{"id":"256.16.4.a","row":926,"stored":{"file":"master_catalog.json","row":926,"construction":null,"columns_sha256":null},"parameters":{"n":256,"k":16,"d":4,"N":28,"r":12,"level":3},"gate":{"string":"0,1,2+0,1,4+0,1,9+0,1,10+0,1,12+0,1,14+0,2,4+0,2,8+0,2,10+0,2,11+0,2,12+0,2,13+0,2,14+0,2,15+0,4,8+0,4,9+0,4,11+0,4,13+0,4,15+0,8,9+0,8,10+0,8,12+0,8,14+0,9,10+0,9,11+0,9,12+0,9,13+0,9,14+0,9,15+0,10,11+0,10,13+0,10,15+0,11,12+0,11,14+0,12,13+0,12,15+0,13,14+0,14,15+1,2,3+1,2,4+1,2,7+1,2,10+1,2,11+1,2,12+1,2,13+1,2,14+1,2,15+1,3,10+1,3,12+1,4,6+1,4,8+1,4,10+1,4,11+1,4,13+1,4,15+1,6,7+1,6,8+1,6,10+1,6,12+1,6,13+1,6,14+1,6,15+1,7,9+1,7,12+1,7,13+1,7,15+1,8,10+1,8,13+1,8,14+1,8,15+1,9,11+1,9,13+1,9,15+1,10,11+1,10,12+1,10,13+1,10,14+1,10,15+1,11,12+1,11,14+1,13,14+1,14,15+2,3,6+2,3,9+2,3,11+2,3,13+2,3,14+2,4,5+2,4,7+2,4,10+2,4,11+2,4,12+2,4,13+2,4,15+2,5,6+2,5,7+2,5,8+2,5,9+2,5,10+2,5,11+2,5,14+2,6,7+2,6,8+2,6,9+2,6,11+2,6,12+2,6,13+2,7,8+2,7,9+2,7,11+2,7,13+2,7,14+2,7,15+2,8,10+2,8,11+2,8,12+2,8,13+2,8,14+2,8,15+2,9,10+2,9,14+2,9,15+2,10,13+2,10,14+2,11,13+2,13,15+2,14,15+3,4,5+3,4,7+3,4,8+3,4,9+3,4,11+3,4,13+3,5,6+3,5,10+3,5,11+3,5,15+3,6,7+3,6,8+3,6,10+3,6,12+3,7,8+3,7,10+3,7,13+3,7,14+3,7,15+3,8,11+3,8,14+3,9,11+3,10,14+3,11,12+3,11,15+3,12,13+3,13,14+3,13,15+3,14,15+4,5,8+4,5,9+4,5,10+4,5,11+4,5,12+4,5,13+4,5,14+4,6,8+4,6,12+4,6,13+4,6,15+4,7,9+4,7,12+4,7,13+4,8,9+4,8,10+4,8,11+4,8,14+4,8,15+4,9,10+4,9,13+4,10,11+4,10,12+4,11,13+4,12,13+4,12,14+4,12,15+4,13,14+4,14,15+5,6,11+5,6,14+5,6,15+5,7,8+5,7,10+5,7,11+5,7,14+5,8,9+5,8,10+5,8,11+5,9,10+5,9,11+5,9,14+5,9,15+5,10,11+5,10,15+5,11,12+5,11,13+5,11,15+5,12,13+5,12,14+5,12,15+5,13,14+5,14,15+6,7,8+6,7,9+6,7,10+6,7,12+6,7,15+6,8,9+6,8,12+6,9,11+6,9,13+6,9,14+6,10,12+6,10,13+6,10,14+6,10,15+6,11,12+6,11,13+6,11,15+6,13,14+6,13,15+7,8,9+7,8,10+7,8,11+7,8,12+7,8,13+7,8,14+7,8,15+7,9,11+7,9,12+7,9,13+7,10,11+7,10,13+7,10,14+7,11,12+7,11,13+7,13,14+8,9,12+8,9,13+8,9,14+8,9,15+8,10,11+8,10,12+8,10,13+8,10,14+8,11,13+8,12,15+8,13,15+8,14,15+9,10,11+9,10,14+9,10,15+9,11,12+9,11,13+9,11,15+9,12,13+9,12,14+9,12,15+9,13,14+10,11,12+10,11,13+10,11,14+10,12,15+10,13,15+11,12,14+11,13,15+11,14,15+12,13,14+12,13,15+12,14,15+13,14,15","human":"CCZ0,1,2\u00b7CCZ0,1,4\u00b7CCZ0,1,9\u00b7CCZ0,1,10\u00b7CCZ0,1,12\u00b7CCZ0,1,14\u00b7CCZ0,2,4\u00b7CCZ0,2,8\u00b7CCZ0,2,10\u00b7CCZ0,2,11\u00b7CCZ0,2,12\u00b7CCZ0,2,13\u00b7CCZ0,2,14\u00b7CCZ0,2,15\u00b7CCZ0,4,8\u00b7CCZ0,4,9\u00b7CCZ0,4,11\u00b7CCZ0,4,13\u00b7CCZ0,4,15\u00b7CCZ0,8,9\u00b7CCZ0,8,10\u00b7CCZ0,8,12\u00b7CCZ0,8,14\u00b7CCZ0,9,10\u00b7CCZ0,9,11\u00b7CCZ0,9,12\u00b7CCZ0,9,13\u00b7CCZ0,9,14\u00b7CCZ0,9,15\u00b7CCZ0,10,11\u00b7CCZ0,10,13\u00b7CCZ0,10,15\u00b7CCZ0,11,12\u00b7CCZ0,11,14\u00b7CCZ0,12,13\u00b7CCZ0,12,15\u00b7CCZ0,13,14\u00b7CCZ0,14,15\u00b7CCZ1,2,3\u00b7CCZ1,2,4\u00b7CCZ1,2,7\u00b7CCZ1,2,10\u00b7CCZ1,2,11\u00b7CCZ1,2,12\u00b7CCZ1,2,13\u00b7CCZ1,2,14\u00b7CCZ1,2,15\u00b7CCZ1,3,10\u00b7CCZ1,3,12\u00b7CCZ1,4,6\u00b7CCZ1,4,8\u00b7CCZ1,4,10\u00b7CCZ1,4,11\u00b7CCZ1,4,13\u00b7CCZ1,4,15\u00b7CCZ1,6,7\u00b7CCZ1,6,8\u00b7CCZ1,6,10\u00b7CCZ1,6,12\u00b7CCZ1,6,13\u00b7CCZ1,6,14\u00b7CCZ1,6,15\u00b7CCZ1,7,9\u00b7CCZ1,7,12\u00b7CCZ1,7,13\u00b7CCZ1,7,15\u00b7CCZ1,8,10\u00b7CCZ1,8,13\u00b7CCZ1,8,14\u00b7CCZ1,8,15\u00b7CCZ1,9,11\u00b7CCZ1,9,13\u00b7CCZ1,9,15\u00b7CCZ1,10,11\u00b7CCZ1,10,12\u00b7CCZ1,10,13\u00b7CCZ1,10,14\u00b7CCZ1,10,15\u00b7CCZ1,11,12\u00b7CCZ1,11,14\u00b7CCZ1,13,14\u00b7CCZ1,14,15\u00b7CCZ2,3,6\u00b7CCZ2,3,9\u00b7CCZ2,3,11\u00b7CCZ2,3,13\u00b7CCZ2,3,14\u00b7CCZ2,4,5\u00b7CCZ2,4,7\u00b7CCZ2,4,10\u00b7CCZ2,4,11\u00b7CCZ2,4,12\u00b7CCZ2,4,13\u00b7CCZ2,4,15\u00b7CCZ2,5,6\u00b7CCZ2,5,7\u00b7CCZ2,5,8\u00b7CCZ2,5,9\u00b7CCZ2,5,10\u00b7CCZ2,5,11\u00b7CCZ2,5,14\u00b7CCZ2,6,7\u00b7CCZ2,6,8\u00b7CCZ2,6,9\u00b7CCZ2,6,11\u00b7CCZ2,6,12\u00b7CCZ2,6,13\u00b7CCZ2,7,8\u00b7CCZ2,7,9\u00b7CCZ2,7,11\u00b7CCZ2,7,13\u00b7CCZ2,7,14\u00b7CCZ2,7,15\u00b7CCZ2,8,10\u00b7CCZ2,8,11\u00b7CCZ2,8,12\u00b7CCZ2,8,13\u00b7CCZ2,8,14\u00b7CCZ2,8,15\u00b7CCZ2,9,10\u00b7CCZ2,9,14\u00b7CCZ2,9,15\u00b7CCZ2,10,13\u00b7CCZ2,10,14\u00b7CCZ2,11,13\u00b7CCZ2,13,15\u00b7CCZ2,14,15\u00b7CCZ3,4,5\u00b7CCZ3,4,7\u00b7CCZ3,4,8\u00b7CCZ3,4,9\u00b7CCZ3,4,11\u00b7CCZ3,4,13\u00b7CCZ3,5,6\u00b7CCZ3,5,10\u00b7CCZ3,5,11\u00b7CCZ3,5,15\u00b7CCZ3,6,7\u00b7CCZ3,6,8\u00b7CCZ3,6,10\u00b7CCZ3,6,12\u00b7CCZ3,7,8\u00b7CCZ3,7,10\u00b7CCZ3,7,13\u00b7CCZ3,7,14\u00b7CCZ3,7,15\u00b7CCZ3,8,11\u00b7CCZ3,8,14\u00b7CCZ3,9,11\u00b7CCZ3,10,14\u00b7CCZ3,11,12\u00b7CCZ3,11,15\u00b7CCZ3,12,13\u00b7CCZ3,13,14\u00b7CCZ3,13,15\u00b7CCZ3,14,15\u00b7CCZ4,5,8\u00b7CCZ4,5,9\u00b7CCZ4,5,10\u00b7CCZ4,5,11\u00b7CCZ4,5,12\u00b7CCZ4,5,13\u00b7CCZ4,5,14\u00b7CCZ4,6,8\u00b7CCZ4,6,12\u00b7CCZ4,6,13\u00b7CCZ4,6,15\u00b7CCZ4,7,9\u00b7CCZ4,7,12\u00b7CCZ4,7,13\u00b7CCZ4,8,9\u00b7CCZ4,8,10\u00b7CCZ4,8,11\u00b7CCZ4,8,14\u00b7CCZ4,8,15\u00b7CCZ4,9,10\u00b7CCZ4,9,13\u00b7CCZ4,10,11\u00b7CCZ4,10,12\u00b7CCZ4,11,13\u00b7CCZ4,12,13\u00b7CCZ4,12,14\u00b7CCZ4,12,15\u00b7CCZ4,13,14\u00b7CCZ4,14,15\u00b7CCZ5,6,11\u00b7CCZ5,6,14\u00b7CCZ5,6,15\u00b7CCZ5,7,8\u00b7CCZ5,7,10\u00b7CCZ5,7,11\u00b7CCZ5,7,14\u00b7CCZ5,8,9\u00b7CCZ5,8,10\u00b7CCZ5,8,11\u00b7CCZ5,9,10\u00b7CCZ5,9,11\u00b7CCZ5,9,14\u00b7CCZ5,9,15\u00b7CCZ5,10,11\u00b7CCZ5,10,15\u00b7CCZ5,11,12\u00b7CCZ5,11,13\u00b7CCZ5,11,15\u00b7CCZ5,12,13\u00b7CCZ5,12,14\u00b7CCZ5,12,15\u00b7CCZ5,13,14\u00b7CCZ5,14,15\u00b7CCZ6,7,8\u00b7CCZ6,7,9\u00b7CCZ6,7,10\u00b7CCZ6,7,12\u00b7CCZ6,7,15\u00b7CCZ6,8,9\u00b7CCZ6,8,12\u00b7CCZ6,9,11\u00b7CCZ6,9,13\u00b7CCZ6,9,14\u00b7CCZ6,10,12\u00b7CCZ6,10,13\u00b7CCZ6,10,14\u00b7CCZ6,10,15\u00b7CCZ6,11,12\u00b7CCZ6,11,13\u00b7CCZ6,11,15\u00b7CCZ6,13,14\u00b7CCZ6,13,15\u00b7CCZ7,8,9\u00b7CCZ7,8,10\u00b7CCZ7,8,11\u00b7CCZ7,8,12\u00b7CCZ7,8,13\u00b7CCZ7,8,14\u00b7CCZ7,8,15\u00b7CCZ7,9,11\u00b7CCZ7,9,12\u00b7CCZ7,9,13\u00b7CCZ7,10,11\u