{"id":"758.10.2.a","row":1216,"stored":{"file":"master_catalog.json","row":1216,"construction":null,"columns_sha256":null},"parameters":{"n":758,"k":10,"d":2,"N":17,"r":7,"level":3},"gate":{"string":"0+1+2+3+4+5+6+7+8+9","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6\u00b7T7\u00b7T8\u00b7T9","monomials":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9]],"sk_key":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9]],"sk_fingerprint":"97115137a69484d8","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,16],[0,1,2,3,4,5,6,7,8,9,10,11,12,14,15],[0,1,2,3,4,5,6,7,8,9,10,11,12,14,16],[0,1,2,3,4,5,6,7,8,9,10,11,12,15,16],[0,1,2,3,4,5,6,7,8,9,10,11,13],[0,1,2,3,4,5,6,7,8,9,10,11,13,14,15],[0,1,2,3,4,5,6,7,8,9,10,11,13,14,16],[0,1,2,3,4,5,6,7,8,9,10,11,13,15,16],[0,1,2,3,4,5,6,7,8,9,10,11,14],[0,1,2,3,4,5,6,7,8,9,10,11,14,15,16],[0,1,2,3,4,5,6,7,8,9,10,11,15],[0,1,2,3,4,5,6,7,8,9,10,11,16],[0,1,2,3,4,5,6,7,8,9,10,12,13],[0,1,2,3,4,5,6,7,8,9,10,12,13,14,15],[0,1,2,3,4,5,6,7,8,9,10,12,13,14,16],[0,1,2,3,4,5,6,7,8,9,10,12,13,15,16],[0,1,2,3,4,5,6,7,8,9,10,12,14],[0,1,2,3,4,5,6,7,8,9,10,12,14,15,16],[0,1,2,3,4,5,6,7,8,9,10,12,15],[0,1,2,3,4,5,6,7,8,9,10,12,16],[0,1,2,3,4,5,6,7,8,9,10,13,14],[0,1,2,3,4,5,6,7,8,9,10,13,14,15,16],[0,1,2,3,4,5,6,7,8,9,10,13,15],[0,1,2,3,4,5,6,7,8,9,10,13,16],[0,1,2,3,4,5,6,7,8,9,10,14,15],[0,1,2,3,4,5,6,7,8,9,10,14,16],[0,1,2,3,4,5,6,7,8,9,10,15,16],[0,1,2,3,4,5,6,7,8,9,11],[0,1,2,3,4,5,6,7,8,9,11,12,13],[0,1,2,3,4,5,6,7,8,9,11,12,13,14,15],[0,1,2,3,4,5,6,7,8,9,11,12,13,14,16],[0,1,2,3,4,5,6,7,8,9,11,12,13,15,16],[0,1,2,3,4,5,6,7,8,9,11,12,14],[0,1,2,3,4,5,6,7,8,9,11,12,14,15,16],[0,1,2,3,4,5,6,7,8,9,11,12,15],[0,1,2,3,4,5,6,7,8,9,11,12,16],[0,1,2,3,4,5,6,7,8,9,11,13,14],[0,1,2,3,4,5,6,7,8,9,11,13,14,15,16],[0,1,2,3,4,5,6,7,8,9,11,13,15],[0,1,2,3,4,5,6,7,8,9,11,13,16],[0,1,2,3,4,5,6,7,8,9,11,14,15],[0,1,2,3,4,5,6,7,8,9,11,14,16],[0,1,2,3,4,5,6,7,8,9,11,15,16],[0,1,2,3,4,5,6,7,8,9,12],[0,1,2,3,4,5,6,7,8,9,12,13,14],[0,1,2,3,4,5,6,7,8,9,12,13,14,15,16],[0,1,2,3,4,5,6,7,8,9,12,13,15],[0,1,2,3,4,5,6,7,8,9,12,13,16],[0,1,2,3,4,5,6,7,8,9,12,14,15],[0,1,2,3,4,5,6,7,8,9,12,14,16],[0,1,2,3,4,5,6,7,8,9,12,15,16],[0,1,2,3,4,5,6,7,8,9,13],[0,1,2,3,4,5,6,7,8,9,13,14,15],[0,1,2,3,4,5,6,7,8,9,13,14,16],[0,1,2,3,4,5,6,7,8,9,13,15,16],[0,1,2,3,4,5,6,7,8,9,14],[0,1,2,3,4,5,6,7,8,9,14,15,16],[0,1,2,3,4