{"id":"99.13.3.b","row":655,"stored":{"file":"master_catalog.json","row":655,"construction":null,"columns_sha256":null},"parameters":{"n":99,"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":[[0,13,14,15,17,18],[0,13,14,17],[0,13,15,17],[0,13,17,18],[0,14,15],[0,14,18],[0,15,18],[1,14,15,17],[1,14,15,17,18,19],[1,14,16,17],[1,14,16,17,18,19],[1,15,16],[1,15,16,18,19],[1,18,19],[2,14,15,16,17,18],[2,14,15,16,19],[2,14,17],[2,14,18,19],[2,15,16,17,19],[2,15,16,18],[2,17,18,19],[3,14,15,18],[3,14,15,18,19],[3,14,17,18],[3,14,17,18,19],[3,15,17],[3,15,17,19],[3,19],[4,14,15,16],[4,14,15,16,17,19],[4,14,16,17,18],[4,14,16,18,19],[4,15,17,18],[4,15,18,19],[4,17,19],[5,13,15,16,17,19],[5,13,15,16,18,19],[5,13,17],[5,13,18],[5,15,16,17,18,19],[5,15,16,19],[5,17,18],[6,13],[6,13,14,15,16,18,19],[6,13,14,15,19],[6,13,16,18],[6,14,15,16,18,19],[6,14,15,19],[6,16,18],[7,13,14,15,16,17,18,19],[7,13,14,15,17],[7,13,14,16],[7,13,14,18,19],[7,15,16,17],[7,15,17,18,19],[7,16,18,19],[8,13,14,16,18],[8,13,14,17,19],[8,13,15],[8,13,15,16,17,18,19],[8,14,15,16,18],[8,14,15,17,19],[8,16,17,18,19],[9,13,15,16,19],[9,13,15,17,18,19],[9,13,16,19],[9,13,17,18,19],[9,15],[9,15,16,17,18],[9,16,17,18],[10,14,16,17,19],[10,14,16,19],[10,14,17,19],[10,14,19],[10,16],[10,16,17],[10,17],[11,13,14,15,16,18],[11,13,14,15,18,19],[11,13,16,17],[11,13,17,19],[11,14,15,16,17,18,19],[11,14,15,17,18],[11,16,19],[12,13,14,15],[12,13,14,15,18],[12,13,15,16],[12,13,15,16,18],[12,14,16],[12,14,16,18],[12,18],[13,14],[13,14,15,16,17],[13,15,19],[13,16,17,19],[14],[14,15,16,17],[15,19],[16,17,19]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,6],"A_d":1281,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,1],[1,1],[2,1],[3,1],[4,1],[5,1],[6,1],[7,1],[8,1],[9,1],[10,1],[11,1],[12,1],[13,2],[15,2]],"CZ":[[14,15],[14,16],[14,17],[14,19],[15,16],[15,18],[15,19],[16,17],[17,18]]},"rotation_powers":[[0,5],[1,7],[2,7],[4,3],[7,3],[9,3],[11,7],[14,7],[16,3],[19,3],[21,5],[25,3],[26,3],[27,3],[28,5],[32,3],[33,3],[34,3],[35,5],[39,3],[40,3],[41,3],[42,5],[46,3],[47,3],[48,3],[49,5],[51,3],[52,3],[55,3],[56,5],[57,3],[58,3],[61,3],[63,5],[64,3],[65,3],[68,3],[70,7],[72,3],[74,3],[77,5],[78,3],[79,3],[81,3],[84,7],[85,3],[90,3],[92,3],[93,3],[95,3],[98,3]]},"metrics":{"gamma":1.8479408191713451,"gamma_t":null,"gamma_rho":1.8479408191713451,"gamma_claim":1.8479408191713451,"gamma_t_claim":null,"gamma_rho_claim":1.8479408191713451,"v_ex":13,"rate":0.13131313131313133,"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:c77eb049d8fb6695","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"}]}