{"id":"74.6.3.a","row":520,"stored":{"file":"master_catalog.json","row":520,"construction":null,"columns_sha256":null},"parameters":{"n":74,"k":6,"d":3,"N":14,"r":8,"level":3},"gate":{"string":"0+1+2+3+4+5","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5","monomials":[[0],[1],[2],[3],[4],[5]],"sk_key":[[0],[1],[2],[3],[4],[5]],"sk_fingerprint":"4d2289762630b30d","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,7],[0,7,8,9,11,12,13],[0,7,8,9,11,13],[0,7,12],[0,8,9,11,12,13],[0,8,9,11,13],[0,12],[1,7,8],[1,7,8,10,11],[1,7,10,11,13],[1,7,13],[1,8,10,11,13],[1,8,13],[1,10,11],[2,6,7,8,9,10],[2,6,7,10],[2,6,8,9,10,11,12],[2,6,10,11,12],[2,7,8,9,11,12],[2,7,11,12],[2,8,9],[3,6,7,8,9,12,13],[3,6,7,8,12],[3,6,8,9,11],[3,6,8,11,13],[3,7,9,11,12],[3,7,11,12,13],[3,9,13],[4,6,7,8,10,11,12],[4,6,7,8,10,13],[4,6,8,9,11,13],[4,6,8,9,12],[4,7,9,10,11],[4,7,9,10,12,13],[4,11,12,13],[5,6,8,9,10,13],[5,6,8,10,11,12,13],[5,6,9,12,13],[5,6,11,13],[5,8,9,10,11],[5,8,10,12],[5,9,11,12],[6,7,8,9,10,11,12,13],[6,7,8,9,10,13],[6,7,8,9,11],[6,7,8,10],[6,7,8,11,13],[6,7,9,10,11,12],[6,7,9,10,13],[6,7,9,12],[6,7,10,11,12,13],[6,7,12,13],[6,8,10],[6,8,11],[6,8,12,13],[6,9,10,11,12,13],[6,9,11],[6,12],[7,8,9,10,11,13],[7,8,9,13],[7,8,11,13],[7,9,11,12,13],[7,9,12],[7,10,12],[8,9,10,12,13],[8,11,12,13],[8,11,13],[9],[9,10,11,13],[9,10,12],[9,10,12,13],[9,12],[10,12],[10,12,13]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,4],"A_d":462,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,1],[1,1],[2,1],[3,1],[4,1],[5,1],[7,2],[8,1],[9,1],[11,1],[12,1],[13,1]],"CZ":[[7,8],[7,9],[7,11],[7,12],[7,13],[8,11],[8,12],[8,13],[11,12],[11,13],[12,13]]},"rotation_powers":[[0,3],[1,3],[4,7],[7,3],[8,5],[9,3],[11,3],[14,3],[15,7],[20,3],[21,5],[25,3],[26,3],[27,3],[28,5],[32,3],[33,3],[34,3],[35,7],[37,3],[40,3],[46,3],[48,3],[49,3],[50,3],[52,3],[53,3],[54,3],[56,3],[60,3],[61,3],[62,3],[63,3],[64,3],[66,3],[69,3],[70,3],[71,3],[72,3]]},"metrics":{"gamma":2.2867991282182727,"gamma_t":2.2867991282182727,"gamma_rho":2.2867991282182727,"gamma_claim":2.2867991282182727,"gamma_t_claim":2.2867991282182727,"gamma_rho_claim":2.2867991282182727,"v_ex":6,"rate":0.08108108108108109,"t_count":6,"poly_degree":1,"effective_width":6},"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:839464f6d79edba5","N":14,"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"}]}