{"id":"80.8.3.a","row":561,"stored":{"file":"master_catalog.json","row":561,"construction":null,"columns_sha256":null},"parameters":{"n":80,"k":8,"d":3,"N":15,"r":7,"level":3},"gate":{"string":"0+1+2+3+4+5+6+7","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6\u00b7T7","monomials":[[0],[1],[2],[3],[4],[5],[6],[7]],"sk_key":[[0],[1],[2],[3],[4],[5],[6],[7]],"sk_fingerprint":"2daea1c2f1d6f117","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,8,9,11,12,13,14],[0,8,9,12,13,14],[0,8,10,11,13],[0,8,10,13],[0,9,10,11,12,14],[0,9,10,12,14],[0,11],[1,8,9,11,13],[1,8,9,12,14],[1,8,11],[1,8,12,13,14],[1,9,11,12,14],[1,9,13],[1,11,12,13,14],[2,8,9,10,12,13,14],[2,8,9,11,12,14],[2,8,10,11,12,13,14],[2,8,12,14],[2,9,10,13],[2,9,11],[2,10,11,13],[3,8,9,10,11,12,14],[3,8,9,11],[3,8,10,12,13,14],[3,8,13],[3,9,10,11,12,13,14],[3,9,11,13],[3,10,12,14],[4,8,9,10,11,13],[4,8,9,13],[4,8,10,12,14],[4,8,11,12,14],[4,9,10,12,13,14],[4,9,11,12,13,14],[4,10,11],[5,8,10,11],[5,8,10,11,12,14],[5,8,11,12,13,14],[5,8,11,13],[5,10,12,13,14],[5,10,13],[5,12,14],[6,9,10,11],[6,9,10,11,13],[6,9,12,13,14],[6,9,12,14],[6,10,11,12,13,14],[6,10,11,12,14],[6,13],[7,8,9,10,11],[7,8,9,10,11,12,13,14],[7,8,9,10,12,14],[7,8,9,10,13],[7,11,12,14],[7,11,13],[7,12,13,14],[8,9,10,11,14],[8,9,10,12,13],[8,9,10,13,14],[8,9,11,14],[8,9,12,13],[8,9,13,14],[8,10,11,14],[8,10,12,13],[8,10,13,14],[8,11,14],[8,12,13],[8,13,14],[9,10,11,14],[9,10,12,13],[9,10,13,14],[9,11,14],[9,12,13],[9,13,14],[10,11,14],[10,12,13],[10,13,14],[11,14],[12,13],[13,14]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,6],"A_d":640,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,1],[1,1],[2,1],[3,1],[4,1],[5,1],[6,1],[7,1]],"CZ":[]},"rotation_powers":[[0,7],[1,7],[2,7],[3,7],[4,7],[5,7],[6,7],[7,7],[8,7],[9,7],[10,7],[11,7],[12,7],[13,7],[14,7],[15,7],[16,7],[17,7],[18,7],[19,7],[20,7],[21,7],[22,7],[23,7],[24,7],[25,7],[26,7],[27,7],[28,7],[29,7],[30,7],[31,7],[32,7],[33,7],[34,7],[35,7],[36,7],[37,7],[38,7],[39,7],[40,7],[41,7],[42,7],[43,7],[44,7],[45,7],[46,7],[47,7],[48,7],[49,7],[50,7],[51,7],[52,7],[53,7],[54,7],[55,7],[56,7],[57,7],[58,7],[59,7],[60,7],[61,7],[62,7],[63,7],[64,7],[65,7],[66,7],[67,7],[68,7],[69,7],[70,7],[71,7],[72,7],[73,7],[74,7],[75,7],[76,7],[77,7],[78,7],[79,7]]},"metrics":{"gamma":2.095903274289385,"gamma_t":null,"gamma_rho":2.095903274289385,"gamma_claim":2.095903274289385,"gamma_t_claim":null,"gamma_rho_claim":2.095903274289385,"v_ex":8,"rate":0.1,"t_count":null,"poly_degree":null,"effective_width":8},"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:2ab2ac6864f4a388","N":15,"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"}]}