{"id":"72.1.4.a","row":509,"stored":{"file":"master_catalog.json","row":509,"construction":null,"columns_sha256":null},"parameters":{"n":72,"k":1,"d":4,"N":10,"r":9,"level":3},"gate":{"string":"0","human":"T0","monomials":[[0]],"sk_key":[[0]],"sk_fingerprint":"bc179efd84e614ba","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,7],[0,8],[0,9],[7,8,9],[4,7,8],[4,7,9],[4,8,9],[5,7,8],[5,7,9],[5,8,9],[6,7,8],[6,7,9],[6,8,9],[0,4,7,8,9],[0,5,7,8,9],[0,6,7,8,9],[4,5,7,8,9],[4,6,7,8,9],[5,6,7,8,9],[4,5,6,7,8,9],[0,1],[0,2],[0,3],[1,7],[1,8],[1,9],[2,7],[2,8],[2,9],[3,7],[3,8],[3,9],[0,1,7,8,9],[0,2,7,8,9],[0,3,7,8,9],[0,1,4,5,6,7],[0,1,4,5,6,8],[0,1,4,5,6,9],[0,2,4,5,6,7],[0,2,4,5,6,8],[0,2,4,5,6,9],[0,3,4,5,6,7],[0,3,4,5,6,8],[0,3,4,5,6,9],[1,2,7,8,9],[1,3,7,8,9],[2,3,7,8,9],[0,1,2,4],[0,1,2,5],[0,1,2,6],[0,1,3,4],[0,1,3,5],[0,1,3,6],[0,2,3,4],[0,2,3,5],[0,2,3,6],[1,2,3,4,7,8],[1,2,3,4,7,9],[1,2,3,4,8,9],[1,2,3,5,7,8],[1,2,3,5,7,9],[1,2,3,5,8,9],[1,2,3,6,7,8],[1,2,3,6,7,9],[1,2,3,6,8,9],[1,2,3,4,5],[1,2,3,4,6],[1,2,3,5,6],[0,1,2,3,4,5,6],[1,2,3,4,5,6,7],[1,2,3,4,5,6,8],[1,2,3,4,5,6,9]]},"distance":{"d":4,"is_exact":true,"upper":4,"witness":[0,1,2,3],"A_d":1109,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,1],[4,2],[5,2],[6,2],[7,3],[8,3],[9,3]],"CZ":[[0,4],[0,5],[0,6],[0,7],[0,8],[0,9],[1,4],[1,5],[1,6],[2,4],[2,5],[2,6],[3,4],[3,5],[3,6]]},"rotation_powers":null},"metrics":{"gamma":3.084962500721156,"gamma_t":3.084962500721156,"gamma_rho":3.084962500721156,"gamma_claim":3.084962500721156,"gamma_t_claim":3.084962500721156,"gamma_rho_claim":3.084962500721156,"v_ex":1,"rate":0.013888888888888888,"t_count":1,"poly_degree":1,"effective_width":1},"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":"T0","N":10,"d":4,"d_is_exact":true,"origin":"ai_campaign/circuits","provenance":"ai_campaign/circuits \u00b7 catalogue.jsonl:301"}]},"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"}]}