{"id":"48.2.3.a","row":246,"stored":{"file":"master_catalog.json","row":246,"construction":null,"columns_sha256":null},"parameters":{"n":48,"k":2,"d":3,"N":14,"r":12,"level":3},"gate":{"string":"0+1","human":"T0\u00b7T1","monomials":[[0],[1]],"sk_key":[[0],[1]],"sk_fingerprint":"68f83724f5668f5b","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1,6],[1,6,7],[1,6,7,8],[1,6,8],[1,7],[1,7,8],[1,8,10],[1,8,10,11],[1,8,11],[1,10,11,12],[1,10,12],[1,11,12],[1,12],[2,3,4,5],[2,3,5],[2,4,5],[2,5],[3,4,5],[3,5],[4,5],[5],[6,7,8,9],[6,7,9],[6,8,9],[6,9],[7,8,9],[7,9],[8,9,10],[8,9,10,11],[8,9,11],[9,10],[9,10,11],[9,11],[10,11,12,13],[10,11,13],[10,12,13],[10,13],[11,12,13],[11,13],[12,13],[13]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,4],"A_d":73,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,1],[1,2],[8,2],[9,2],[10,2],[11,2]],"CZ":[[1,8],[8,9],[10,11]]},"rotation_powers":[[0,7],[1,7],[4,7],[8,3],[9,3],[20,3],[22,3],[24,3],[26,3],[30,3],[31,3],[32,3],[33,3],[34,3],[35,3],[36,3],[37,3],[38,3],[39,3],[40,3],[42,3],[44,3],[46,3]]},"metrics":{"gamma":2.8927892607143724,"gamma_t":2.8927892607143724,"gamma_rho":2.8927892607143724,"gamma_claim":2.8927892607143724,"gamma_t_claim":2.8927892607143724,"gamma_rho_claim":2.8927892607143724,"v_ex":2,"rate":0.041666666666666664,"t_count":2,"poly_degree":1,"effective_width":2},"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:41ba22afb024ef5a","N":14,"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":"wills2026classification","short":"Wills et al. (2026)","full":"A. Wills, S. P. Jain, and S. Singh, \"Classification of Generalised Triorthogonal Codes through Length 54,\" arXiv:2609.30860 (2026).","url":"https://arxiv.org/abs/2609.30860","date":"2026-09-25"},{"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"}]}