{"id":"95.13.3.a","row":641,"stored":{"file":"master_catalog.json","row":641,"construction":null,"columns_sha256":null},"parameters":{"n":95,"k":13,"d":3,"N":20,"r":7,"level":3},"gate":{"string":"0+1+2+3+4+5+6+7+8+9+10+11+12","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6\u00b7T7\u00b7T8\u00b7T9\u00b7T10\u00b7T11\u00b7T12","monomials":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]],"sk_key":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]],"sk_fingerprint":"1bbd29c89d73191c","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,9,10,12,14,16,17,18],[0,9,10,14,15,17],[0,9,12,15,17],[0,9,16,17,18],[0,10,12,14],[0,10,14,15,16,18],[0,12,15,16,18],[1,9,10,11,12,13,15,17,18],[1,9,10,11,13,16,17,18],[1,9,11,12,13,14,17],[1,9,11,13,14,15,16,17],[1,10,12,14,16,18],[1,10,14,15,18],[1,12,15,16],[2,9,10,11,12,13,14,15,17,18],[2,9,10,12,13,14,15],[2,9,11,13,15,17],[2,9,13,15,18],[2,10,11,12,14,17],[2,10,12,14,18],[2,11,17,18],[3,9,10,11,13,14,15,16,18],[3,9,10,14,15,16,17,18],[3,9,11,12,14,15,18,19],[3,9,12,13,14,15,17,18,19],[3,10,11,12,16,17,19],[3,10,12,13,16,19],[3,11,13,17],[4,9,10,11,12,13,19],[4,9,10,12,13,14,15,16],[4,9,11,12,13,14,15,16,19],[4,9,12,13],[4,10,11,19],[4,10,14,15,16],[4,11,14,15,16,19],[5,9,10,12,15],[5,9,10,13,15,17,18,19],[5,9,11,12,13,15,16],[5,9,11,15,16,17,18,19],[5,10,11,12,16,17,18,19],[5,10,11,13,16],[5,12,13,17,18,19],[6,9,10,12,14,15,16,18,19],[6,9,10,12,14,17,18],[6,9,14,15],[6,9,14,16,17,19],[6,10,12,15,17,18],[6,10,12,16,18,19],[6,15,16,17,19],[7,9,10,11,12,14,15,17,18],[7,9,10,11,13,15,16,18],[7,9,10,12,13,15],[7,9,10,14,15,16,17],[7,11,12,16,18],[7,11,13,14,17,18],[7,12,13,14,16,17],[8,9,10,11,13,17,18],[8,9,10,14,16],[8,9,11,13,18],[8,9,14,16,17],[8,10,11,13,14,16,18],[8,10,17],[8,11,13,14,16,17,18],[9,10,11,12,13,14,15,18,19],[9,10,11,12,13,14,17,19],[9,10,11,12,13,16,17],[9,10,11,13,14,15,17,19],[9,10,12,13,14,15,16,17,18],[9,10,12,15,16,17],[9,11,12,13,14,16],[9,11,12,16,19],[9,11,12,18,19],[9,11,14,15,19],[9,12,14,16,17,18,19],[9,12,16,17],[9,13,14],[9,13,15,17,19],[9,16],[10,11,12,13,14,18],[10,11,12,13,16,18,19],[10,11,12,15,16,17,18],[10,11,12,18],[10,11,13,14,15,18],[10,11,15,18],[10,12,13,14,15,16,18,19],[10,13,15,16,17],[10,14,15,16,17,18,19],[11,13,15,16,17,18],[11,13,16,18],[11,14,15,16,17,19],[12,13,14,15,17],[12,13,18,19],[13,14,15,19],[13,14,17,18,19],[13,17,19]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,6],"A_d":1147,"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],[9,3],[10,3],[11,2]],"CZ":[[9,10],[9,15],[9,18],[10,12],[10,16],[10,18],[10,19],[11,12],[11,16],[11,17],[11,18],[12,15],[12,17],[12,18],[12,19]]},"rotation_powers":null},"metrics":{"gamma":1.8103998604915097,"gamma_t":null,"gamma_rho":1.8103998604915097,"gamma_claim":1.8103998604915097,"gamma_t_claim":null,"gamma_rho_claim":1.8103998604915097,"v_ex":13,"rate":0.1368421052631579,"t_count":null,"poly_degree":null,"effective_width":13},"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:8914a4fe0b7711b0","N":20,"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"}]}