{"id":"34.8.2.c","row":83,"stored":{"file":"master_catalog.json","row":83,"construction":null,"columns_sha256":null},"parameters":{"n":34,"k":8,"d":2,"N":11,"r":3,"level":3},"gate":{"string":"0+1+2+3+4+567","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7CCZ567","monomials":[[0],[1],[2],[3],[4],[5,6,7]],"sk_key":[[0],[1],[2],[3],[4],[5,6,7]],"sk_fingerprint":"01f33ec3289d62d9","sk_canonical_frame":true,"relabelled_into_canonical_frame":true},"circuit":{"columns":[[5,6,7,10],[5,6,10],[5,7,10],[5,10],[6,7,10],[6,10],[7,10],[0,1,4,8],[0,1,4,9,10],[0,1,8,10],[0,1,9],[0,4,8,9],[0,4,10],[0,8,9,10],[1,4,8,9],[1,4,10],[1,8,9,10],[2,3,8],[2,3,8,9],[2,3,9,10],[2,3,10],[2,8,9,10],[2,8,10],[2,9],[3,8,9,10],[3,8,10],[3,9],[4,8,9],[4,8,9,10],[4,8,10],[4,9],[4,10],[8,9,10],[10]]},"distance":{"d":2,"is_exact":true,"upper":2,"witness":[0,1],"A_d":101,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,1],[1,1],[2,1],[3,1],[4,3],[5,2],[6,2],[7,2]],"CZ":[[4,8],[4,9],[4,10],[5,6],[5,7],[6,7],[8,9],[8,10]]},"rotation_powers":[[1,3],[2,3],[4,3],[7,5],[8,3],[9,3],[11,3],[14,3],[17,7],[20,3],[22,3],[25,3],[29,3],[31,3],[32,3],[33,3]]},"metrics":{"gamma":2.0874628412503395,"gamma_t":null,"gamma_rho":2.2801079191927354,"gamma_claim":2.0874628412503395,"gamma_t_claim":null,"gamma_rho_claim":2.2801079191927354,"v_ex":7,"rate":0.23529411764705882,"t_count":null,"poly_degree":null,"effective_width":8},"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":"k78-0014","N":11,"d":2,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at 4627014, outputs/l3_k78_targets.csv line 14","provenance":"unified search l=3, gluing blocks=3+1+1+1+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"}]}