00b7CCZ7,10,13\u00b7CCZ7,10,14\u00b7CCZ7,11,12\u00b7CCZ7,11,13\u00b7CCZ7,13,14\u00b7CCZ8,9,12\u00b7CCZ8,9,13\u00b7CCZ8,9,14\u00b7CCZ8,9,15\u00b7CCZ8,10,11\u00b7CCZ8,10,12\u00b7CCZ8,10,13\u00b7CCZ8,10,14\u00b7CCZ8,11,13\u00b7CCZ8,12,15\u00b7CCZ8,13,15\u00b7CCZ8,14,15\u00b7CCZ9,10,11\u00b7CCZ9,10,14\u00b7CCZ9,10,15\u00b7CCZ9,11,12\u00b7CCZ9,11,13\u00b7CCZ9,11,15\u00b7CCZ9,12,13\u00b7CCZ9,12,14\u00b7CCZ9,12,15\u00b7CCZ9,13,14\u00b7CCZ10,11,12\u00b7CCZ10,11,13\u00b7CCZ10,11,14\u00b7CCZ10,12,15\u00b7CCZ10,13,15\u00b7CCZ11,12,14\u00b7CCZ11,13,15\u00b7CCZ11,14,15\u00b7CCZ12,13,14\u00b7CCZ12,13,15\u00b7CCZ12,14,15\u00b7CCZ13,14,15","monomials":[[0,1,2],[0,1,4],[0,1,9],[0,1,10],[0,1,12],[0,1,14],[0,2,4],[0,2,8],[0,2,10],[0,2,11],[0,2,12],[0,2,13],[0,2,14],[0,2,15],[0,4,8],[0,4,9],[0,4,11],[0,4,13],[0,4,15],[0,8,9],[0,8,10],[0,8,12],[0,8,14],[0,9,10],[0,9,11],[0,9,12],[0,9,13],[0,9,14],[0,9,15],[0,10,11],[0,10,13],[0,10,15],[0,11,12],[0,11,14],[0,12,13],[0,12,15],[0,13,14],[0,14,15],[1,2,3],[1,2,4],[1,2,7],[1,2,10],[1,2,11],[1,2,12],[1,2,13],[1,2,14],[1,2,15],[1,3,10],[1,3,12],[1,4,6],[1,4,8],[1,4,10],[1,4,11],[1,4,13],[1,4,15],[1,6,7],[1,6,8],[1,6,10],[1,6,12],[1,6,13],[1,6,14],[1,6,15],[1,7,9],[1,7,12],[1,7,13],[1,7,15],[1,8,10],[1,8,13],[1,8,14],[1,8,15],[1,9,11],[1,9,13],[1,9,15],[1,10,11],[1,10,12],[1,10,13],[1,10,14],[1,10,15],[1,11,12],[1,11,14],[1,13,14],[1,14,15],[2,3,6],[2,3,9],[2,3,11],[2,3,13],[2,3,14],[2,4,5],[2,4,7],[2,4,10],[2,4,11],[2,4,12],[2,4,13],[2,4,15],[2,5,6],[2,5,7],[2,5,8],[2,5,9],[2,5,10],[2,5,11],[2,5,14],[2,6,7],[2,6,8],[2,6,9],[2,6,11],[2,6,12],[2,6,13],[2,7,8],[2,7,9],[2,7,11],[2,7,13],[2,7,14],[2,7,15],[2,8,10],[2,8,11],[2,8,12],[2,8,13],[2,8,14],[2,8,15],[2,9,10],[2,9,14],[2,9,15],[2,10,13],[2,10,14],[2,11,13],[2,13,15],[2,14,15],[3,4,5],[3,4,7],[3,4,8],[3,4,9],[3,4,11],[3,4,13],[3,5,6],[3,5,10],[3,5,11],[3,5,15],[3,6,7],[3,6,8],[3,6,10],[3,6,12],[3,7,8],[3,7,10],[3,7,13],[3,7,14],[3,7,15],[3,8,11],[3,8,14],[3,9,11],[3,10,14],[3,11,12],[3,11,15],[3,12,13],[3,13,14],[3,13,15],[3,14,15],[4,5,8],[4,5,9],[4,5,10],[4,5,11],[4,5,12],[4,5,13],[4,5,14],[4,6,8],[4,6,12],[4,6,13],[4,6,15],[4,7,9],[4,7,12],[4,7,13],[4,8,9],[4,8,10],[4,8,11],[4,8,14],[4,8,15],[4,9,10],[4,9,13],[4,10,11],[4,10,12],[4,11,13],[4,12,13],[4,12,14],[4,12,15],[4,13,14],[4,14,15],[5,6,11],[5,6,14],[5,6,15],[5,7,8],[5,7,10],[5,7,11],[5,7,14],[5,8,9],[5,8,10],[5,8,11],[5,9,10],[5,9,11],[5,9,14],[5,9,15],[5,10,11],[5,10,15],[5,11,12],[5,11,13],[5,11,15],[5,12,13],[5,12,14],[5,12,15],[5,13,14],[5,14,15],[6,7,8],[6,7,9],[6,7,10],[6,7,12],[6,7,15],[6,8,9],[6,8,12],[6,9,11],[6,9,13],[6,9,14],[6,10,12],[6,10,13],[6,10,14],[6,10,15],[6,11,12],[6,11,13],[6,11,15],[6,13,14],[6,13,15],[7,8,9],[7,8,10],[7,8,11],[7,8,12],[7,8,13],[7,8,14],[7,8,15],[7,9,11],[7,9,12],[7,9,13],[7,10,11],[7,10,13],[7,10,14],[7,11,12],[7,11,13],[7,13,14],[8,9,12],[8,9,13],[8,9,14],[8,9,15],[8,10,11],