{"id":"61.7.3.a","row":425,"stored":{"file":"master_catalog.json","row":425,"construction":null,"columns_sha256":null},"parameters":{"n":61,"k":7,"d":3,"N":15,"r":8,"level":3},"gate":{"string":"0+1+2+3+4+5+6","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6","monomials":[[0],[1],[2],[3],[4],[5],[6]],"sk_key":[[0],[1],[2],[3],[4],[5],[6]],"sk_fingerprint":"4227720e4bdc2b66","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,4,7,8],[0,4,7,8,10,11],[0,4,10,11,13],[0,4,13],[0,7,8,10,11,13],[0,7,8,13],[0,10,11],[1,7,8,9,12,13],[1,7,8,11,12,13],[1,7,9,11,12,14],[1,7,12,14],[1,8,9,13,14],[1,8,11,13,14],[1,9,11],[2,6,7,8,9,12],[2,6,7,11,12],[2,6,8,9,11,13,14],[2,6,13,14],[2,7,8,9,12,13,14],[2,7,11,12,13,14],[2,8,9,11],[3,7,9,11,13,14],[3,7,9,12,13],[3,7,11,14],[3,7,12],[3,9,11,12,13,14],[3,9,13],[3,11,12,14],[4,5,6,7,9,11,13],[4,5,6,8,9,11,12,13,14],[4,5,7],[4,5,8,12,14],[4,6,7,8,11,12],[4,6,7,9,11,12,13],[4,6,7,11,13],[4,6,9,11,12,14],[4,7,8,13,14],[4,7,10,11,13],[4,7,13,14],[4,8,9,12,14],[4,8,10,11],[4,9,13,14],[4,14],[5,6,7,8,9,11,12,13,14],[5,6,9,11,13],[5,7,8,12,14],[6,7,8,9,11,13,14],[6,7,8,9,14],[6,7,8,11,14],[6,7,9,12,13,14],[6,7,9,14],[7,8,11,12,14],[7,9,13],[7,10,11],[8,9,11,13],[8,10,11,13],[8,11,12,13,14],[8,13,14],[9],[9,14],[11,12,13,14]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,6],"A_d":204,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,1],[1,1],[2,1],[3,1],[4,3],[5,1],[7,3],[8,2],[9,2],[11,3],[13,3]],"CZ":[[4,6],[4,7],[4,9],[4,11],[4,12],[4,13],[6,13],[6,14],[7,9],[7,11],[7,13],[9,11],[9,13],[11,12],[13,14]]},"rotation_powers":null},"metrics":{"gamma":1.970634897724171,"gamma_t":null,"gamma_rho":1.970634897724171,"gamma_claim":1.970634897724171,"gamma_t_claim":null,"gamma_rho_claim":1.970634897724171,"v_ex":7,"rate":0.11475409836065574,"t_count":null,"poly_degree":null,"effective_width":7},"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:0b316e69636eda22","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"}]}