,89,101],[38,87,89,95,101],[39,87,89,101,114],[0,1,2,3,8,9,10,11,29,30,31,32,37,38,39,86,87,89,95,101,114],[40,87,89,92,101],[41,87,89,92,95,101],[42,87,89,92,101,114],[0,1,2,3,8,9,10,11,33,34,35,36,40,41,42,86,87,89,92,95,101,110,114],[43,88,89,101],[44,88,89,95,101],[45,88,89,101,114],[46,88,89,95,101,114],[47,88,89,92,101],[0,1,4,5,15,16,19,20,29,30,33,34,43,44,47,88,89,90,92,95,101],[48,88,89,92,101,114],[0,1,4,5,15,16,19,20,31,32,35,36,45,46,48,88,89,90,92,95,101,109,114],[49,87,88,89,101],[50,87,88,89,95,101],[0,2,8,10,15,17,22,24,29,31,37,39,43,45,49,87,88,89,93,101,114],[0,2,8,10,16,18,23,25,29,31,37,39,44,46,50,86,87,88,89,93,95,101,114],[0,4,8,12,15,19,22,26,29,33,37,40,43,47,49,87,88,89,92,94,101],[0,4,9,13,15,19,23,27,29,33,38,41,43,47,50,87,88,89,90,92,94,95,101],[0,6,8,14,15,21,22,28,29,35,37,42,43,48,49,87,88,89,92,93,94,101,114],[0,6,9,12,13,14,16,17,18,21,22,24,25,26,27,28,30,31,32,33,34,36,38,40,41,42,44,45,46,48,50,86,87,88,89,90,92,93,94,95,101,109,110,114],[51,100,101],[52,95,100,101],[53,100,101,114],[54,95,100,101,114],[55,92,100,101],[56,92,95,100,101],[57,92,100,101,114],[58,92,95,100,101,114],[59,87,100,101],[60,87,95,100,101],[61,87,100,101,114],[62,87,95,100,101,114],[63,87,92,100,101],[64,87,92,95,100,101],[0,2,4,6,8,10,12,14,51,53,55,57,59,61,63,87,92,98,100,101,114],[0,2,4,6,8,10,12,14,52,54,56,58,60,62,64,87,92,95,98,100,101,110,114],[65,88,100,101],[66,88,95,100,101],[67,88,100,101,114],[0,1,2,3,15,16,17,18,51,52,53,54,65,66,67,88,95,99,100,101,114],[68,88,92,100,101],[69,88,92,95,100,101],[70,88,92,100,101,114],[0,1,2,3,15,16,17,18,55,56,57,58,68,69,70,88,92,95,99,100,101,109,114],[71,87,88,100,101],[0,1,8,9,15,16,22,23,51,52,59,60,65,66,71,87,88,95,100,101,102],[72,87,88,100,101,114],[0,1,10,11,15,16,24,25,51,52,61,62,65,66,72,87,88,95,99,100,101,102,114],[0,4,8,12,15,19,22,26,51,55,59,63,65,68,71,87,88,92,100,101,104],[0,5,8,13,15,20,22,27,51,56,59,64,65,69,71,87,88,92,95,100,101,102,104],[0,4,8,12,17,21,24,28,51,55,59,63,67,70,72,87,88,92,98,100,101,104,114],[0,5,9,10,11,13,17,19,20,21,22,23,25,26,27,28,52,53,54,55,57,58,60,61,62,64,67,68,69,70,72,87,88,92,95,98,99,100,101,102,104,109,110,114],[73,89,100,101],[74,89,95,100,101],[75,89,100,101,114],[76,89,95,100,101,114],[77,89,92,100,101],[0,1,4,5,29,30,33,34,51,52,55,56,73,74,77,89,92,95,100,101,106],[0,2,4,6,29,31,33,35,51,53,55,57,73,75,77,89,92,100,101,107,114],[0,3,4,7,29,32,33,36,51,54,55,58,73,76,77,89,92,95,100,101,106,107,114],[78,87,89,100,101],[0,1,8,9,29,30,37,38,51,52,59,60,73,74,78,87,89,95,100,101,108],[79,87,89,100,101,114],[0,1,8,9,29,30,37,38,53,54,61,62,75,76,79,86,87,89,95,100,101,108,114],[80,87,89,92,100,101],[0,1,12,13,29,30,40,41,51,52,63,64,73,74,80,87,89,92,95,100,101,106,108],[0,2,4,6,37,39,40,42,51,53,55,57,78,79,80,87,89,92,98,100,101,107,114],[0,3,5,7,12,13,31,32,33,34,35,36,37,39,41,42,52,53,56,58,59