{"id":"255.5.5.a","row":909,"stored":{"file":"master_catalog.json","row":909,"construction":null,"columns_sha256":null},"parameters":{"n":255,"k":5,"d":5,"N":21,"r":16,"level":3},"gate":{"string":"0+1+2+3+4","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4","monomials":[[0],[1],[2],[3],[4]],"sk_key":[[0],[1],[2],[3],[4]],"sk_fingerprint":"65a2b287ec4a80f7","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,3,4,5,13],[2,6,16],[0,1,3,5,6,13,14,15,16],[1,2,4,7,19],[1,2,5,7,13,15,17,19],[1,2,4,6,7,16,17,18,19],[4,5,6,7,13,14,16,18,19],[1,2,4,8,14,16,17,18],[2,5,8,13,14,17,18,19],[1,3,4,6,8,14,17,20],[1,2,3,4,5,6,8,13,15,16,17,19,20],[0,1,2,3,7,8,13,14,15,18,19,20],[2,4,5,7,8,14,16,17,18,20],[0,1,2,6,7,8,13,14,15,16,17,18,19],[1,3,5,6,7,8,15,18],[1,3,9,13,15,16,19,20],[4,5,9,13,19,20],[0,1,4,6,9,13,14,15,16,17,18,20],[0,1,2,3,4,5,6,9,13,15,17,18,20],[2,3,7,9,15,18,19,20],[0,1,2,3,4,5,7,9,15,16,17,18,19,20],[0,4,6,7,9,14,15,18,20],[2,4,5,6,7,9,16,17,18,20],[0,8,9,13,14,16,18,19],[4,5,8,9,13,14,15,16,18],[4,6,8,9,13,16,17,18,20],[0,1,2,4,5,6,8,9,13,14,16,17,18,19,20],[3,7,8,9,13,14,15,16,17,19,20],[4,5,7,8,9,13,14,15,16,20],[0,2,3,4,6,7,8,9,13,15,16,17,18],[0,1,4,5,6,7,8,9,13,14,16,18,19],[1,2,3,10,14,15,18],[5,10,13,14,17,18,19],[3,6,10,14,15,19],[4,5,6,10,13,15,17],[0,1,2,7,10,13,17,20],[5,7,10,17,19,20],[0,2,6,7,10,13,19,20],[2,4,5,6,7,10,14,15,20],[1,2,3,4,8,10,13,14,17,18,19],[0,1,3,4,5,8,10,14,15,16,18,19],[4,6,8,10,13,14,17,18,20],[0,1,5,6,8,10,16,18,20],[3,4,7,8,10,13,16,17,19],[2,4,5,7,8,10,17,19],[1,4,6,7,8,10,13,16,18,20],[3,5,6,7,8,10,14,15,18,20],[2,3,9,10,13,14,15,16,17,18,19],[0,5,9,10,13,14,15,18],[0,1,2,4,6,9,10,13,15,18,19],[2,3,5,6,9,10,13,14,16,17,18],[0,2,4,7,9,10,13,18,20],[0,4,5,7,9,10,13,15,16,18,19,20],[1,3,6,7,9,10,13,14,16,20],[3,4,5,6,7,9,10,13,19,20],[0,8,9,10,14,15,17,18,20],[0,1,2,5,8,9,10,14,15,18,20],[1,4,6,8,9,10,15,16],[1,5,6,8,9,10,14,16,17],[0,1,2,4,7,8,9,10,13,15,17,18,19,20],[3,4,5,7,8,9,10,13,17,18,19,20],[6,7,8,9,10,13,14,15,16,17,18,19],[1,2,5,6,7,8,9,10,13,15,16,17,18,19],[0,1,11,13,15,16,18],[3,4,5,11,13,18,20],[2,3,6,11,13,14,15,16,17,18,20],[0,5,6,11,13,15,17,18],[1,2,7,11,14,16],[2,4,5,7,11,14,17,20],[0,2,3,4,6,7,11,16,18,20],[0,3,4,5,6,7,11,14,15,17,18],[1,2,8,11,15,16,17,18,19,20],[1,2,5,8,11,16,17,18],[0,4,6,8,11,14,15,16,19,20],[0,1,2,5,6