[8,10,12],[8,10,13],[8,10,14],[8,11,13],[8,12,15],[8,13,15],[8,14,15],[9,10,11],[9,10,14],[9,10,15],[9,11,12],[9,11,13],[9,11,15],[9,12,13],[9,12,14],[9,12,15],[9,13,14],[10,11,12],[10,11,13],[10,11,14],[10,12,15],[10,13,15],[11,12,14],[11,13,15],[11,14,15],[12,13,14],[12,13,15],[12,14,15],[13,14,15]],"sk_key":null,"sk_fingerprint":"ce1cddf45efbb8bb","sk_canonical_frame":false,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[1,2,5,6,7,8,10,11,15,16],[1,3,8,9,12,14,15,17],[1,2,6,8,9,11,12,13,14,15,18],[0,2,3,4,5,6,10,12,14,19],[0,1,3,4,6,7,12,14,20],[4,9,12,13,21],[0,1,3,4,5,6,9,10,13,14,16,18,20],[0,1,2,5,6,8,10,12,13,17,19,21],[0,1,4,10,11,13,15,22],[1,2,4,7,8,9,10,11,14,15,23],[2,5,6,8,9,11,13,14,15,17,19,22],[1,2,4,5,8,11,12,13,15,16,18,23],[4,7,8,10,11,12,13,15,16,18,19,20,23],[1,4,5,9,13,15,17,18,19,21,22],[0,1,2,5,6,7,9,11,12,13,15,16,17,18,20,23],[1,4,7,10,12,15,16,17,19,21,22],[1,2,3,4,5,6,8,10,11,13,15,24],[1,4,7,8,9,12,13,14,15,16,17,24],[1,2,3,5,9,10,12,14,15,16,19,20,21,24],[0,2,4,8,11,12,13,14,15,16,18,20,21,24],[2,4,7,8,13,15,17,18,19,20,24],[0,1,2,3,4,6,8,9,14,17,18,19,21,24],[2,6,7,9,11,12,15,16,17,18,21,24],[3,4,6,7,8,11,13,14,19,20,24],[0,1,3,4,5,6,8,15,16,18,19,20,21,22,24],[1,2,3,4,5,6,7,9,13,14,15,16,18,19,20,21,23,24],[2,3,4,5,6,7,8,9,11,13,14,16,17,19,22,24],[1,2,3,5,7,8,11,12,13,15,18,23,24],[0,1,2,3,5,8,14,16,17,18,19,21,23,24],[0,2,3,7,9,10,11,12,13,14,15,18,19,20,22,24],[3,5,7,8,9,11,16,19,20,23,24],[0,2,3,4,6,7,8,10,13,14,15,16,18,21,22,24],[0,3,4,7,9,11,12,13,14,25],[0,1,3,4,5,8,10,12,14,15,16,17,20,21,22,23,25],[0,1,2,4,5,6,8,10,11,12,13,14,16,18,20,21,22,23,25],[1,8,9,12,14,15,16,19,25],[1,3,4,8,9,11,12,14,16,18,19,20,22,23,25],[0,1,2,3,4,7,11,15,16,18,19,20,25],[2,4,5,6,7,10,11,13,15,19,21,25],[1,2,5,7,9,10,11,12,16,17,18,21,22,23,25],[0,1,3,6,8,9,10,12,13,17,20,21,22,25],[7,8,10,15,17,22,25],[1,4,5,6,8,13,15,19,23,25],[1,2,3,5,6,9,12,13,14,16,17,18,20,21,23,25],[1,2,4,5,6,9,12,16,17,21,22,25],[1,3,4,7,10,11,14,21,22,25],[0,1,2,3,6,10,11,15,16,19,20,23,25],[2,4,5,6,8,9,12,14,16,18,20,23,25],[1,2,4,6,7,8,9,11,12,13,15,17,18,19,24,25],[2,4,5,6,10,13,14,15,16,18,19,20,21,22,23,24,25],[3,6,7,8,11,14,16,17,18,22,23,24,25],[0,2,3,4,5,7,8,9,10,12,15,16,17,19,20,21,24,25],[1,7,8,9,11,18,19,20,22,23,24,25],[0,1,2,11,14,18,19,20,24,25],[2,3,4,7,8,12,15,16,18,20,24,25],[1,2,3,6,7,8,9,15,17,19,20,22,23,24,25],[2,4,5,6,7,8,9,11,12,14,15,22,24,25],[0,1,2,3,4,5,8,10,11,12,13,15,20,21,22,24,25],[0,2,3,4,5,10,11,15,17,18,23,24,25],[0,5,8,9,11,13,15,16,19,20,21,23,24,25],[1,2,3,4,8,9,12,15,17,18,19,20,22,24,25],[1,4,5,6,7,8,10,11,12,13,15,16,18,19,20,22,24,25],[0,1,2,4,6,7,11,14,19,20,23,24,25],[2,3,5,6,7,8,9,10,12,13,18,20,23,24,25],[1,3,4,5,6,7,12,13,15,26],[0,1,2,3,4,5,6,8,9,10,11,22,23,26],[0,1,6,7,9,11,17,19,20,21,22,23,26],[0,4,7,10,12,13,15,16,18,20,21,26],[0,3,7,11,15,16,21,22,23,26],[0,1,3,5,8,9,11,12,17,20,26],[4,5,7,9,14