{"id":"64.2.4.a","row":469,"stored":{"file":"master_catalog.json","row":469,"construction":null,"columns_sha256":null},"parameters":{"n":64,"k":2,"d":4,"N":11,"r":9,"level":3},"gate":{"string":"01","human":"CS01","monomials":[[0,1]],"sk_key":[[0,1]],"sk_fingerprint":"f076b3dc759b1665","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,1,2,5,6,7],[0,1,3,5,6,7],[0,1,4,5,6,7],[0,1,2,3,4,8],[0,1,2,3,4,9],[0,1,2,3,4,10],[0,1,5,8,9,10],[0,1,6,8,9,10],[0,1,7,8,9,10],[2,3,4,5,6,7],[2,3,4,8,9,10],[5,6,7,8,9,10],[0,1,2,5,8],[0,1,3,6,9],[0,1,4,7,10],[0,2,4,5,8],[0,2,5,7,8],[0,2,3,6,9],[0,3,5,6,9],[0,3,6,8,9],[0,3,4,7,10],[0,4,6,7,10],[0,2,5,8,10],[0,4,7,9,10],[1,2,4,6,8],[1,4,6,7,8],[1,2,3,7,9],[1,2,5,7,9],[1,4,6,8,9],[1,3,4,5,10],[1,3,5,6,10],[1,3,5,8,10],[1,2,7,9,10],[0,1,2,3,4,6,8],[0,1,4,5,6,7,8],[0,1,2,3,4,7,9],[0,1,2,5,6,7,9],[0,1,2,3,4,5,10],[0,1,3,5,6,7,10],[0,1,3,5,8,9,10],[0,1,4,6,8,9,10],[0,1,2,7,8,9,10],[3,5,6,8],[2,4,7,8],[2,3,5,9],[4,6,7,9],[2,6,8,9],[3,4,6,10],[2,5,7,10],[4,5,8,10],[3,7,9,10],[0,1,3,7,8],[0,1,4,5,9],[0,1,2,6,10],[2,4,5,6,7,8],[2,3,5,6,7,9],[2,3,4,6,8,9],[3,4,5,6,7,10],[2,3,4,5,8,10],[2,3,4,7,9,10],[3,5,6,8,9,10],[2,5,7,8,9,10],[4,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10]]},"distance":{"d":4,"is_exact":true,"upper":4,"witness":[0,1,2,9],"A_d":1224,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,3],[1,3]],"CZ":[[0,1]]},"rotation_powers":[[0,7],[1,7],[2,7],[3,7],[4,7],[5,7],[6,7],[7,7],[8,7],[51,3],[52,3],[53,3],[54,3],[55,3],[56,3],[57,3],[58,3],[59,3],[60,3],[61,3],[62,3],[63,3]]},"metrics":{"gamma":2.5,"gamma_t":2.207518749639422,"gamma_rho":3.0,"gamma_claim":2.5,"gamma_t_claim":2.207518749639422,"gamma_rho_claim":3.0,"v_ex":1,"rate":0.03125,"t_count":3,"poly_degree":2,"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":"master_catalog/catalogue_new","label":"CS01","N":11,"d":4,"d_is_exact":true,"origin":"ai_campaign/circuits","provenance":"ai_campaign/circuits \u00b7 catalogue.jsonl:289"}]},"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"}]}