,60,61,62,63,64,75,76,78,79,80,86,87,89,92,95,98,100,101,106,107,108,110,114],[81,88,89,100,101],[82,88,89,95,100,101],[0,2,15,17,29,31,43,45,51,53,65,67,73,75,81,88,89,100,101,112,114],[0,2,15,17,30,32,44,46,51,53,65,67,74,76,82,88,89,95,99,100,101,112,114],[83,88,89,92,100,101],[0,1,4,5,29,30,33,34,65,66,68,69,81,82,83,88,89,90,92,95,100,101,106],[0,2,19,21,29,31,47,48,51,53,68,70,73,75,83,88,89,92,100,101,107,112,114],[0,3,6,7,19,21,30,31,35,36,43,44,45,46,47,48,52,54,55,56,57,58,65,66,69,70,74,76,81,82,83,88,89,90,92,95,99,100,101,106,107,109,112,114],[84,87,88,89,100,101],[0,1,8,9,43,44,49,50,51,52,59,60,81,82,84,87,88,89,95,100,101,102,108],[0,2,15,17,29,31,43,45,59,61,71,72,78,79,84,87,88,89,93,100,101,112,114],[0,3,10,11,16,18,22,23,24,25,30,32,43,46,49,50,53,54,59,62,71,72,73,74,75,76,78,79,81,82,84,86,87,88,89,93,95,99,100,101,102,108,112,114],[0,4,8,12,15,19,22,26,73,77,78,80,81,83,84,87,88,89,92,94,100,101,104],[0,5,9,12,16,20,23,27,37,38,40,41,43,44,49,50,55,56,63,64,65,66,68,69,73,77,78,80,82,83,84,87,88,89,90,92,94,95,100,101,102,104,106,108],[0,6,10,14,17,19,24,28,33,35,37,39,40,42,47,48,59,61,65,67,68,70,71,72,73,77,79,80,81,83,84,87,88,89,92,93,94,98,100,101,104,107,112,114],[0,7,11,14,18,20,25,26,27,28,34,36,38,39,41,42,45,46,47,48,49,50,57,58,60,62,63,64,66,67,69,70,71,72,74,75,76,77,79,80,82,83,84,86,87,88,89,90,92,93,94,95,98,99,100,101,102,104,106,107,108,109,110,112,114],[0,91,101],[1,91,95,96,101],[2,91,101,113,114],[3,91,95,96,101,113,114],[4,91,92,97,101],[5,91,92,95,96,97,101],[6,91,92,97,101,113,114],[7,91,92,95,96,97,101,113,114],[8,87,91,101,105],[9,87,91,95,96,101,105],[10,87,91,101,105,113,114],[11,87,91,95,96,101,105,113,114],[12,87,91,92,97,101,105],[13,87,91,92,95,96,97,101,105],[14,87,91,92,97,101,105,113,114],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,87,91,92,95,96,97,101,105,110,113,114],[15,88,91,101,103],[16,88,91,95,96,101,103],[17,88,91,101,103,113,114],[18,88,91,95,96,101,103,113,114],[19,88,91,92,97,101,103],[20,88,91,92,95,96,97,101,103],[21,88,91,92,97,101,103,113,114],[0,1,2,3,4,5,6,7,15,16,17,18,19,20,21,88,91,92,95,96,97,101,103,109,113,114],[22,87,88,91,101,103,105],[23,87,88,91,95,96,101,103,105],[24,87,88,91,101,103,105,113,114],[25,87,88,91,95,96,101,103,105,113,114],[26,87,88,91,92,97,101,103,105],[27,87,88,91,92,95,96,97,101,103,105],[28,87,88,91,92,97,101,103,105,113,114],[0,1,2,3,4,5,6,7,22,23,24,25,26,27,28,87,88,91,92,95,96,97,101,103,105,109,110,113,114],[29,85,89,91,101],[30,85,89,91,95,96,101],[31,85,89,91,101,113,114],[32,85,89,91,95,96,101,113,114],[33,85,89,91,92,97,101],[34,85,89,91,92,95,96,97,101],[35,85,89,91,92,97,101,113,114],[36,85,89,91,92,95,96,97,101,113,114],[37,85,87,89,91,101,105],[38,85,87,89,91,95,96,101,105],[39,85,87,89,91,101,105,113,114],[0,1,2,3,8,9,10,11,29,30,31,32,37,38,39,85,86,87,89,91,95,96,101,105,113,114],[40,85