{"id":"53.3.3.a","row":309,"stored":{"file":"master_catalog.json","row":309,"construction":null,"columns_sha256":null},"parameters":{"n":53,"k":3,"d":3,"N":17,"r":14,"level":3},"gate":{"string":"0+1+2","human":"T0\u00b7T1\u00b7T2","monomials":[[0],[1],[2]],"sk_key":[[0],[1],[2]],"sk_fingerprint":"b0744d1878b2f54b","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,3,4,5,6],[0,3,4,5,6,7],[0,3,5,6],[0,3,5,6,7],[0,4,5,6],[0,4,5,6,7],[0,5],[0,5,7],[0,6],[0,6,7],[0,7],[1,9],[1,9,10],[1,9,10,11],[1,9,11],[1,10],[1,10,11],[1,11],[2,13],[2,13,14],[2,13,14,15],[2,13,15],[2,14],[2,14,15],[2,15],[3,4,5,6,7,8],[3,4,5,6,8],[3,5,6,7,8],[3,5,6,8],[4,5,6,7,8],[4,5,6,8],[5,7,8],[5,8],[6,7,8],[6,8],[7,8],[8],[9,10,11,12],[9,10,12],[9,11,12],[9,12],[10,11,12],[10,12],[11,12],[12],[13,14,15,16],[13,14,16],[13,15,16],[13,16],[14,15,16],[14,16],[15,16],[16]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,10],"A_d":101,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,3],[1,1],[2,1],[7,2],[8,2]],"CZ":[[0,7],[7,8]]},"rotation_powers":[[0,5],[1,3],[2,7],[4,7],[6,7],[8,7],[11,7],[12,7],[15,7],[18,7],[19,7],[22,7],[25,3],[28,3],[30,3],[32,3],[34,3],[36,3],[37,3],[39,3],[41,3],[43,3],[45,3],[47,3],[49,3],[51,3]]},"metrics":{"gamma":2.61391544087447,"gamma_t":2.61391544087447,"gamma_rho":2.61391544087447,"gamma_claim":2.61391544087447,"gamma_t_claim":2.61391544087447,"gamma_rho_claim":2.61391544087447,"v_ex":3,"rate":0.05660377358490566,"t_count":3,"poly_degree":1,"effective_width":3},"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:467e35b75cc0b3c6","N":17,"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"}]}