{"id":"70.6.3.a","row":499,"stored":{"file":"master_catalog.json","row":499,"construction":null,"columns_sha256":null},"parameters":{"n":70,"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":[[0,1,2,6,9,11],[0,1,2,6,10,13],[0,1,6,9,13],[0,1,6,10,11],[0,2,5,6,8,9,10,13],[0,2,5,6,8,11],[0,5,7,8,9,10,12],[0,5,7,8,11,12,13],[0,6,7,8,9,10,11],[0,6,7,8,9,12],[0,6,7,9,11,13],[0,6,7,11,12],[0,8,9,10,12],[0,8,9,11],[0,9,12,13],[1,2,6,7,9,11,12,13],[1,2,6,10,12,13],[1,2,7,8,10,11,13],[1,2,8,10,11],[1,4,6,7,8,9,11],[1,4,6,7,10,13],[1,4,8,11,12],[1,4,9,10,12,13],[1,6,7,8,9,10,12,13],[1,6,8,9,10,12],[1,6,8,10,11,12],[1,6,10,11,12],[1,7,8,9,10,11],[2,3,4,5,6,8,9,11,13],[2,3,4,6,12,13],[2,3,5,7,8,11,13],[2,3,7,9,12,13],[2,4,5,6,8,9,11,12,13],[2,4,6,13],[2,5,6,7,8,9,10,12],[2,5,6,7,8,9,11,12,13],[2,5,7,8,9,11,12,13],[2,6,7,8,11,12],[2,6,7,9,13],[2,6,7,13],[2,6,8,11,12,13],[3,4,5,6,7,10,11,12,13],[3,4,5,6,8,10,11,13],[3,4,5,6,11],[3,4,6,7,8,9,10,13],[3,4,6,8,9,12],[3,4,6,9,10,12,13],[3,5,8,9,11,12],[4,5,6,7,8,11],[4,6,7,8,10,11,12,13],[4,8,9,10,11,13],[5,6,7,9,10,12,13],[5,6,7,10,12,13],[5,7,8,9,10,11,12,13],[5,7,8,9,12],[5,7,8,10,11,12,13],[5,7,9,10,12,13],[6,7,8,9,10,11,13],[6,7,8,10,11,13],[6,7,10,11,13],[6,7,11],[6,7,12,13],[6,8,9,10,12,13],[6,9,11,12],[6,11,12],[7,8,9,11],[8,9,10,11,12,13],[8,9,12],[8,10,11,12,13],[8,11,13]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,12,25],"A_d":206,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,1],[2,2],[3,3],[5,2],[6,1],[7,2],[8,3],[9,1],[10,3],[11,3],[13,3]],"CZ":[[0,6],[0,7],[0,9],[0,10],[0,12],[0,13],[1,2],[1,7],[1,11],[2,7],[2,9],[2,10],[2,12],[3,5],[3,8],[3,9],[3,11],[3,12],[4,5],[4,6],[4,7],[4,8],[4,11],[5,7],[5,10],[5,11],[5,12],[5,13],[6,8],[6,9],[6,10],[6,11],[7,8],[7,10],[7,11],[8,9],[8,10],[8,11],[8,13],[9,10],[9,11],[9,13],[10,11],[11,13]]},"rotation_powers":[[0,5],[2,5],[4,5],[6,5],[8,7],[9,7],[10,7],[15,5],[18,3],[19,7],[21,3],[24,3],[29,5],[32,3],[33,3],[36,3],[37,3],[38,3],[41,3],[43,3],[44,3],[45,3],[47,3],[52,3],[53,3],[54,3],[55,3],[56,3],[57,3],[59,3],[61,3],[63,3],[64,3],[65,3],[66,3],[67,3],[68,3],[69,3]]},"metrics":{"gamma":2.236217269879349,"gamma_t":2.236217269879349,"gamma_rho":2.236217269879349,"gamma_claim":2.236217269879349,"gamma_t_claim":2.236217269879349,"gamma_rho_claim":2.236217269879349,"v_ex":6,"rate":0.08571428571428572,"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:a8465291634149d6","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"}]}