,5,6,7,8,9,15],[0,1,2,3,4,5,6,7,8,9,16],[0,10,11],[0,10,11,12,13],[0,10,11,12,13,14,15],[0,10,11,12,13,14,16],[0,10,11,12,13,15,16],[0,10,11,12,14],[0,10,11,12,14,15,16],[0,10,11,12,15],[0,10,11,12,16],[0,10,11,13,14],[0,10,11,13,14,15,16],[0,10,11,13,15],[0,10,11,13,16],[0,10,11,14,15],[0,10,11,14,16],[0,10,11,15,16],[0,10,12],[0,10,12,13,14],[0,10,12,13,14,15,16],[0,10,12,13,15],[0,10,12,13,16],[0,10,12,14,15],[0,10,12,14,16],[0,10,12,15,16],[0,10,13],[0,10,13,14,15],[0,10,13,14,16],[0,10,13,15,16],[0,10,14],[0,10,14,15,16],[0,10,15],[0,10,16],[0,11,12],[0,11,12,13,14],[0,11,12,13,14,15,16],[0,11,12,13,15],[0,11,12,13,16],[0,11,12,14,15],[0,11,12,14,16],[0,11,12,15,16],[0,11,13],[0,11,13,14,15],[0,11,13,14,16],[0,11,13,15,16],[0,11,14],[0,11,14,15,16],[0,11,15],[0,11,16],[0,12,13],[0,12,13,14,15],[0,12,13,14,16],[0,12,13,15,16],[0,12,14],[0,12,14,15,16],[0,12,15],[0,12,16],[0,13,14],[0,13,14,15,16],[0,13,15],[0,13,16],[0,14,15],[0,14,16],[0,15,16],[1,10,11],[1,10,11,12,13],[1,10,11,12,13,14,15],[1,10,11,12,13,14,16],[1,10,11,12,13,15,16],[1,10,11,12,14],[1,10,11,12,14,15,16],[1,10,11,12,15],[1,10,11,12,16],[1,10,11,13,14],[1,10,11,13,14,15,16],[1,10,11,13,15],[1,10,11,13,16],[1,10,11,14,15],[1,10,11,14,16],[1,10,11,15,16],[1,10,12],[1,10,12,13,14],[1,10,12,13,14,15,16],[1,10,12,13,15],[1,10,12,13,16],[1,10,12,14,15],[1,10,12,14,16],[1,10,12,15,16],[1,10,13],[1,10,13,14,15],[1,10,13,14,16],[1,10,13,15,16],[1,10,14],[1,10,14,15,16],[1,10,15],[1,10,16],[1,11,12],[1,11,12,13,14],[1,11,12,13,14,15,16],[1,11,12,13,15],[1,11,12,13,16],[1,11,12,14,15],[1,11,12,14,16],[1,11,12,15,16],[1,11,13],[1,11,13,14,15],[1,11,13,14,16],[1,11,13,15,16],[1,11,14],[1,11,14,15,16],[1,11,15],[1,11,16],[1,12,13],[1,12,13,14,15],[1,12,13,14,16],[1,12,13,15,16],[1,12,14],[1,12,14,15,16],[1,12,15],[1,12,16],[1,13,14],[1,13,14,15,16],[1,13,15],[1,13,16],[1,14,15],[1,14,16],[1,15,16],[2,10,11],[2,10,11,12,13],[2,10,11,12,13,14,15],[2,10,11,12,13,14,16],[2,10,11,12,13,15,16],[2,10,11,12,14],[2,10,11,12,14,15,16],[2,10,11,12,15],[2,10,11,12,16],[2,10,11,13,14],[2,10,11,13,14,15,16],[2,10,11,13,15],[2,10,11,13,16],[2,10,11,14,15],[2,10,11,14,16],[2,10,11,15,16],[2,10,12],[2,10,12,13,14],[2,10,12,13,14,15,16],[2,10,12,13,15],[2,10,12,13,16],[2,10,12,14,15],[2,10,12,14,16],[2,10,12,15,16],[2,10,13],[2,10,13,14,15],[2,10,13,14,16],[2,10,13,15,16],[2,10,14