,8,11,15,16],[2,3,7,8,11,14,15,19],[0,2,5,7,8,11,14,15,17,20],[0,1,2,3,6,7,8,11,15,19],[5,6,7,8,11,14,17,20],[0,1,3,4,9,11,13,14,15,16,17,18,20],[0,1,4,5,9,11,14,15,16,17,18],[0,3,4,6,9,11,13,14,15,17,19],[0,1,2,4,5,6,9,11,17,19,20],[1,2,3,4,7,9,11,13,17,18,19,20],[0,1,2,3,5,7,9,11,15,18,19],[3,6,7,9,11,13,16,18],[0,1,2,3,4,5,6,7,9,11,14,16,17,18,20],[0,1,8,9,11,14,17,18,19,20],[3,4,5,8,9,11,13,14,16,17,18],[0,6,8,9,11,14,16,17,18,20],[2,3,5,6,8,9,11,13,15,17,18,19],[0,3,7,8,9,11,13,18],[0,1,4,5,7,8,9,11,15,16,17,18,19,20],[0,1,2,3,4,6,7,8,9,11,13,16,17,19],[2,3,4,5,6,7,8,9,11,14,20],[0,1,10,11,13,14,15,16,17,19,20],[0,1,2,4,5,10,11,13,14,15],[1,2,3,4,6,10,11,13,15,18],[2,4,5,6,10,11,13,14,16,17,18,19,20],[0,4,7,10,11,13,14,15,16],[2,5,7,10,11,13,14,19,20],[3,4,6,7,10,11,13,15,19,20],[0,1,2,3,4,5,6,7,10,11,13,14,15,16],[3,8,10,11,13,18,19],[0,1,2,3,4,5,8,10,11,13,17,18,19,20],[0,2,6,8,10,11,13,14,16,17,18],[5,6,8,10,11,13,15,16,18,20],[0,2,3,4,7,8,10,11,15,16,18],[4,5,7,8,10,11,16,18,20],[2,3,6,7,8,10,11,14,15,19],[4,5,6,7,8,10,11,15,19,20],[0,1,3,9,10,11,13,16,17,19,20],[2,3,5,9,10,11,15,16],[0,1,3,4,6,9,10,11,13,16,17,19],[0,3,4,5,6,9,10,11,14,16,20],[0,2,3,4,7,9,10,11,18,19],[0,1,4,5,7,9,10,11,13,18,20],[0,3,4,6,7,9,10,11,17,19,20],[0,5,6,7,9,10,11,13,14,15,17],[0,1,3,4,8,9,10,11,13,14,16,17,18,19,20],[0,1,2,3,5,8,9,10,11,14,15,18,19],[3,4,6,8,9,10,11,13,14,16,17,19,20],[1,3,5,6,8,9,10,11,19],[0,7,8,9,10,11,13,14,15,16,17,19,20],[5,7,8,9,10,11,14,15,17,19],[0,6,7,8,9,10,11,13,14,15,16,19,20],[0,2,5,6,7,8,9,10,11,19],[0,2,4,12,13,15,17,18,19],[3,4,5,12,13,14,15,18,19,20],[0,2,3,4,6,12,13,18,19],[1,3,4,5,6,12,13,15,17,18,19,20],[0,1,2,3,4,7,12,13,17,20],[0,1,3,5,7,12,13,14,15,17],[0,1,2,3,4,6,7,12,13,15,17,18,20],[0,2,3,4,5,6,7,12,13,15,17,18],[0,1,2,8,12,17,19],[0,2,4,5,8,12,14,16,20],[0,1,4,6,8,12,15,18,19,20],[0,4,5,6,8,12,16,17,18],[1,3,7,8,12,13,16,18],[0,2,4,5,7,8,12,13,14,15,18,19,20],[1,3,6,7,8,12,13,15,16,18,20],[0,1,2,3,4,5,6,7,8,12,13,15,18,19],[3,4,9,12,13,14,17,18,20],[1,3,5,9,12,15,16,18],[0,1,2,6,9,12,13,15,16,17,19,20],[0,1,5,6,9,12,15,19],[1,4,7,9,12,14,15,16,17,18],[0,2,3,4,5,7,9,12,13,15,17,18,20],[0,1,3,4,6,7,9,12,18,19],[2,3,4,5,6,7,9,12,13,15,16,18,19,20],[0,3,8,9,12,14,16],[1,3,5,8,9,12,13,15,16,17,19,20],[1,3,6,8,9,12,15,19,20],[0,1,3,4,5,6,8,9,12,13,15,17],[1,3,7,8,9