,15,16,17,19,20,26],[0,2,6,7,14,15,16,17,18,21,22,23,26],[0,1,2,3,4,5,6,7,9,11,14,15,16,18,19,20,21,22,26],[0,1,4,12,13,15,17,18,19,20,21,22,26],[0,4,8,12,13,14,19,23,26],[1,3,5,10,15,18,23,26],[1,4,5,9,12,15,20,22,26],[0,3,4,5,6,7,13,14,21,22,26],[2,3,4,6,7,8,13,16,18,21,23,26],[6,7,9,13,15,17,19,20,23,26],[0,1,3,8,12,13,14,17,22,23,24,26],[1,2,3,7,11,13,15,17,24,26],[1,6,7,9,11,12,13,15,18,24,26],[4,7,14,15,16,17,19,22,23,24,26],[0,1,2,3,5,7,11,13,14,18,19,21,24,26],[0,2,3,9,11,16,17,18,19,20,22,23,24,26],[1,2,5,6,8,9,11,12,14,15,17,19,21,22,23,24,26],[0,1,4,8,9,12,13,17,18,20,24,26],[1,2,3,4,5,6,7,14,15,16,17,23,24,26],[1,4,8,9,11,12,15,23,24,26],[5,6,7,8,9,10,11,13,14,15,17,19,22,24,26],[0,1,3,4,6,7,8,9,12,13,14,15,17,18,22,24,26],[2,5,6,7,9,11,13,16,21,23,24,26],[0,1,2,3,5,8,9,13,14,16,20,23,24,26],[1,3,4,5,6,7,8,9,10,13,14,19,21,22,24,26],[1,2,5,6,7,9,10,11,13,14,16,17,18,20,22,24,26],[1,4,6,9,11,15,17,18,19,25,26],[0,3,4,7,9,17,18,19,20,21,25,26],[0,2,5,8,10,15,18,25,26],[0,3,4,5,8,9,11,12,13,16,17,19,20,21,25,26],[0,1,2,3,4,9,12,15,16,17,21,25,26],[0,1,4,5,6,7,9,11,12,14,21,25,26],[3,5,6,10,11,13,15,16,19,21,25,26],[0,1,4,6,7,10,13,15,16,18,21,25,26],[4,5,6,8,10,12,22,25,26],[1,4,6,9,10,15,16,17,20,21,23,25,26],[4,6,9,12,14,15,16,18,22,25,26],[0,2,5,11,13,16,19,20,21,23,25,26],[0,1,7,8,13,14,16,21,23,25,26],[1,2,12,16,21,22,25,26],[0,1,5,9,11,13,14,15,18,21,23,25,26],[0,4,5,6,9,11,13,16,17,19,21,22,25,26],[2,4,5,6,7,9,12,14,16,17,22,23,24,25,26],[0,1,2,3,4,5,7,8,11,14,16,17,20,21,22,23,24,25,26],[0,1,4,5,7,10,13,14,16,18,20,21,22,23,24,25,26],[0,1,2,3,5,6,7,8,11,14,17,19,22,23,24,25,26],[1,2,3,5,7,9,10,12,13,14,15,16,21,22,23,24,25,26],[1,8,9,10,11,17,21,22,23,24,25,26],[0,3,5,9,10,11,12,13,14,15,16,17,18,20,22,23,24,25,26],[1,4,9,10,11,13,14,16,17,19,20,22,23,24,25,26],[1,2,5,7,8,9,12,13,16,20,21,23,24,25,26],[2,6,9,11,12,14,17,22,24,25,26],[1,2,4,5,7,9,10,11,14,15,19,23,24,25,26],[0,1,6,7,10,18,20,21,22,24,25,26],[1,6,7,9,12,13,14,15,16,17,18,19,20,22,24,25,26],[0,1,2,6,9,12,13,16,17,18,19,20,23,24,25,26],[1,4,7,9,12,14,17,18,21,22,24,25,26],[16,19,21,23,24,25,26],[1,2,4,6,12,13,14,27],[0,2,3,5,6,7,11,12,13,18,19,27],[1,2,4,5,6,7,10,13,15,16,18,27],[1,3,4,6,7,9,10,13,17,18,27],[1,7,8,9,10,12,14,17,20,22,23,27],[1,2,3,4,7,10,12,15,16,18,19,21,22,23,27],[1,6,7,9,12,13,15,16,17,18,20,22,23,27],[0,3,5,11,12,15,16,17,18,21,22,23,27],[0,2,3,5,6,8,9,13,16,20,21,23,27],[0,1,2,3,4,8,11,12,13,15,17,18,19,20,21,22,27],[1,3,4,10,12,13,14,16,17,19,20,21,23,27],[0,1,2,3,4,5,10,11,14,15,16,17,19,20,21,22,27],[0,1,2,7,8,9,11,12,14,16,17,18,19,21,23,27],[1,4,7,8,9,10,11,12,13,15,16,17,20,22,27],[4,8,11,12,14,16,18,21,23,27],[1,4,5,6,7,8,12,17,18,20,22,27],[5,6,8,9,10,12,13,14,16,20,21,22,23,24,27],[0,1,3,4,5,6,7,8,11,16,18,19,20,21,22,23,24,27],[7,9,10,11,12,13,15,19,22,23,24,27],[2,3,4,5,7,9,10,11,12,13,15,16,17,19,22,23,24,27],[0,1,4,7,8,10,11,12,14,18,19