],[2,10,14,15,16],[2,10,15],[2,10,16],[2,11,12],[2,11,12,13,14],[2,11,12,13,14,15,16],[2,11,12,13,15],[2,11,12,13,16],[2,11,12,14,15],[2,11,12,14,16],[2,11,12,15,16],[2,11,13],[2,11,13,14,15],[2,11,13,14,16],[2,11,13,15,16],[2,11,14],[2,11,14,15,16],[2,11,15],[2,11,16],[2,12,13],[2,12,13,14,15],[2,12,13,14,16],[2,12,13,15,16],[2,12,14],[2,12,14,15,16],[2,12,15],[2,12,16],[2,13,14],[2,13,14,15,16],[2,13,15],[2,13,16],[2,14,15],[2,14,16],[2,15,16],[3,10,11],[3,10,11,12,13],[3,10,11,12,13,14,15],[3,10,11,12,13,14,16],[3,10,11,12,13,15,16],[3,10,11,12,14],[3,10,11,12,14,15,16],[3,10,11,12,15],[3,10,11,12,16],[3,10,11,13,14],[3,10,11,13,14,15,16],[3,10,11,13,15],[3,10,11,13,16],[3,10,11,14,15],[3,10,11,14,16],[3,10,11,15,16],[3,10,12],[3,10,12,13,14],[3,10,12,13,14,15,16],[3,10,12,13,15],[3,10,12,13,16],[3,10,12,14,15],[3,10,12,14,16],[3,10,12,15,16],[3,10,13],[3,10,13,14,15],[3,10,13,14,16],[3,10,13,15,16],[3,10,14],[3,10,14,15,16],[3,10,15],[3,10,16],[3,11,12],[3,11,12,13,14],[3,11,12,13,14,15,16],[3,11,12,13,15],[3,11,12,13,16],[3,11,12,14,15],[3,11,12,14,16],[3,11,12,15,16],[3,11,13],[3,11,13,14,15],[3,11,13,14,16],[3,11,13,15,16],[3,11,14],[3,11,14,15,16],[3,11,15],[3,11,16],[3,12,13],[3,12,13,14,15],[3,12,13,14,16],[3,12,13,15,16],[3,12,14],[3,12,14,15,16],[3,12,15],[3,12,16],[3,13,14],[3,13,14,15,16],[3,13,15],[3,13,16],[3,14,15],[3,14,16],[3,15,16],[4,10,11],[4,10,11,12,13],[4,10,11,12,13,14,15],[4,10,11,12,13,14,16],[4,10,11,12,13,15,16],[4,10,11,12,14],[4,10,11,12,14,15,16],[4,10,11,12,15],[4,10,11,12,16],[4,10,11,13,14],[4,10,11,13,14,15,16],[4,10,11,13,15],[4,10,11,13,16],[4,10,11,14,15],[4,10,11,14,16],[4,10,11,15,16],[4,10,12],[4,10,12,13,14],[4,10,12,13,14,15,16],[4,10,12,13,15],[4,10,12,13,16],[4,10,12,14,15],[4,10,12,14,16],[4,10,12,15,16],[4,10,13],[4,10,13,14,15],[4,10,13,14,16],[4,10,13,15,16],[4,10,14],[4,10,14,15,16],[4,10,15],[4,10,16],[4,11,12],[4,11,12,13,14],[4,11,12,13,14,15,16],[4,11,12,13,15],[4,11,12,13,16],[4,11,12,14,15],[4,11,12,14,16],[4,11,12,15,16],[4,11,13],[4,11,13,14,15],[4,11,13,14,16],[4,11,13,15,16],[4,11,14],[4,11,14,15,16],[4,11,15],[4,11,16],[4,12,13],[4,12,13,14,15],[4,12,13,14,16],[4,12,13,15,16],[4,12,14],[4,12,14,15,16],[4,12,15],[4,12,16],[4,13,14],[4,13,14,15,16],[4,13,15],[4,13,16],[4,14,15],[4,14,16],[4,15,16],[5,10,11],[5,10,11,12,13],[5,10,11,12,13,14,15],[5,10,11,12,13,14