,12,14,16,17],[0,4,5,7,8,9,12,13,16,17,19,20],[1,6,7,8,9,12,15,18,19,20],[2,3,5,6,7,8,9,12,13,18],[1,2,4,10,12,13,17,20],[3,4,5,10,12,13,14,15,17,19],[1,4,6,10,12,13,15,16,18,19,20],[2,4,5,6,10,12,13,15,16,18],[0,2,3,7,10,12,14,20],[0,1,2,4,5,7,10,12,17,19],[0,6,7,10,12,14,15,16,19,20],[0,1,2,3,5,6,7,10,12,14,16,17],[1,2,4,8,10,12,13,14,16,17,19,20],[0,1,2,3,4,5,8,10,12,13,15,17,19],[2,6,8,10,12,13,14,15],[0,1,5,6,8,10,12,13,14,15,16,20],[2,3,4,7,8,10,12,13,15,17,19],[0,2,3,4,5,7,8,10,12,13,14,15,16,19,20],[1,3,6,7,8,10,12,13,16,17,18,20],[5,6,7,8,10,12,13,15,18],[0,2,3,9,10,12,13,14,19,20],[1,2,3,5,9,10,12,16],[1,3,6,9,10,12,13,15,19,20],[0,2,3,5,6,9,10,12,16],[0,1,3,4,7,9,10,12,13,16,17,18,20],[5,7,9,10,12,14,15,18,19],[1,4,6,7,9,10,12,13,14,15,16,20],[2,3,5,6,7,9,10,12,14,15,17,19],[1,3,8,9,10,12,13,15,17],[0,4,5,8,9,10,12,14,15,17,20],[2,4,6,8,9,10,12,13,14,17,18,20],[2,3,5,6,8,9,10,12,14,15,17,18],[0,1,2,4,7,8,9,10,12,14,17,18,19,20],[1,2,5,7,8,9,10,12,13,15,18,19],[0,2,4,6,7,8,9,10,12,15,18,19],[5,6,7,8,9,10,12,13,15,17,18,19,20],[0,1,2,3,11,12,14,15,17,18,20],[3,4,5,11,12,13,16,18,20],[2,3,4,6,11,12,16,17,18],[1,3,5,6,11,12,13,18],[1,2,7,11,12,13,15,17,18],[0,4,5,7,11,12,14,15,16,17,18],[0,2,3,4,6,7,11,12,13,14,16,20],[0,2,5,6,7,11,12,14,15,20],[1,2,8,11,12,16,17,18,19],[1,3,5,8,11,12,13,14,15,16,18],[1,2,6,8,11,12,14,15,17,19],[0,4,5,6,8,11,12,13,14,15],[0,1,3,7,8,11,12,14,15,18,19],[1,2,3,4,5,7,8,11,12,13,15,18],[6,7,8,11,12,16,17,18,19],[0,3,5,6,7,8,11,12,13,15,16,17,18],[1,4,9,11,12,13,14,15,16,18],[0,2,5,9,11,12,13,15,16,17,18],[1,3,6,9,11,12,13,14,16,17,19,20],[2,5,6,9,11,12,13,14,15,16,19,20],[0,7,9,11,12,13,15,19,20],[0,3,4,5,7,9,11,12,13,14,19,20],[0,1,2,6,7,9,11,12,13],[0,2,4,5,6,7,9,11,12,13],[1,2,8,9,11,12,13,15,16,17,18,19],[1,2,4,5,8,9,11,12,13,14,15,18],[0,1,3,6,8,9,11,12,13,16,18],[0,3,5,6,8,9,11,12,13,15,17,18,19],[0,3,7,8,9,11,12,14,16],[0,3,4,5,7,8,9,11,12,15,19],[0,1,2,6,7,8,9,11,12,14,15,16,18,19],[5,6,7,8,9,11,12,14,15,18],[1,3,4,10,11,12,14,15,20],[0,4,5,10,11,12,13,15,16,19,20],[0,3,6,10,11,12,18,19],[0,1,4,5,6,10,11,12,13,15,16,18],[7,10,11,12,14,17,18,19,20],[0,5,7,10,11,12,13,15,16,18,20],[0,4,6,7,10,11,12,15,18],[2,3,4,5,6,7,10,11,12,13,15,16,17,18,19],[1,8,10,11,12,13,14,15,18],[0,2,3,5,8,10,11,12,15,18],[0,1,3,6,8,10,11,12,13,18,19],[5,6,8,10,11,12,15,18,19