,21,24,27],[0,1,2,3,8,10,13,15,16,17,20,24,27],[0,1,4,6,7,8,9,11,12,13,14,16,18,20,24,27],[3,4,5,7,10,11,12,13,16,18,21,24,27],[0,1,3,4,5,7,8,9,10,15,18,19,20,21,22,24,27],[0,3,5,6,7,8,13,15,16,17,20,21,23,24,27],[2,3,6,7,8,11,15,17,19,22,24,27],[0,3,4,5,6,7,11,12,13,14,15,17,19,23,24,27],[1,2,4,5,6,9,11,13,14,15,16,18,19,21,22,24,27],[0,1,5,6,7,8,10,11,14,16,20,23,24,27],[0,5,7,10,11,12,14,16,17,19,20,22,24,27],[0,1,6,7,15,19,21,23,24,27],[0,1,2,3,5,9,12,13,14,16,20,21,22,23,25,27],[1,3,4,5,6,8,9,14,15,16,18,19,25,27],[0,3,6,8,9,10,11,13,18,25,27],[0,1,3,5,6,7,8,11,12,13,16,17,18,20,21,22,23,25,27],[0,2,4,6,7,10,11,12,16,17,18,19,21,22,23,25,27],[0,1,2,5,6,9,10,12,13,15,21,25,27],[0,1,3,7,9,10,11,12,13,17,19,20,25,27],[1,2,5,7,9,10,11,12,13,17,19,20,22,23,25,27],[0,1,4,5,6,7,9,12,16,17,20,21,22,25,27],[0,1,2,4,7,8,10,12,14,18,19,22,25,27],[1,5,7,11,16,19,23,25,27],[0,2,3,6,9,11,15,16,19,20,21,23,25,27],[0,1,2,3,6,13,15,16,21,23,25,27],[2,3,6,7,8,9,13,16,18,19,21,23,25,27],[1,2,4,7,9,10,12,13,14,15,16,17,19,20,22,25,27],[1,2,4,5,12,14,19,20,22,25,27],[1,3,4,5,6,7,8,16,17,18,19,24,25,27],[0,1,4,7,11,12,14,15,16,17,20,21,22,23,24,25,27],[4,5,6,7,14,15,17,18,22,23,24,25,27],[1,2,6,7,8,9,13,14,15,16,18,20,21,24,25,27],[0,1,2,3,4,5,6,7,9,11,12,14,17,18,19,20,24,25,27],[0,3,6,7,11,12,13,14,15,16,20,22,23,24,25,27],[0,2,4,8,9,11,12,13,16,17,18,20,22,23,24,25,27],[2,5,10,11,12,15,16,17,18,20,24,25,27],[1,3,6,8,9,12,13,14,15,16,20,21,23,24,25,27],[1,2,6,8,10,11,12,13,17,18,19,23,24,25,27],[0,1,2,3,6,7,9,15,16,17,18,20,21,22,24,25,27],[5,6,7,8,10,12,13,15,16,17,18,22,24,25,27],[0,2,3,4,5,9,11,12,13,14,15,18,19,21,22,24,25,27],[1,2,3,5,6,9,10,15,21,22,24,25,27],[3,5,6,7,8,9,10,12,14,15,17,19,21,23,24,25,27],[16,19,21,23,24,25,27],[0,3,5,6,8,9,17,20,21,26,27],[0,1,4,5,7,12,13,14,15,16,18,19,20,21,22,23,26,27],[1,2,4,8,9,10,12,13,15,19,22,23,26,27],[0,1,2,4,7,8,9,10,11,12,19,26,27],[0,4,10,11,12,13,20,26,27],[2,6,7,9,11,12,13,18,19,21,22,23,26,27],[2,3,8,9,13,14,17,19,21,22,23,26,27],[1,2,3,4,7,11,14,16,19,20,26,27],[1,7,8,9,10,11,12,14,16,17,18,19,20,21,23,26,27],[0,1,7,8,11,14,16,17,20,21,23,26,27],[1,2,7,9,14,17,19,22,26,27],[4,5,6,9,13,14,16,19,22,26,27],[0,1,6,7,8,12,13,15,16,20,22,26,27],[1,2,3,4,6,7,9,13,15,17,18,19,21,22,26,27],[0,2,4,8,9,10,12,18,21,23,26,27],[0,1,5,8,9,10,14,18,20,23,26,27],[1,4,7,8,10,11,13,14,15,24,26,27],[6,7,8,9,10,11,12,13,15,16,17,18,19,22,23,24,26,27],[0,1,3,4,6,9,10,13,14,17,18,22,23,24,26,27],[1,2,3,4,6,7,8,10,14,17,18,24,26,27],[0,1,2,3,4,6,8,10,11,12,13,14,15,16,18,19,21,24,26,27],[1,4,5,9,10,11,12,13,16,20,22,23,24,26,27],[3,6,7,8,9,10,16,17,19,21,22,23,24,26,27],[1,2,3,4,6,11,12,13,19,20,24,26,27],[0,3,5,8,10,11,15,16,20,21,23,24,26,27],[0,1,4,8,9,15,16,18,19,20,21,23,24,26,27],[2,6,10,11,13,14,15,19,20,21,22,24,26,27],[0,2,8,10,12,14,16,17,19,20,21,22,24,26,27],[1,11,12,13,15,20,22,24,26,27],[2,4,11,16,17,18,19,21,22,24,26