,16],[5,10,11,12,13,15,16],[5,10,11,12,14],[5,10,11,12,14,15,16],[5,10,11,12,15],[5,10,11,12,16],[5,10,11,13,14],[5,10,11,13,14,15,16],[5,10,11,13,15],[5,10,11,13,16],[5,10,11,14,15],[5,10,11,14,16],[5,10,11,15,16],[5,10,12],[5,10,12,13,14],[5,10,12,13,14,15,16],[5,10,12,13,15],[5,10,12,13,16],[5,10,12,14,15],[5,10,12,14,16],[5,10,12,15,16],[5,10,13],[5,10,13,14,15],[5,10,13,14,16],[5,10,13,15,16],[5,10,14],[5,10,14,15,16],[5,10,15],[5,10,16],[5,11,12],[5,11,12,13,14],[5,11,12,13,14,15,16],[5,11,12,13,15],[5,11,12,13,16],[5,11,12,14,15],[5,11,12,14,16],[5,11,12,15,16],[5,11,13],[5,11,13,14,15],[5,11,13,14,16],[5,11,13,15,16],[5,11,14],[5,11,14,15,16],[5,11,15],[5,11,16],[5,12,13],[5,12,13,14,15],[5,12,13,14,16],[5,12,13,15,16],[5,12,14],[5,12,14,15,16],[5,12,15],[5,12,16],[5,13,14],[5,13,14,15,16],[5,13,15],[5,13,16],[5,14,15],[5,14,16],[5,15,16],[6,10,11],[6,10,11,12,13],[6,10,11,12,13,14,15],[6,10,11,12,13,14,16],[6,10,11,12,13,15,16],[6,10,11,12,14],[6,10,11,12,14,15,16],[6,10,11,12,15],[6,10,11,12,16],[6,10,11,13,14],[6,10,11,13,14,15,16],[6,10,11,13,15],[6,10,11,13,16],[6,10,11,14,15],[6,10,11,14,16],[6,10,11,15,16],[6,10,12],[6,10,12,13,14],[6,10,12,13,14,15,16],[6,10,12,13,15],[6,10,12,13,16],[6,10,12,14,15],[6,10,12,14,16],[6,10,12,15,16],[6,10,13],[6,10,13,14,15],[6,10,13,14,16],[6,10,13,15,16],[6,10,14],[6,10,14,15,16],[6,10,15],[6,10,16],[6,11,12],[6,11,12,13,14],[6,11,12,13,14,15,16],[6,11,12,13,15],[6,11,12,13,16],[6,11,12,14,15],[6,11,12,14,16],[6,11,12,15,16],[6,11,13],[6,11,13,14,15],[6,11,13,14,16],[6,11,13,15,16],[6,11,14],[6,11,14,15,16],[6,11,15],[6,11,16],[6,12,13],[6,12,13,14,15],[6,12,13,14,16],[6,12,13,15,16],[6,12,14],[6,12,14,15,16],[6,12,15],[6,12,16],[6,13,14],[6,13,14,15,16],[6,13,15],[6,13,16],[6,14,15],[6,14,16],[6,15,16],[7,10,11],[7,10,11,12,13],[7,10,11,12,13,14,15],[7,10,11,12,13,14,16],[7,10,11,12,13,15,16],[7,10,11,12,14],[7,10,11,12,14,15,16],[7,10,11,12,15],[7,10,11,12,16],[7,10,11,13,14],[7,10,11,13,14,15,16],[7,10,11,13,15],[7,10,11,13,16],[7,10,11,14,15],[7,10,11,14,16],[7,10,11,15,16],[7,10,12],[7,10,12,13,14],[7,10,12,13,14,15,16],[7,10,12,13,15],[7,10,12,13,16],[7,10,12,14,15],[7,10,12,14,16],[7,10,12,15,16],[7,10,13],[7,10,13,14,15],[7,10,13,14,16],[7,10,13,15,16],[7,10,14],[7,10,14,15,16],[7,10,15],[7,10,16],[7,11,12],[7,11,12,13,14],[7,11,12,13,14,15,16],[7,11,12,13,15],[7