{"id":"66.6.3.a","row":484,"stored":{"file":"master_catalog.json","row":484,"construction":null,"columns_sha256":null},"parameters":{"n":66,"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":[[0,1,3,6,7,8],[0,1,3,6,8,9,10,12],[0,1,6,7,8,10,13],[0,1,6,8,9,12,13],[0,3,7,9,12,13],[0,3,10,13],[0,7,9,10,12],[1,3,7,10,13],[1,3,9,12,13],[1,7,9,10,13],[1,7,9,12],[1,7,10,12,13],[1,9,10,12],[1,9,10,13],[1,9,12],[1,10,12,13],[2,5,6,7,9,10,11,12],[2,5,6,8,9,10,12,13],[2,5,7,9,11,12,13],[2,5,8,9,12],[2,6,7,8,10,11],[2,6,10,13],[2,7,8,11,13],[3,4,5,6,7,8,10],[3,4,5,6,7,9,10,13],[3,4,5,6,7,9,12,13],[3,4,5,7,8,13],[3,4,6,7,8,10,11,12,13],[3,4,6,7,9,10,12],[3,4,6,7,9,11,12],[3,4,6,9,10,12],[3,4,6,9,12],[3,4,7,8,10],[3,5,6,7,8,11,13],[3,5,6,8,10,11,12,13],[3,5,6,8,10,11,13],[3,5,7,8,11],[3,6,7,8,11],[3,6,7,10,13],[3,6,9,10,13],[3,7,9,10,11,12],[3,8,9,12,13],[4,5,6,7,8,9,10,11,12,13],[4,5,6,7,8,9,10,11,13],[4,5,6,7,8,13],[4,5,7,8],[4,6,7,10,12,13],[4,6,8,9,12],[4,6,9,12,13],[4,7,8,9,10,12,13],[4,7,8,10,11,13],[4,7,9,11,12],[4,8,10,13],[5,6,7,9,10,11,12,13],[5,6,7,9,11,12,13],[5,6,10,12,13],[6,7,9,12],[6,8,9,10,11,12,13],[6,8,9,10,11,13],[7,8,9,10,13],[7,8,10,11],[7,8,10,12,13],[7,9,10,11,12,13],[8,9,10,12],[8,9,10,13],[8,10,12,13]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,6],"A_d":216,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,1],[1,2],[2,1],[4,2],[5,3],[6,3],[8,3],[9,1],[10,3],[11,1],[12,1],[13,3]],"CZ":[[1,7],[3,4],[3,10],[3,13],[4,6],[4,11],[5,6],[5,7],[5,9],[5,10],[5,11],[5,12],[5,13],[6,8],[6,10],[6,11],[6,13],[7,11],[8,9],[8,10],[8,11],[8,12],[8,13],[9,10],[9,12],[9,13],[10,11],[10,12],[10,13],[11,13],[12,13]]},"rotation_powers":null},"metrics":{"gamma":2.182658338644138,"gamma_t":2.182658338644138,"gamma_rho":2.182658338644138,"gamma_claim":2.182658338644138,"gamma_t_claim":2.182658338644138,"gamma_rho_claim":2.182658338644138,"v_ex":6,"rate":0.09090909090909091,"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:385f12d9937404b9","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"}]}