,87,89,91,92,97,101,105],[41,85,87,89,91,92,95,96,97,101,105],[42,85,87,89,91,92,97,101,105,113,114],[0,1,2,3,8,9,10,11,33,34,35,36,40,41,42,85,86,87,89,91,92,95,96,97,101,105,110,113,114],[43,85,88,89,91,101,103],[44,85,88,89,91,95,96,101,103],[45,85,88,89,91,101,103,113,114],[46,85,88,89,91,95,96,101,103,113,114],[47,85,88,89,91,92,97,101,103],[0,1,4,5,15,16,19,20,29,30,33,34,43,44,47,85,88,89,90,91,92,95,96,97,101,103],[48,85,88,89,91,92,97,101,103,113,114],[0,1,4,5,15,16,19,20,31,32,35,36,45,46,48,85,88,89,90,91,92,95,96,97,101,103,109,113,114],[49,85,87,88,89,91,101,103,105],[50,85,87,88,89,91,95,96,101,103,105],[0,2,8,10,15,17,22,24,29,31,37,39,43,45,49,85,87,88,89,91,93,101,103,105,113,114],[0,2,8,10,16,18,23,25,29,31,37,39,44,46,50,85,86,87,88,89,91,93,95,96,101,103,105,113,114],[0,4,8,12,15,19,22,26,29,33,37,40,43,47,49,85,87,88,89,91,92,94,97,101,103,105],[0,4,9,13,15,19,23,27,29,33,38,41,43,47,50,85,87,88,89,90,91,92,94,95,96,97,101,103,105],[0,6,8,14,15,21,22,28,29,35,37,42,43,48,49,85,87,88,89,91,92,93,94,97,101,103,105,113,114],[0,6,9,12,13,14,16,17,18,21,22,24,25,26,27,28,30,31,32,33,34,36,38,40,41,42,44,45,46,48,50,85,86,87,88,89,90,91,92,93,94,95,96,97,101,103,105,109,110,113,114],[51,91,100,101,111],[52,91,95,96,100,101,111],[53,91,100,101,111,113,114],[54,91,95,96,100,101,111,113,114],[55,91,92,97,100,101,111],[56,91,92,95,96,97,100,101,111],[57,91,92,97,100,101,111,113,114],[58,91,92,95,96,97,100,101,111,113,114],[59,87,91,100,101,105,111],[60,87,91,95,96,100,101,105,111],[61,87,91,100,101,105,111,113,114],[62,87,91,95,96,100,101,105,111,113,114],[63,87,91,92,97,100,101,105,111],[64,87,91,92,95,96,97,100,101,105,111],[0,2,4,6,8,10,12,14,51,53,55,57,59,61,63,87,91,92,97,98,100,101,105,111,113,114],[0,2,4,6,8,10,12,14,52,54,56,58,60,62,64,87,91,92,95,96,97,98,100,101,105,110,111,113,114],[65,88,91,100,101,103,111],[66,88,91,95,96,100,101,103,111],[67,88,91,100,101,103,111,113,114],[0,1,2,3,15,16,17,18,51,52,53,54,65,66,67,88,91,95,96,99,100,101,103,111,113,114],[68,88,91,92,97,100,101,103,111],[69,88,91,92,95,96,97,100,101,103,111],[70,88,91,92,97,100,101,103,111,113,114],[0,1,2,3,15,16,17,18,55,56,57,58,68,69,70,88,91,92,95,96,97,99,100,101,103,109,111,113,114],[71,87,88,91,100,101,103,105,111],[0,1,8,9,15,16,22,23,51,52,59,60,65,66,71,87,88,91,95,96,100,101,102,103,105,111],[72,87,88,91,100,101,103,105,111,113,114],[0,1,10,11,15,16,24,25,51,52,61,62,65,66,72,87,88,91,95,96,99,100,101,102,103,105,111,113,114],[0,4,8,12,15,19,22,26,51,55,59,63,65,68,71,87,88,91,92,97,100,101,103,104,105,111],[0,5,8,13,15,20,22,27,51,56,59,64,65,69,71,87,88,91,92,95,96,97,100,101,102,103,104,105,111],[0,4,8,12,17,21,24,28,51,55,59,63,67,70,72,87,88,91,92,97,98,100,101,103,104,105,111,113,114],[0,5,9,10,11,13,17,19,20,21,22,23,25,26,27,28,52,53,54,55,57,58,60,61,62,64,67,68,69,70,72,87,88,91,92,95,96,97,98,99,100,101