{"id":"76.1.4.a","row":529,"stored":{"file":"master_catalog.json","row":529,"construction":null,"columns_sha256":null},"parameters":{"n":76,"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":[[8],[9],[8,9],[1,2],[2,3],[3,4],[4,5],[5,6],[1,7],[6,7],[1,2,8,9],[2,3,8,9],[3,4,8,9],[4,5,8,9],[5,6,8,9],[1,7,8,9],[6,7,8,9],[0,1,4],[0,1,5],[0,2,5],[0,2,6],[0,3,6],[0,3,7],[0,4,7],[0,1,4,8,9],[0,1,5,8,9],[0,2,5,8,9],[0,2,6,8,9],[0,3,6,8,9],[0,3,7,8,9],[0,4,7,8,9],[1,3,4],[2,4,5],[1,2,6],[3,5,6],[2,3,7],[1,5,7],[4,6,7],[1,3,5,8],[1,3,5,9],[1,3,6,8],[1,3,6,9],[1,4,6,8],[1,4,6,9],[2,4,6,8],[2,4,6,9],[2,4,7,8],[2,4,7,9],[2,5,7,8],[2,5,7,9],[3,5,7,8],[3,5,7,9],[0,1,2,3,5,8,9],[0,2,3,4,6,8,9],[0,1,4,5,6,8,9],[0,1,2,4,7,8,9],[0,3,4,5,7,8,9],[0,1,3,6,7,8,9],[0,2,5,6,7,8,9],[1,2,4,5,8],[1,2,4,5,9],[1,2,5,6,8],[1,2,5,6,9],[2,3,5,6,8],[2,3,5,6,9],[1,3,4,7,8],[1,3,4,7,9],[1,4,5,7,8],[1,4,5,7,9],[2,3,6,7,8],[2,3,6,7,9],[3,4,6,7,8],[3,4,6,7,9],[1,2,3,4,5,6,7],[1,2,3,4,5,6,7,8],[1,2,3,4,5,6,7,9]]},"distance":{"d":4,"is_exact":true,"upper":4,"witness":[0,3,57,70],"A_d":973,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,2],[8,1],[9,1]],"CZ":[[0,8],[0,9],[8,9]]},"rotation_powers":[[0,3],[1,3],[17,3],[24,3],[63,3],[64,3],[67,3],[68,3],[69,3],[70,3]]},"metrics":{"gamma":3.123963756721793,"gamma_t":3.123963756721793,"gamma_rho":3.123963756721793,"gamma_claim":3.123963756721793,"gamma_t_claim":3.123963756721793,"gamma_rho_claim":3.123963756721793,"v_ex":1,"rate":0.013157894736842105,"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:310"}]},"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"}]}