,11,12,13,16],[7,11,12,14,15],[7,11,12,14,16],[7,11,12,15,16],[7,11,13],[7,11,13,14,15],[7,11,13,14,16],[7,11,13,15,16],[7,11,14],[7,11,14,15,16],[7,11,15],[7,11,16],[7,12,13],[7,12,13,14,15],[7,12,13,14,16],[7,12,13,15,16],[7,12,14],[7,12,14,15,16],[7,12,15],[7,12,16],[7,13,14],[7,13,14,15,16],[7,13,15],[7,13,16],[7,14,15],[7,14,16],[7,15,16],[8,10,11],[8,10,11,12,13],[8,10,11,12,13,14,15],[8,10,11,12,13,14,16],[8,10,11,12,13,15,16],[8,10,11,12,14],[8,10,11,12,14,15,16],[8,10,11,12,15],[8,10,11,12,16],[8,10,11,13,14],[8,10,11,13,14,15,16],[8,10,11,13,15],[8,10,11,13,16],[8,10,11,14,15],[8,10,11,14,16],[8,10,11,15,16],[8,10,12],[8,10,12,13,14],[8,10,12,13,14,15,16],[8,10,12,13,15],[8,10,12,13,16],[8,10,12,14,15],[8,10,12,14,16],[8,10,12,15,16],[8,10,13],[8,10,13,14,15],[8,10,13,14,16],[8,10,13,15,16],[8,10,14],[8,10,14,15,16],[8,10,15],[8,10,16],[8,11,12],[8,11,12,13,14],[8,11,12,13,14,15,16],[8,11,12,13,15],[8,11,12,13,16],[8,11,12,14,15],[8,11,12,14,16],[8,11,12,15,16],[8,11,13],[8,11,13,14,15],[8,11,13,14,16],[8,11,13,15,16],[8,11,14],[8,11,14,15,16],[8,11,15],[8,11,16],[8,12,13],[8,12,13,14,15],[8,12,13,14,16],[8,12,13,15,16],[8,12,14],[8,12,14,15,16],[8,12,15],[8,12,16],[8,13,14],[8,13,14,15,16],[8,13,15],[8,13,16],[8,14,15],[8,14,16],[8,15,16],[9,10,11],[9,10,11,12,13],[9,10,11,12,13,14,15],[9,10,11,12,13,14,16],[9,10,11,12,13,15,16],[9,10,11,12,14],[9,10,11,12,14,15,16],[9,10,11,12,15],[9,10,11,12,16],[9,10,11,13,14],[9,10,11,13,14,15,16],[9,10,11,13,15],[9,10,11,13,16],[9,10,11,14,15],[9,10,11,14,16],[9,10,11,15,16],[9,10,12],[9,10,12,13,14],[9,10,12,13,14,15,16],[9,10,12,13,15],[9,10,12,13,16],[9,10,12,14,15],[9,10,12,14,16],[9,10,12,15,16],[9,10,13],[9,10,13,14,15],[9,10,13,14,16],[9,10,13,15,16],[9,10,14],[9,10,14,15,16],[9,10,15],[9,10,16],[9,11,12],[9,11,12,13,14],[9,11,12,13,14,15,16],[9,11,12,13,15],[9,11,12,13,16],[9,11,12,14,15],[9,11,12,14,16],[9,11,12,15,16],[9,11,13],[9,11,13,14,15],[9,11,13,14,16],[9,11,13,15,16],[9,11,14],[9,11,14,15,16],[9,11,15],[9,11,16],[9,12,13],[9,12,13,14,15],[9,12,13,14,16],[9,12,13,15,16],[9,12,14],[9,12,14,15,16],[9,12,15],[9,12,16],[9,13,14],[9,13,14,15,16],[9,13,15],[9,13,16],[9,14,15],[9,14,16],[9,15,16],[10],[10,11,12],[10,11,12,13,14],[10,11,12,13,14,15,16],[10,11,12,13,15],[10,11,12,13,16],[10,11,12,14,15],[10,11,12,14,16],[10,11,12,15,16],[10,11,13],[10,11,13,14,15],