],[4,7,8,10,11,12,14,15,16,19,20],[5,7,8,10,11,12,13,16,17,19,20],[0,1,2,3,4,6,7,8,10,11,12,16,17,18,20],[5,6,7,8,10,11,12,13,16,18,20],[2,4,9,10,11,12,13,14,16,20],[2,3,5,9,10,11,12,13,15,16,19,20],[0,2,4,6,9,10,11,12,13,14,15,17],[5,6,9,10,11,12,13,14,15,17,19],[1,4,7,9,10,11,12,14,15,17,20],[5,7,9,10,11,12,15,19,20],[6,7,9,10,11,12,14,16,17,18],[5,6,7,9,10,11,12,14,15,16,18,19],[1,2,4,8,9,10,11,12,14,15,17,18,20],[5,8,9,10,11,12,16,17,18,20],[6,8,9,10,11,12,14,16,20],[5,6,8,9,10,11,12,14,20],[7,8,9,10,11,12,14,15,17,18],[5,7,8,9,10,11,12,15,16,18],[6,7,8,9,10,11,12,14,16,17,18],[5,6,7,8,9,10,11,12,14,15,18]]},"distance":{"d":5,"is_exact":true,"upper":5,"witness":[10,127,146,171,179],"A_d":128978,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,1],[1,1],[3,3],[4,3]],"CZ":[[0,1],[0,2],[0,4],[0,5],[0,7],[0,8],[0,9],[0,12],[0,14],[0,15],[0,16],[0,17],[0,18],[1,4],[1,7],[1,8],[1,9],[1,10],[1,15],[1,17],[1,18],[1,19],[1,20],[2,3],[2,6],[2,12],[2,13],[2,15],[2,16],[3,4],[3,5],[3,6],[3,9],[3,10],[3,12],[3,14],[3,15],[3,16],[3,20],[4,9],[4,10],[4,11],[4,13],[4,14],[4,16],[4,20]]},"rotation_powers":[[1,3],[2,5],[3,7],[4,7],[5,7],[7,7],[11,7],[15,7],[17,5],[19,3],[62,5],[63,3],[69,7],[78,3],[80,3],[81,3],[84,3],[85,3],[88,5],[91,3],[95,3],[97,3],[99,3],[101,3],[104,3],[105,3],[106,3],[107,3],[108,3],[109,3],[110,3],[114,3],[116,3],[120,3],[122,3],[123,3],[127,3],[129,3],[131,3],[134,3],[135,3],[137,3],[138,3],[139,3],[145,3],[148,3],[151,3],[152,3],[153,3],[154,3],[156,3],[158,3],[159,3],[160,3],[161,3],[162,3],[165,3],[169,3],[177,3],[178,3],[182,3],[183,3],[186,3],[188,3],[194,3],[200,3],[202,3],[203,3],[205,3],[209,3],[212,3],[213,3],[215,3],[218,3],[219,3],[220,3],[221,3],[222,3],[223,3],[224,3],[225,3],[228,3],[229,3],[230,3],[232,3],[233,3],[238,3],[239,3],[241,3],[243,3],[244,3],[245,3],[246,3],[247,3],[248,3],[251,3]]},"metrics":{"gamma":2.4429806222085735,"gamma_t":2.4429806222085735,"gamma_rho":2.4429806222085735,"gamma_claim":2.4429806222085735,"gamma_t_claim":2.4429806222085735,"gamma_rho_claim":2.4429806222085735,"v_ex":5,"rate":0.0196078431372549,"t_count":5,"poly_degree":1,"effective_width":5},"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","N":21,"d":5,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:360"}]},"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"}]}