{"id":"64.8.3.a","row":476,"stored":{"file":"master_catalog.json","row":476,"construction":null,"columns_sha256":null},"parameters":{"n":64,"k":8,"d":3,"N":15,"r":7,"level":3},"gate":{"string":"0+1+2+3+4+5+6+7","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6\u00b7T7","monomials":[[0],[1],[2],[3],[4],[5],[6],[7]],"sk_key":[[0],[1],[2],[3],[4],[5],[6],[7]],"sk_fingerprint":"2daea1c2f1d6f117","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,8,9,10],[0,8,9,10,12,13],[0,8,11,12],[0,8,11,13],[0,9,10,11,12],[0,9,10,11,13],[0,12,13],[1,2,6,8,9,12,14],[1,2,6,8,10,11,12,13],[1,2,6,9,10,11,14],[1,2,6,13],[1,8,9,12,13,14],[1,8,10,11,12],[1,9,10,11,13,14],[2,8,9,10,11,14],[2,8,9,11,12],[2,8,9,11,13,14],[2,8,10,11,13,14],[2,8,10,12,13,14],[2,8,11,14],[2,9,13],[2,10,13],[2,11,13,14],[3,8,9,10,11,13,14],[3,8,9,10,12,13,14],[3,8,10,11,12,14],[3,8,10,14],[3,9,11,13],[3,9,12,13],[3,11,12],[4,5,6,8,9,11,13],[4,5,6,8,9,11,14],[4,5,6,9,11,12],[4,5,6,9,11,12,13,14],[4,8,12,13],[4,8,12,14],[4,13,14],[5,8,9,10,12],[5,8,9,13],[5,8,10,11,13],[5,8,11,12,13,14],[5,9,10,11,12,13],[5,9,10,12,13,14],[5,9,10,13],[5,9,11,12,14],[5,10,11,12],[5,10,11,13],[5,10,13,14],[6,8,9,13,14],[6,8,10,11,12,13,14],[6,8,10,12,14],[6,8,10,13],[6,8,13],[6,8,14],[6,9,10,11,12,13,14],[6,11,12,14],[6,11,13],[7,8,9,10,11],[7,8,9,10,11,12,13,14],[7,8,9,12,13],[7,8,9,14],[7,10,11,12,13],[7,10,11,14],[7,12,13,14]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,6],"A_d":328,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,1],[1,1],[2,2],[3,1],[4,1],[5,1],[7,1],[8,2],[11,2]],"CZ":[[2,9],[2,10],[5,8],[5,9],[5,11],[5,13],[5,14],[6,8],[6,10],[6,11],[6,13],[6,14],[8,9],[8,10],[8,11],[8,12],[9,11],[11,12],[11,14],[12,13],[13,14]]},"rotation_powers":null},"metrics":{"gamma":1.892789260714372,"gamma_t":null,"gamma_rho":1.892789260714372,"gamma_claim":1.892789260714372,"gamma_t_claim":null,"gamma_rho_claim":1.892789260714372,"v_ex":8,"rate":0.125,"t_count":null,"poly_degree":null,"effective_width":8},"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:8019c4cfb79e0ce4","N":15,"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"}]}