[10,11,13,14,16],[10,11,13,15,16],[10,11,14],[10,11,14,15,16],[10,11,15],[10,11,16],[10,12,13],[10,12,13,14,15],[10,12,13,14,16],[10,12,13,15,16],[10,12,14],[10,12,14,15,16],[10,12,15],[10,12,16],[10,13,14],[10,13,14,15,16],[10,13,15],[10,13,16],[10,14,15],[10,14,16],[10,15,16],[11],[11,12,13],[11,12,13,14,15],[11,12,13,14,16],[11,12,13,15,16],[11,12,14],[11,12,14,15,16],[11,12,15],[11,12,16],[11,13,14],[11,13,14,15,16],[11,13,15],[11,13,16],[11,14,15],[11,14,16],[11,15,16],[12],[12,13,14],[12,13,14,15,16],[12,13,15],[12,13,16],[12,14,15],[12,14,16],[12,15,16],[13],[13,14,15],[13,14,16],[13,15,16],[14],[14,15,16],[15],[16]]},"distance":{"d":2,"is_exact":true,"upper":2,"witness":[0,694],"A_d":2899,"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]],"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],[427,7],[428,7],[429,7],[430,7],[431,7],[432,7],[433,7],[434,7],[435,7],[436,7],[437,7],[438,7],[439,7],[440,7],[441,7],[442,7],[443,7],[444,7],[445,7],[446,7],[447,7],[448,7],[449,7],[450,7],[451,7],[452,7],[453,7],[454,7],[455,7],[456,7],[457,7],[458,7],[459,7],[460,7],[461,7],[462,7],[463,7],[464,7],[465,7],[466,7],[467,7],[468,7],[469,7],[470,7],[471,7],[472,7],[473,7],[474,7],[475,7],[476,7],[477,7],[478,7],[479,7],[480,7],[481,7],[482,7],[483,7],[484,7],[485,7],[486,7],[487,7],[488,7],[489,7],[490,7],[491,7],[492,7],[493,7],[494,7],[495,7],[496,7],[497,7],[498,7],[499,7],[500,7],[501,7],[502,7],[503,7],[504,7],[505,7],[506,7],[507,7],[508,7],[509,7],[510,7],[511,7],[512,7],[513,7],[514,7],[515,7],[516,7],[517,7],[518,7],[519,7],[520,7],[521,7],[522,7],[523,7],[524,7],[525,7],[526,7],[527,7],[528,7],[529,7],[530,7],[531,7],[532,7],[533,7],[534,7],[535,7],[536,7],[537,7],[538,7],[539,7],[540,7],[541,7],[542,7],[543,7],[544,7],[545,7],[546,7],[547,7],[548,7],[549,7],[550,7],[551,7],[552,7],[553,7],[554,7],[555,7],[556,7],[557,7],[558,7],[559,7],[560,7],[561,7],[562,7],[563,7],[564,7],[565,7],[566,7],[567,7],[568,7],[569,7],[570,7],[571,7],[572,7],[573,7],[574,7],[575,7],[576,7],[577,7],[578,7],[579,7],[580,7],[581,7],[582,7],[583,7],[584,7],[585,7],[586,7],[587,7],[588,7],[589,7],[590,7],[591,7],[592,7],[593,7],[594,7],[595,7],[596,7],[597,7],[598,7],[599,7],[600,7],[601,7],[602,7],[603,7],[604,7],[605,7],[606,7],[607,7],[608,7],[609,7],[610,7],[611,7],[612,7],[613,7],[614,7],[615,7],[616,7],[617,7],[618,7],[619,7