{"id":"135.17.3.a","row":756,"stored":{"file":"master_catalog.json","row":756,"construction":null,"columns_sha256":null},"parameters":{"n":135,"k":17,"d":3,"N":25,"r":8,"level":3},"gate":{"string":"0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6\u00b7T7\u00b7T8\u00b7T9\u00b7T10\u00b7T11\u00b7T12\u00b7T13\u00b7T14\u00b7T15\u00b7T16","monomials":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15],[16]],"sk_key":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15],[16]],"sk_fingerprint":"54780f2effb2fd97","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[1,3,9,11,17],[5,6,18],[1,9,11,19],[4,5,9,20],[9,11,21],[4,11,22],[1,5,9,15,18,19],[1,2,11,23],[4,5,9,21,22],[5,9,11,14,18,19,23],[1,3,5,11,18,23],[1,4,5,14,19,20],[4,5,7,12,24],[1,4,5,6,9,17,22],[0,1,7,19,20,24],[1,4,5,7,9,15,19,24],[0,4,5,11,20,21],[9,19,21,23],[0,1,5,9,11,17,18],[4,5,11,13,19,20,23],[4,5,9,19,20,21,23],[4,5,7,8,9,11,20,22,24],[3,7,11,20,21,24],[4,5,7,16,20,21,22,24],[1,2,17,19,23],[4,5,9,19,22,23],[1,5,11,17,19,22,23],[5,6,7,9,18,20,24],[1,7,11,16,17,20,24],[1,5,7,11,17,18,20,24],[1,4,5,7,9,11,20,23],[5,7,9,21,22,24],[1,4,5,11,16,17,21,22],[1,4,5,7,8,11,20,21,22,23,24],[1,7,9,11,15,21,22,23,24],[5,11,16,17,18,19],[6,7,9,20,24],[4,5,11,15,19,21,22,23],[1,4,5,9,12,17,19,21,22,23],[1,4,7,9,18,19,20,21,22,24],[1,4,5,7,9,11,14,17,20,21,22,24],[4,7,11,16,17,18,19,20,21,22,24],[4,7,9,11,21,24],[1,7,9,11,12,19,20,21,24],[0,1,4,5,7,11,19,21,24],[1,4,5,17,18,19,23],[7,9,18,19,20,21,23,24],[1,3,7,9,17,20,21,24],[1,5,7,11,17,18,19,20,21,23,24],[2,7,11,22,24],[4,5,7,9,20,22,23,24],[1,2,7,22,23,24],[3,5,9,17,18,23],[1,4,7,9,18,20,22,23,24],[1,4,5,6,7,17,20,22,24],[4,7,11,13,17,18,20,22,23,24],[1,4,6,9,17,18,22],[1,2,7,11,17,19,22,23,24],[1,7,9,12,17,19,21,22,23,24],[1,4,11,18,19,20],[9,11,19,23],[1,4,6,7,17,18,20,22,24],[11,12,17,20,22,23],[1,4,10,11,17,18,19,22,23],[5,8,11,17,18,20,22,23],[9,19,20,22,23],[9,11,19,20,21,22,23],[1,5,7,16,18,19,20,24],[4,9,13,18,19,22,23],[1,9,17,19,21,23],[1,4,5,7,10,17,19,23,24],[1,4,5,9,11,17,19,21,23,24],[1,4,7,9,18,19,24],[4,5,7,9,13,17,23,24],[4,7,8,9,17,18,23,24],[1,4,7,14,17,18,19,20,21,22,23,24],[1,4,5,9,11,12,19,20,21],[1,4,7,8,17,18,21,24],[0,5,7,9,11,17,18,19,20,24],[0,4,7,9,17,18,19,21,24],[7,9,11,13,17,19,20,24],[4,9,11,18,20,22,24],[4,5,7,9,11,18,19,20,21,22,23,24],[1,5,20,21,23],[1,4,7,18,19,21,23,24],[1,4,7,9,18,21,23,24],[9,20,21,22],[1,4,9,11,15,18,21,22,23],[1,4,9,11,14,18,20,23],[1,4,5,11,18,20,21,22,23],[4,5,11,18,19,20,23],[17,23],[4,5,7,11,12,17,20,22,23,24],[2,7,17,19,22,24],[7,9,11,14,17,19,21,22,24],[4,7,15,18,24],[4,7,17,18,19,23,24],[1,4,17,18,19,20,21,23],[1,5,7,17,18,19,20,21,22,23],[1,8,9,21,23],[1,3,5,7,18,20,21,23,24],[4,7,9,11,17,18,19,21,22],[4,11,17,19,20,21,22],[4,10,17,18,21,22,23],[1,5,8,9,11,17,18,20,21,22],[5,7,11,15,18,19,21,22,23,24],[1,5,7,11,17,18,21,22,24],[3,5,7,9,11,17,18,20,21,23,24],[5,7,13,17,18,19,22,24],[1,5,7,11,17,18,19,22,23,24],[1,4,5,7,9,17,20,21,22,23,24],[1,5,18,22,23,24],[5,7,10,11,18,22,24],[9,11,20,22],[11,18,22],[4,9,11,18,20],[5,9,11,13,18,20,22],[2,11,17,19],[4,5,7,10,11,17,21,23,24],[1,5,7,10,18,19,21,22,24],[5,7,14,17,18,21,22,23,24],[4,9,17,18,20,21,23],[1,10,11,19,21],[1,5,9,17,18,19,20,22],[17,19,20,21,24],[1,4,16,18,19,21,22],[5,9,18,19,20,21,22],[0,1,4,9,17,18,20,21],[18,19,20,22,23],[17,18,19,20,21],[17,21,23],[17,21],[17,19,21],[17,20,21,22,23],[17,19,20,22]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,18],"A_d":1575,"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]],"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]]},"metrics":{"gamma":1.8860715975553612,"gamma_t":null,"gamma_rho":1.8860715975553612,"gamma_claim":1.8860715975553612,"gamma_t_claim":null,"gamma_rho_claim":1.8860715975553612,"v_ex":17,"rate":0.1259259259259259,"t_count":null,"poly_degree":null,"effective_width":17},"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":"T0.T1.T2.T3.T4.T5.T6.T7.T8.T9.T10.T11.T12.T13.T14.T15.T16","N":25,"d":3,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:219"}]},"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"}]}