{"id":"28.7.2.a","row":56,"stored":{"file":"master_catalog.json","row":56,"construction":null,"columns_sha256":null},"parameters":{"n":28,"k":7,"d":2,"N":10,"r":3,"level":3},"gate":{"string":"0+1+23+456","human":"T0\u00b7T1\u00b7CS23\u00b7CCZ456","monomials":[[0],[1],[2,3],[4,5,6]],"sk_key":[[0],[1],[2,3],[4,5,6]],"sk_fingerprint":"890f2d96708f6890","sk_canonical_frame":true,"relabelled_into_canonical_frame":true},"circuit":{"columns":[[4,5,6,8],[4,5,8],[4,6,8],[4,8],[5,6,8],[5,8],[6,8],[0,2,3,7],[0,2,3,8],[2,3,7,8],[0,2,7],[0,2,8],[2,7,8],[0,3,7],[0,3,8],[3,7,8],[0,1,7,8],[0,1,7,9],[0,1,8],[0,1,9],[0,7,8,9],[0,8],[0,8,9],[1,7],[1,7,8,9],[1,8,9],[7,9],[9]]},"distance":{"d":2,"is_exact":true,"upper":2,"witness":[0,1],"A_d":82,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,2],[1,1],[2,1],[3,1],[4,2],[5,2],[6,2],[7,2],[8,2]],"CZ":[[0,7],[4,5],[4,6],[5,6],[7,8]]},"rotation_powers":[[1,7],[2,7],[4,7],[7,5],[8,3],[9,3],[10,3],[13,3],[16,5],[20,3],[21,3],[22,3],[23,3],[24,3],[25,3]]},"metrics":{"gamma":2.0,"gamma_t":null,"gamma_rho":2.485426827170242,"gamma_claim":2.0,"gamma_t_claim":null,"gamma_rho_claim":2.485426827170242,"v_ex":5,"rate":0.25,"t_count":null,"poly_degree":null,"effective_width":7},"provenance":{"regimes":["borrowed-identity search: symmetry-free"],"discovery":"pre-existing","strongest_claim":"found by the symmetry-free, targeted-output borrowed-identity search of Singh, Gidney and Jones (arXiv:2606.28518; borrowed_identities/), which solves for the check couplings of a chosen output; a verified witness, not a maximum","sources":[{"regime":"borrowed-identity search: symmetry-free","file":"borrowed_identities/circuits/unified_l3.json","label":"k78-0004","N":10,"d":2,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at 4627014, outputs/l3_k78_targets.csv line 4","provenance":"unified search l=3, gluing blocks=3+2+1+1"}]},"references":[{"key":"singh2026borrowed","short":"Singh et al. (2026)","full":"S. Singh, C. Gidney, and C. Jones, \"Borrowed Identities: Malleable Distillation Factories and a Unified Numerical Search,\" arXiv:2606.28518 (2026).","url":"https://arxiv.org/abs/2606.28518","date":"2026-06-26"}]}