{"id":"100.14.3.a","row":665,"stored":{"file":"master_catalog.json","row":665,"construction":null,"columns_sha256":null},"parameters":{"n":100,"k":14,"d":3,"N":21,"r":7,"level":3},"gate":{"string":"0+1+2+3+4+5+6+7+8+9+10+11+12+13","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6\u00b7T7\u00b7T8\u00b7T9\u00b7T10\u00b7T11\u00b7T12\u00b7T13","monomials":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13]],"sk_key":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13]],"sk_fingerprint":"f9f4dff44ba31df9","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,13,14,16,19],[0,13,14,17,20],[0,13,15,16,18,20],[0,13,15,17,18,19],[0,14,15,16,17,18],[0,14,15,18,19,20],[0,16,17,19,20],[1,12,13,14,15,16,17],[1,12,13,16,18,20],[1,12,14,15,16,17,19,20],[1,12,16,18,19],[1,13,14,15,17,18,19],[1,13,19,20],[1,14,15,17,18,20],[2,12,13,14,15],[2,12,13,14,16,20],[2,12,13,15,18,19],[2,12,13,16,18,19,20],[2,14,15,16,18,19,20],[2,14,18,19],[2,15,16,20],[3,12,13,14,15,16,18,20],[3,12,13,15],[3,12,14,15,17],[3,12,15,16,17,18,20],[3,13,14,17],[3,13,16,17,18,20],[3,14,16,18,20],[4,12,14,15,18,19],[4,12,14,16,17,18],[4,12,15,17,19],[4,12,16],[4,14,15,16,18,19],[4,14,17,18],[4,15,16,17,19],[5,12,13,14,16],[5,12,13,16,17,18,19],[5,12,14,15,17,18],[5,12,15,19],[5,13,14,15,16,19],[5,13,15,16,17,18],[5,14,17,18,19],[6,12,13,15,16,17,20],[6,12,13,15,18,20],[6,12,14,15,16,17,18,20],[6,12,14,15,20],[6,13,14,16,17],[6,13,14,18],[6,16,17,18],[7,12,13,14,15,16,17,18,19],[7,12,13,14,15,18],[7,12,15,16,17,18,19],[7,12,15,18],[7,13,14],[7,13,14,16,17,19],[7,16,17,19],[8,12,13,14,15,18,20],[8,12,13,14,19],[8,12,14,15,17,19],[8,12,14,17,18,20],[8,13,15,17],[8,13,17,18,19,20],[8,15,18,19,20],[9,12,14,15,16,20],[9,12,14,18,20],[9,12,15,17,18],[9,12,16,17],[9,14,15,17,20],[9,14,16,17,18,20],[9,15,16,18],[10,14,15,16],[10,14,15,19],[10,14,16,17,20],[10,14,17,19,20],[10,15,16,17,19,20],[10,15,17,20],[10,16,19],[11,12,13,14,15,17,19,20],[11,12,13,14,16,17,19,20],[11,12,13,15,20],[11,12,13,16,20],[11,14,15,16,17,19],[11,14,17,19],[11,15,16],[12,13,14,15,16,18],[12,13,14,16,17,18,19],[12,13,14,16,18,19],[12,13,15,17,19,20],[12,14,16,18,19,20],[13,14,16,18],[13,15,16,17],[13,15,16,18,19],[13,16,17,20],[13,16,18],[14,15,16,17,20],[14,18,19,20],[14,20],[15,16,18,19,20],[15,16,19],[15,17,18,20]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,6],"A_d":1288,"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],[12,2],[13,2],[17,3],[18,3],[19,2],[20,2]],"CZ":[[12,14],[12,19],[13,15],[13,16],[13,18],[13,19],[13,20],[17,18],[17,19],[17,20],[18,19],[18,20]]},"rotation_powers":[[0,5],[1,7],[2,3],[4,7],[8,7],[9,7],[11,7],[14,3],[16,7],[19,3],[21,7],[24,3],[25,3],[28,7],[29,3],[34,3],[35,7],[37,3],[40,3],[42,5],[43,3],[45,3],[47,3],[49,5],[53,3],[54,3],[55,3],[56,7],[57,3],[62,3],[63,7],[65,3],[68,3],[70,5],[74,3],[75,3],[76,3],[77,7],[78,3],[83,3],[84,3],[85,3],[89,3],[90,3],[92,3],[93,3],[95,3]]},"metrics":{"gamma":1.7896330458458893,"gamma_t":null,"gamma_rho":1.7896330458458893,"gamma_claim":1.7896330458458893,"gamma_t_claim":null,"gamma_rho_claim":1.7896330458458893,"v_ex":14,"rate":0.14,"t_count":null,"poly_degree":null,"effective_width":14},"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":"/private/tmp/claude-501/-Users-shubhamjain-Documents-Claude-remote-magic-states-AI/25937cc1-0367-40c1-acc9-031067b831d4/scratchpad/msai_for_merge.jsonl","label":"msAI:33833ccae6d61927","N":21,"d":3,"d_is_exact":true,"origin":"magic-states-AI/master_catalogue/master_catalogue.jsonl","provenance":"magic-states-AI/master_catalogue/master_catalogue.jsonl","notes":"gamma_campaign"}]},"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"}]}