,27],[0,7,8,11,14,15,16,19,20,23,24,26,27],[16,19,21,23,24,26,27],[0,1,3,6,7,9,10,12,18,19,22,23,25,26,27],[0,1,2,4,6,7,8,10,16,17,20,21,22,23,25,26,27],[2,3,4,5,7,8,12,17,18,22,23,25,26,27],[7,11,15,17,18,20,21,22,23,25,26,27],[1,2,10,12,15,17,21,25,26,27],[0,2,6,7,9,11,12,17,18,19,21,25,26,27],[0,1,4,10,11,12,13,15,19,21,25,26,27],[2,5,6,9,10,13,16,17,19,21,25,26,27],[1,2,4,6,9,10,11,13,17,20,21,22,25,26,27],[1,2,3,5,6,7,10,11,14,17,18,19,23,25,26,27],[0,4,6,7,8,9,12,13,14,16,17,18,20,21,22,25,26,27],[0,3,4,6,7,8,10,11,18,23,25,26,27],[0,2,4,5,7,9,11,12,13,20,22,25,26,27],[0,7,8,11,14,15,16,17,18,19,20,23,25,26,27],[4,6,7,9,12,13,16,18,20,22,25,26,27],[16,18,20,23,25,26,27],[2,4,7,8,13,14,15,16,20,21,22,23,24,25,26,27],[0,1,4,5,6,7,9,10,11,12,13,17,18,19,22,23,24,25,26,27],[0,2,6,7,8,10,13,16,17,18,22,23,24,25,26,27],[1,2,4,6,8,12,16,17,18,20,21,22,23,24,25,26,27],[0,1,2,4,6,8,9,10,11,13,14,20,24,25,26,27],[0,1,2,8,12,13,14,15,18,19,20,24,25,26,27],[17,18,21,24,25,26,27],[16,18,21,24,25,26,27],[1,2,7,10,11,12,16,17,20,21,22,24,25,26,27],[1,5,6,7,9,11,13,14,16,17,18,19,23,24,25,26,27],[17,19,22,24,25,26,27],[16,19,20,21,23,24,25,26,27],[17,18,19,20,22,24,25,26,27],[16,20,23,24,25,26,27],[16,17,18,21,22,24,25,26,27],[16,17,18,21,23,24,25,26,27]]},"distance":{"d":4,"is_exact":true,"upper":4,"witness":[0,1,60,61],"A_d":91734,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,3],[1,1],[2,3],[3,1],[4,3],[5,2],[6,2],[8,2],[9,1],[10,2],[11,3],[12,1],[13,1],[14,2]],"CZ":[[0,1],[0,2],[0,3],[0,5],[0,6],[0,7],[0,9],[0,10],[0,11],[0,12],[0,13],[0,17],[0,18],[0,22],[0,23],[0,24],[0,26],[0,27],[1,3],[1,6],[1,8],[1,11],[1,13],[1,14],[1,15],[1,17],[1,18],[1,22],[1,23],[1,24],[1,26],[1,27],[2,4],[2,5],[2,6],[2,7],[2,9],[2,10],[2,12],[2,13],[2,14],[2,17],[2,19],[2,20],[2,23],[2,27],[3,4],[3,5],[3,9],[3,13],[3,14],[3,15],[3,19],[3,21],[3,24],[3,26],[3,27],[4,5],[4,9],[4,10],[4,14],[4,16],[4,17],[4,18],[4,19],[4,21],[4,22],[4,23],[4,24],[4,27],[5,6],[5,9],[5,13],[5,14],[5,16],[5,17],[5,18],[5,19],[5,20],[5,23],[5,24],[5,25],[6,8],[6,9],[6,12],[6,14],[6,20],[6,23],[6,24],[6,27],[7,8],[7,9],[7,10],[7,12],[7,13],[7,14],[7,15],[7,16],[7,17],[7,18],[7,19],[7,20],[7,22],[7,23],[7,27],[8,9],[8,11],[8,13],[8,14],[8,15],[8,17],[8,19],[8,20],[8,22],[8,24],[8,25],[9,10],[9,13],[9,14],[9,16],[9,18],[9,19],[9,20],[9,23],[10,13],[10,14],[10,15],[10,18],[10,21],[10,25],[10,26],[11,12],[11,15],[11,17],[11,19],[11,20],[11,24],[11,25],[12,14],[12,17],[12,18],[12,21],[12,22],[12,27],[13,14],[13,15],[13,16],[13,17],[13,20],[13,22],[13,23],[13,25],[13,27],[14,19],[14,21],[14,22],[14,24],[15,16],[15,19],[15,20],[15,21],[15,23],[15,27]]},"rotation_powers":null},"metrics":{"gamma":2.0,"gamma_t":null,"gamma_rho":null,"gamma_claim":2.0,"gamma_t_claim":null,"gamma_rho_claim":null,"v_ex":null,"rate":0.0625,"t_count":null,"poly_degree":null,"effective_width":16},"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