{"id":"84.12.3.a","row":580,"stored":{"file":"master_catalog.json","row":580,"construction":null,"columns_sha256":null},"parameters":{"n":84,"k":12,"d":3,"N":19,"r":7,"level":3},"gate":{"string":"0+1+2+3+4+5+6+7+8+9+10+11","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6\u00b7T7\u00b7T8\u00b7T9\u00b7T10\u00b7T11","monomials":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11]],"sk_key":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11]],"sk_fingerprint":"418c440ed2e4ddd2","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,12,14,15],[0,12,14,16],[0,12,15,18],[0,12,16,18],[0,14,15,16,18],[0,14,18],[0,15,16],[1,13,14],[1,13,14,15,16,17],[1,13,14,15,16,17,18],[1,13,14,18],[1,15,16,17],[1,15,16,17,18],[1,18],[2,12,13,14,15,16,17,18],[2,12,13,15,17],[2,12,14,16,17,18],[2,12,17],[2,13,14,15,16,18],[2,13,15],[2,14,16,18],[3,12,13],[3,12,13,14,16,17],[3,12,14,15,17,18],[3,12,15,16,18],[3,13,14,15,17,18],[3,13,15,16,18],[3,14,16,17],[4,14],[4,14,15],[4,14,15,17],[4,14,17],[4,15],[4,15,17],[4,17],[5,13],[5,13,14,16],[5,13,14,17,18],[5,13,16,17,18],[5,14,16],[5,14,17,18],[5,16,17,18],[6,12,13,14],[6,12,13,14,15,17,18],[6,12,14,15,17],[6,12,14,18],[6,13,15,17],[6,13,18],[6,15,17,18],[7,12,13,14,16],[7,12,13,15],[7,12,14],[7,12,15,16],[7,13,14,15],[7,13,16],[7,14,15,16],[8,12,13,14,17,18],[8,12,13,16],[8,12,14,15,16,18],[8,12,15,17],[8,13,14,15,18],[8,13,15,16,17],[8,14,16,17,18],[9,13,14,16,17,18],[9,13,14,17],[9,13,15,16],[9,13,15,18],[9,14,15,16,17],[9,14,15,17,18],[9,16,18],[10,12,13,14,17],[10,12,13,14,18],[10,12,16],[10,12,16,17,18],[10,13,14,16,17],[10,13,14,16,18],[10,17,18],[11,13,15,16,17,18],[11,13,15,17,18],[11,13,16,17],[11,13,17],[11,15,16,18],[11,15,18],[11,16]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,6],"A_d":784,"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],[12,2],[14,2]],"CZ":[[13,14],[13,15],[13,16],[13,18],[14,15],[14,17],[14,18],[15,16],[16,17]]},"rotation_powers":[[1,3],[2,3],[4,7],[7,3],[8,7],[9,5],[11,7],[14,3],[15,7],[20,3],[21,5],[25,3],[26,3],[27,3],[28,5],[32,3],[33,3],[34,3],[35,5],[36,3],[38,3],[40,3],[42,7],[45,3],[47,3],[49,7],[50,3],[55,3],[56,5],[60,3],[61,3],[62,3],[63,5],[64,3],[65,3],[67,3],[70,7],[73,3],[75,3],[77,7],[78,3],[79,3],[80,3],[81,3],[82,3],[83,3]]},"metrics":{"gamma":1.7712437491614221,"gamma_t":null,"gamma_rho":1.7712437491614221,"gamma_claim":1.7712437491614221,"gamma_t_claim":null,"gamma_rho_claim":1.7712437491614221,"v_ex":12,"rate":0.14285714285714285,"t_count":null,"poly_degree":null,"effective_width":12},"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:ec65d054eb781ace","N":19,"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"}]}