,102,103,104,105,109,110,111,113,114],[73,85,89,91,100,101,111],[74,85,89,91,95,96,100,101,111],[75,85,89,91,100,101,111,113,114],[76,85,89,91,95,96,100,101,111,113,114],[77,85,89,91,92,97,100,101,111],[0,1,4,5,29,30,33,34,51,52,55,56,73,74,77,85,89,91,92,95,96,97,100,101,106,111],[0,2,4,6,29,31,33,35,51,53,55,57,73,75,77,85,89,91,92,97,100,101,107,111,113,114],[0,3,4,7,29,32,33,36,51,54,55,58,73,76,77,85,89,91,92,95,96,97,100,101,106,107,111,113,114],[78,85,87,89,91,100,101,105,111],[0,1,8,9,29,30,37,38,51,52,59,60,73,74,78,85,87,89,91,95,96,100,101,105,108,111],[79,85,87,89,91,100,101,105,111,113,114],[0,1,8,9,29,30,37,38,53,54,61,62,75,76,79,85,86,87,89,91,95,96,100,101,105,108,111,113,114],[80,85,87,89,91,92,97,100,101,105,111],[0,1,12,13,29,30,40,41,51,52,63,64,73,74,80,85,87,89,91,92,95,96,97,100,101,105,106,108,111],[0,2,4,6,37,39,40,42,51,53,55,57,78,79,80,85,87,89,91,92,97,98,100,101,105,107,111,113,114],[0,3,5,7,12,13,31,32,33,34,35,36,37,39,41,42,52,53,56,58,59,60,61,62,63,64,75,76,78,79,80,85,86,87,89,91,92,95,96,97,98,100,101,105,106,107,108,110,111,113,114],[81,85,88,89,91,100,101,103,111],[82,85,88,89,91,95,96,100,101,103,111],[0,2,15,17,29,31,43,45,51,53,65,67,73,75,81,85,88,89,91,100,101,103,111,112,113,114],[0,2,15,17,30,32,44,46,51,53,65,67,74,76,82,85,88,89,91,95,96,99,100,101,103,111,112,113,114],[83,85,88,89,91,92,97,100,101,103,111],[0,1,4,5,29,30,33,34,65,66,68,69,81,82,83,85,88,89,90,91,92,95,96,97,100,101,103,106,111],[0,2,19,21,29,31,47,48,51,53,68,70,73,75,83,85,88,89,91,92,97,100,101,103,107,111,112,113,114],[0,3,6,7,19,21,30,31,35,36,43,44,45,46,47,48,52,54,55,56,57,58,65,66,69,70,74,76,81,82,83,85,88,89,90,91,92,95,96,97,99,100,101,103,106,107,109,111,112,113,114],[84,85,87,88,89,91,100,101,103,105,111],[0,1,8,9,43,44,49,50,51,52,59,60,81,82,84,85,87,88,89,91,95,96,100,101,102,103,105,108,111],[0,2,15,17,29,31,43,45,59,61,71,72,78,79,84,85,87,88,89,91,93,100,101,103,105,111,112,113,114],[0,3,10,11,16,18,22,23,24,25,30,32,43,46,49,50,53,54,59,62,71,72,73,74,75,76,78,79,81,82,84,85,86,87,88,89,91,93,95,96,99,100,101,102,103,105,108,111,112,113,114],[0,4,8,12,15,19,22,26,73,77,78,80,81,83,84,85,87,88,89,91,92,94,97,100,101,103,104,105,111],[0,5,9,12,16,20,23,27,37,38,40,41,43,44,49,50,55,56,63,64,65,66,68,69,73,77,78,80,82,83,84,85,87,88,89,90,91,92,94,95,96,97,100,101,102,103,104,105,106,108,111],[0,6,10,14,17,19,24,28,33,35,37,39,40,42,47,48,59,61,65,67,68,70,71,72,73,77,79,80,81,83,84,85,87,88,89,91,92,93,94,97,98,100,101,103,104,105,107,111,112,113,114],[0,7,11,14,18,20,25,26,27,28,34,36,38,39,41,42,45,46,47,48,49,50,57,58,60,62,63,64,66,67,69,70,71,72,74,75,76,77,79,80,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,2],"A_d":106,"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],[46,1],[47,1],[48,1],[49,1],[50,1],[51,1],[52,1],[53,1],[54,1],[55,1],[56,1],[57,1],[58,1],[59