{"id":"48.3.3.a","row":248,"stored":{"file":"master_catalog.json","row":248,"construction":null,"columns_sha256":null},"parameters":{"n":48,"k":3,"d":3,"N":9,"r":6,"level":3},"gate":{"string":"012","human":"CCZ012","monomials":[[0,1,2]],"sk_key":[[0,1,2]],"sk_fingerprint":"d0c21becf7c06e56","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[1,7],[2,3,7],[0,2,4,7],[0,2,3,4,7],[5,7],[1,2,3,5,7],[0,1,2,4,5,7],[0,1,2,3,4,5,7],[1,2,6,7],[2,3,6,7],[0,1,2,4,6,7],[0,1,3,4,6,7],[2,5,6,7],[1,2,3,5,6,7],[0,2,4,5,6,7],[0,3,4,5,6,7],[2,8],[0,1,2,3,8],[1,4,8],[0,3,4,8],[2,5,8],[0,1,2,3,5,8],[1,4,5,8],[0,3,4,5,8],[2,6,8],[0,3,6,8],[1,2,4,6,8],[0,1,3,4,6,8],[2,5,6,8],[0,3,5,6,8],[1,2,4,5,6,8],[0,1,3,4,5,6,8],[1,7,8],[3,7,8],[4,7,8],[2,3,4,7,8],[1,2,5,7,8],[2,3,5,7,8],[2,4,5,7,8],[3,4,5,7,8],[2,6,7,8],[2,3,6,7,8],[2,4,6,7,8],[1,3,4,6,7,8],[5,6,7,8],[3,5,6,7,8],[4,5,6,7,8],[1,2,3,4,5,6,7,8]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,16,32],"A_d":224,"certified":null},"clifford":{"kind":"required","correction":{"S":[[1,2],[2,2]],"CZ":[[1,3],[1,5],[1,6],[2,5],[2,6]]},"rotation_powers":null},"metrics":{"gamma":2.5237190142858297,"gamma_t":1.752475265124407,"gamma_rho":2.8927892607143724,"gamma_claim":2.5237190142858297,"gamma_t_claim":1.752475265124407,"gamma_rho_claim":2.8927892607143724,"v_ex":2,"rate":0.0625,"t_count":7,"poly_degree":3,"effective_width":3},"provenance":{"regimes":["AI search: punctured r=7 simplex parents"],"discovery":"AI search","strongest_claim":"found by the 48 < n < 128 AI campaigns, from punctured r=7 simplex parents with free-row appending; a verified witness, not a maximum","sources":[{"regime":"AI search: punctured r=7 simplex parents","file":"magic-states-AI/campaign_48to128/found/n48_ccz1_VALIDATION_not_a_record.json","label":"11","N":9,"d":3,"d_is_exact":true,"origin":null,"provenance":"n48_ccz1_VALIDATION_not_a_record.json[0]"}]},"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"}]}