":"CCZ012.CCZ014.CCZ019.CCZ0,1,10.CCZ0,1,12.CCZ0,1,14.CCZ024.CCZ028.CCZ0,2,10.CCZ0,2,11.CCZ0,2,12.CCZ0,2,13.CCZ0,2,14.CCZ0,2,15.CCZ048.CCZ049.CCZ0,4,11.CCZ0,4,13.CCZ0,4,15.CCZ089.CCZ0,8,10.CCZ0,8,12.CCZ0,8,14.CCZ0,9,10.CCZ0,9,11.CCZ0,9,12.CCZ0,9,13.CCZ0,9,14.CCZ0,9,15.CCZ0,10,11.CCZ0,10,13.CCZ0,10,15.CCZ0,11,12.CCZ0,11,14.CCZ0,12,13.CCZ0,12,15.CCZ0,13,14.CCZ0,14,15.CCZ123.CCZ124.CCZ127.CCZ1,2,10.CCZ1,2,11.CCZ1,2,12.CCZ1,2,13.CCZ1,2,14.CCZ1,2,15.CCZ1,3,10.CCZ1,3,12.CCZ146.CCZ148.CCZ1,4,10.CCZ1,4,11.CCZ1,4,13.CCZ1,4,15.CCZ167.CCZ168.CCZ1,6,10.CCZ1,6,12.CCZ1,6,13.CCZ1,6,14.CCZ1,6,15.CCZ179.CCZ1,7,12.CCZ1,7,13.CCZ1,7,15.CCZ1,8,10.CCZ1,8,13.CCZ1,8,14.CCZ1,8,15.CCZ1,9,11.CCZ1,9,13.CCZ1,9,15.CCZ1,10,11.CCZ1,10,12.CCZ1,10,13.CCZ1,10,14.CCZ1,10,15.CCZ1,11,12.CCZ1,11,14.CCZ1,13,14.CCZ1,14,15.CCZ236.CCZ239.CCZ2,3,11.CCZ2,3,13.CCZ2,3,14.CCZ245.CCZ247.CCZ2,4,10.CCZ2,4,11.CCZ2,4,12.CCZ2,4,13.CCZ2,4,15.CCZ256.CCZ257.CCZ258.CCZ259.CCZ2,5,10.CCZ2,5,11.CCZ2,5,14.CCZ267.CCZ268.CCZ269.CCZ2,6,11.CCZ2,6,12.CCZ2,6,13.CCZ278.CCZ279.CCZ2,7,11.CCZ2,7,13.CCZ2,7,14.CCZ2,7,15.CCZ2,8,10.CCZ2,8,11.CCZ2,8,12.CCZ2,8,13.CCZ2,8,14.CCZ2,8,15.CCZ2,9,10.CCZ2,9,14.CCZ2,9,15.CCZ2,10,13.CCZ2,10,14.CCZ2,11,13.CCZ2,13,15.CCZ2,14,15.CCZ345.CCZ347.CCZ348.CCZ349.CCZ3,4,11.CCZ3,4,13.CCZ356.CCZ3,5,10.CCZ3,5,11.CCZ3,5,15.CCZ367.CCZ368.CCZ3,6,10.CCZ3,6,12.CCZ378.CCZ3,7,10.CCZ3,7,13.CCZ3,7,14.CCZ3,7,15.CCZ3,8,11.CCZ3,8,14.CCZ3,9,11.CCZ3,10,14.CCZ3,11,12.CCZ3,11,15.CCZ3,12,13.CCZ3,13,14.CCZ3,13,15.CCZ3,14,15.CCZ458.CCZ459.CCZ4,5,10.CCZ4,5,11.CCZ4,5,12.CCZ4,5,13.CCZ4,5,14.CCZ468.CCZ4,6,12.CCZ4,6,13.CCZ4,6,15.CCZ479.CCZ4,7,12.CCZ4,7,13.CCZ489.CCZ4,8,10.CCZ4,8,11.CCZ4,8,14.CCZ4,8,15.CCZ4,9,10.CCZ4,9,13.CCZ4,10,11.CCZ4,10,12.CCZ4,11,13.CCZ4,12,13.CCZ4,12,14.CCZ4,12,15.CCZ4,13,14.CCZ4,14,15.CCZ5,6,11.CCZ5,6,14.CCZ5,6,15.CCZ578.CCZ5,7,10.CCZ5,7,11.CCZ5,7,14.CCZ589.CCZ5,8,10.CCZ5,8,11.CCZ5,9,10.CCZ5,9,11.CCZ5,9,14.CCZ5,9,15.CCZ5,10,11.CCZ5,10,15.CCZ5,11,12.CCZ5,11,13.CCZ5,11,15.CCZ5,12,13.CCZ5,12,14.CCZ5,12,15.CCZ5,13,14.CCZ5,14,15.CCZ678.CCZ679.CCZ6,7,10.CCZ6,7,12.CCZ6,7,15.CCZ689.CCZ6,8,12.CCZ6,9,11.CCZ6,9,13.CCZ6,9,14.CCZ6,10,12.CCZ6,10,13.CCZ6,10,14.CCZ6,10,15.CCZ6,11,12.CCZ6,11,13.CCZ6,11,15.CCZ6,13,14.CCZ6,13,15.CCZ789.CCZ7,8,10.CCZ7,8,11.CCZ7,8,12.CCZ7,8,13.CCZ7,8,14.CCZ7,8,15.CCZ7,9,11.CCZ7,9,12.CCZ7,9,13.CCZ7,10,11.CCZ7,10,13.CCZ7,10,14.CCZ7,11,12.CCZ7,11,13.CCZ7,13,14.CCZ8,9,12.CCZ8,9,13.CCZ8,9,14.CCZ8,9,15.CCZ8,10,11.CCZ8,10,12.CCZ8,10,13.CCZ8,10,14.CCZ8,11,13.CCZ8,12,15.CCZ8,13,15.CCZ8,14,15.CCZ9,10,11.CCZ9,10,14.CCZ9,10,15.CCZ9,11,12.CCZ9,11,13.CCZ9,11,15.CCZ9,12,13.CCZ9,12,14.CCZ9,12,15.CCZ9,13,14.CCZ10,11,12.CCZ10,11,13.CCZ10,11,14.CCZ10,12,15.CCZ10,13,15.CCZ11,12,14.CCZ11,13,15.CCZ11,14,15.CCZ12,13,14.CCZ12,13,15.CCZ12,14,15.CCZ13,14,15","N":28,"d":4,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:340"}]},"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"}]}