,1],[60,1],[61,1],[62,1],[63,1],[64,1],[65,1],[66,1],[67,1],[68,1],[69,1],[70,1],[71,1],[72,1],[73,1],[74,1],[75,1],[76,1],[77,1],[78,1],[79,1],[80,1],[81,1],[82,1],[83,1],[84,1]],"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],[210,7],[211,7],[212,7],[213,7],[214,7],[215,7],[216,7],[217,7],[218,7],[219,7],[220,7],[221,7],[222,7],[223,7],[224,7],[225,7],[226,7],[227,7],[228,7],[229,7],[230,7],[231,7],[232,7],[233,7],[234,7],[235,7],[236,7],[237,7],[238,7],[239,7],[240,7],[241,7],[242,7],[243,7],[244,7],[245,7],[246,7],[247,7],[248,7],[249,7],[250,7],[251,7],[252,7],[253,7],[254,7],[255,7],[256,7],[257,7],[258,7],[259,7],[260,7],[261,7],[262,7],[263,7],[264,7],[265,7],[266,7],[267,7],[268,7],[269,7],[270,7],[271,7],[272,7],[273,7],[274,7],[275,7],[276,7],[277,7],[278,7],[279,7],[280,7],[281,7],[282,7],[283,7],[284,7],[285,7],[286,7],[287,7],[288,7],[289,7],[290,7],[291,7],[292,7],[293,7],[294,7],[295,7],[296,7],[297,7],[298,7],[299,7],[300,7],[301,7],[302,7],[303,7],[304,7],[305,7],[306,7],[307,7],[308,7],[309,7],[310,7],[311,7],[312,7],[313,7],[314,7],[315,7],[316,7],[317,7],[318,7],[319,7],[320,7],[321,7],[322,7],[323,7],[324,7],[325,7],[326,7],[327,7],[328,7],[329,7],[330,7],[331,7],[332,7],[333,7],[334,7],[335,7],[336,7],[337,7],[338,7],[339,7],[340,7],[341,7],[342,7],[343,7],[344,7],[345,7],[346,7],[347,7],[348,7],[349,7],[350,7],[351,7],[352,7],[353,7],[354,7],[355,7],[356,7],[357,7],[358,7],[359,7],[360,7],[361,7],[362,7],[363,7],[364,7],[365,7],[366,7],[367,7],[368,7],[369,7],[370,7],[371,7],[372,7],[373,7],[374,7],[375,7],[376,7],[377,7],[378,7],[379,7],[380,7],[381,7],[382,7],[383,7],[384,7],[385,7],[386,7],[387,7],[388,7],[389,7],[390,7],[391,7],[392,7],[393,7],[394,7],[395,7],[396,7],[397,7],[398,7],[399,7],[400,7],[401,7],[402,7],[403,7],[404,7],[405,7],[406,7],[407,7],[408,7],[409,7],[410,7],[411,7],[412,7],[413,7],[414,7],[415,7],[416,7],[417,7],[418,7],[419,7],[420,7],[421,7],[422,7],[423,7],[424,7],[425,7],[426,7]]},"metrics":{"gamma":1.4692469521665226,"gamma_t":null,"gamma_rho":1.4692469521665226,"gamma_claim":1.4692469521665226,"gamma_t_claim":null,"gamma_rho_claim":1.4692469521665226,"v_ex":85,"rate":0.1990632318501171,"t_count":null,"poly_degree":null,"effective_width":85},"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/weighted_sources_427_85_3.json","label":"weighted_sources_427_85_3","N":115,"d":3,"d_is_exact":true,"origin":"Triorthogonal; matrix verified","provenance":"gamma frontier release record weighted_sources_427_85_3 (source catalogue id weighted_sources_427_85_3); construction: Triorthogonal; matrix verified; matrix bd3e4ee56f69be20...; the release states d=3 (exact), gamma=1.4692469521665226 (exact)","notes":"matrix gamma_frontier_release/matrices/bd3e4ee56f69be209ff21cfee37e9b6503df34ddb50c9437a273920af91faed4.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"}]}