],[620,7],[621,7],[622,7],[623,7],[624,7],[625,7],[626,7],[627,7],[628,7],[629,7],[630,7],[631,7],[632,7],[633,7],[634,7],[635,7],[636,7],[637,7],[638,7],[639,7],[640,7],[641,7],[642,7],[643,7],[644,7],[645,7],[646,7],[647,7],[648,7],[649,7],[650,7],[651,7],[652,7],[653,7],[654,7],[655,7],[656,7],[657,7],[658,7],[659,7],[660,7],[661,7],[662,7],[663,7],[664,7],[665,7],[666,7],[667,7],[668,7],[669,7],[670,7],[671,7],[672,7],[673,7],[674,7],[675,7],[676,7],[677,7],[678,7],[679,7],[680,7],[681,7],[682,7],[683,7],[684,7],[685,7],[686,7],[687,7],[688,7],[689,7],[690,7],[691,7],[692,7],[693,7],[694,7],[695,7],[696,7],[697,7],[698,7],[699,7],[700,7],[701,7],[702,7],[703,7],[704,7],[705,7],[706,7],[707,7],[708,7],[709,7],[710,7],[711,7],[712,7],[713,7],[714,7],[715,7],[716,7],[717,7],[718,7],[719,7],[720,7],[721,7],[722,7],[723,7],[724,7],[725,7],[726,7],[727,7],[728,7],[729,7],[730,7],[731,7],[732,7],[733,7],[734,7],[735,7],[736,7],[737,7],[738,7],[739,7],[740,7],[741,7],[742,7],[743,7],[744,7],[745,7],[746,7],[747,7],[748,7],[749,7],[750,7],[751,7],[752,7],[753,7],[754,7],[755,7],[756,7],[757,7]]},"metrics":{"gamma":6.24412594328373,"gamma_t":null,"gamma_rho":6.24412594328373,"gamma_claim":6.24412594328373,"gamma_t_claim":null,"gamma_rho_claim":6.24412594328373,"v_ex":10,"rate":0.013192612137203167,"t_count":null,"poly_degree":null,"effective_width":10},"provenance":{"regimes":["borrowed-identity search: two-group"],"discovery":"pre-existing","strongest_claim":"found by the two-group borrowed-identity search of Singh, Gidney and Jones (arXiv:2606.28518; borrowed_identities/): an identity circuit symmetric within its output and check blocks, with its output-only gates removed; a verified witness, not a maximum","sources":[{"regime":"borrowed-identity search: two-group","file":"borrowed_identities/circuits/large_unified_l3.json","label":"lu-1100","N":17,"d":2,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at ae9fbf8, outputs/large_unified_factories_l3.csv line 1100","provenance":"larger unified search l=3, two-group s_total=2,s_O=9"}]},"references":[{"key":"singh2026borrowed","short":"Singh et al. (2026)","full":"S. Singh, C. Gidney, and C. Jones, \"Borrowed Identities: Malleable Distillation Factories and a Unified Numerical Search,\" arXiv:2606.28518 (2026).","url":"https://arxiv.org/abs/2606.28518","date":"2026-06-26"}]}