{"id":"42.2.3.a","row":150,"stored":{"file":"master_catalog.json","row":150,"construction":null,"columns_sha256":null},"parameters":{"n":42,"k":2,"d":3,"N":12,"r":10,"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],[1,6,7,8,9,10],[1,6,8],[1,6,9],[1,6,10],[1,7],[1,7,8,9,10],[1,8],[1,9],[1,10],[2,3,4,5],[2,3,5],[2,4,5],[2,5],[3,4,5],[3,5],[4,5],[5],[6,7,8,9,11],[6,7,8,10,11],[6,7,8,11],[6,7,9,10,11],[6,7,9,11],[6,7,10,11],[6,8,9,10,11],[6,8,9,11],[6,8,10,11],[6,9,10,11],[7,8,9,10,11],[7,11],[8,11],[9,11],[10,11],[11]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,4],"A_d":80,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,1],[1,3],[7,2],[8,2],[9,2],[10,2]],"CZ":[[1,6],[6,11],[7,8],[7,9],[7,10],[8,9],[8,10],[9,10]]},"rotation_powers":null},"metrics":{"gamma":2.771243749161422,"gamma_t":2.771243749161422,"gamma_rho":2.771243749161422,"gamma_claim":2.771243749161422,"gamma_t_claim":2.771243749161422,"gamma_rho_claim":2.771243749161422,"v_ex":2,"rate":0.047619047619047616,"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:848ebd03254b2575","N":12,"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"}]}