{"id":"92.14.3.a","row":626,"stored":{"file":"master_catalog.json","row":626,"construction":null,"columns_sha256":null},"parameters":{"n":92,"k":14,"d":3,"N":21,"r":7,"level":3},"gate":{"string":"0+1+2+3+4+5+6+7+8+9+10+11+12+13","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6\u00b7T7\u00b7T8\u00b7T9\u00b7T10\u00b7T11\u00b7T12\u00b7T13","monomials":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13]],"sk_key":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13]],"sk_fingerprint":"f9f4dff44ba31df9","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,12,14],[0,12,14,17,19],[0,12,16,17],[0,12,16,19],[0,14,16,17],[0,14,16,19],[0,17,19],[1,11,12,13,14,15,16,19,20],[1,11,12,15,16,18,19],[1,11,13,14,15],[1,11,15,18,20],[1,12,13,14,16,18,19],[1,12,16,19,20],[1,13,14,18,20],[2,11,12,13,14,15,16,17,18,19,20],[2,11,12,15,16,17,19,20],[2,11,13,14,16,20],[2,11,16,18,20],[2,12,13,14,15,17,19],[2,12,15,17,18,19],[2,13,14,18],[3,11,12,13,14,15,16,18,19],[3,11,12,14,16,17,18,19],[3,11,13,14,16],[3,11,14,15,16,17],[3,12,13,17,18,19],[3,12,15,18,19],[3,13,15,17],[4,11,12,13,15,20],[4,11,12,13,16,18,19],[4,11,12,15,16,17,18,19,20],[4,11,12,17],[4,13,15,17,20],[4,13,16,17,18,19],[4,15,16,18,19,20],[5,12,13,14,15,17],[5,12,13,15,16,19,20],[5,12,14,18,19,20],[5,12,16,17,18],[5,13,14,15,16,18],[5,13,15,17,18,19,20],[5,14,16,17,19,20],[6,11,12,13,14,15,16,17,18,19],[6,11,12,13,15,19,20],[6,11,12,14,16,18],[6,11,12,17,20],[6,13,14,15,16,18,19,20],[6,13,15,17,19],[6,14,16,17,18,20],[7,12,13,14,15,18],[7,12,13,14,16,18,20],[7,12,14,15,16,17,20],[7,12,14,17],[7,13,15,17,18],[7,13,16,17,18,20],[7,15,16,20],[8,11,12,13,16,17,19],[8,11,12,18,20],[8,11,13,15,16,17],[8,11,15,18,19,20],[8,12,13,15,16,17,18,20],[8,12,15,19],[8,13,16,17,18,19,20],[9,11,12,13,15,17,19,20],[9,11,12,13,16,18,19,20],[9,11,15,17,18,20],[9,11,16,20],[9,12,13,15,16,17,19],[9,12,13,18,19],[9,15,16,17,18],[10,11,12,13,14,15,16],[10,11,12,19],[10,11,13,14,15,17,19,20],[10,11,16,17,20],[10,12,13,14,15,17,20],[10,12,16,17,19,20],[10,13,14,15,16,19],[11,12,13,15,16,17,20],[11,12,14,20],[11,13,14,17,18,20],[11,15,16,19],[11,18,19,20],[12,13,14,17,18,19,20],[12,15,16,17,18,19],[12,17,19,20],[12,19,20],[12,20],[13,15,16,18,20],[13,17,18],[13,17,18,19,20],[13,17,18,20],[14,19,20]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,6],"A_d":1008,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,1],[1,1],[2,1],[3,1],[4,1],[5,1],[6,1],[7,1],[8,1],[9,1],[10,1],[11,2],[12,3],[13,1],[14,2],[15,2],[18,2]],"CZ":[[11,12],[11,13],[11,14],[11,16],[11,19],[11,20],[12,16],[12,17],[12,18],[13,14],[13,17],[13,18],[15,20],[16,19],[17,18]]},"rotation_powers":null},"metrics":{"gamma":1.713735834610306,"gamma_t":null,"gamma_rho":1.713735834610306,"gamma_claim":1.713735834610306,"gamma_t_claim":null,"gamma_rho_claim":1.713735834610306,"v_ex":14,"rate":0.15217391304347827,"t_count":null,"poly_degree":null,"effective_width":14},"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:f136ce6a264c1ec7","N":21,"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"}]}