{"id":"56.8.2.a","row":337,"stored":{"file":"master_catalog.json","row":337,"construction":null,"columns_sha256":null},"parameters":{"n":56,"k":8,"d":2,"N":11,"r":3,"level":3},"gate":{"string":"0+1+2+3+4+5+6+7","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6\u00b7T7","monomials":[[0],[1],[2],[3],[4],[5],[6],[7]],"sk_key":[[0],[1],[2],[3],[4],[5],[6],[7]],"sk_fingerprint":"2daea1c2f1d6f117","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,8],[0,8,9],[0,8,9,10],[0,8,10],[0,9],[0,9,10],[0,10],[1,8],[1,8,9],[1,8,9,10],[1,8,10],[1,9],[1,9,10],[1,10],[2,8],[2,8,9],[2,8,9,10],[2,8,10],[2,9],[2,9,10],[2,10],[3,8],[3,8,9],[3,8,9,10],[3,8,10],[3,9],[3,9,10],[3,10],[4,8],[4,8,9],[4,8,9,10],[4,8,10],[4,9],[4,9,10],[4,10],[5,8],[5,8,9],[5,8,9,10],[5,8,10],[5,9],[5,9,10],[5,10],[6,8],[6,8,9],[6,8,9,10],[6,8,10],[6,9],[6,9,10],[6,10],[7,8],[7,8,9],[7,8,9,10],[7,8,10],[7,9],[7,9,10],[7,10]]},"distance":{"d":2,"is_exact":true,"upper":2,"witness":[0,7],"A_d":196,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,1],[1,1],[2,1],[3,1],[4,1],[5,1],[6,1],[7,1]],"CZ":[]},"rotation_powers":[[0,7],[1,7],[2,7],[3,7],[4,7],[5,7],[6,7],[7,7],[8,7],[9,7],[10,7],[11,7],[12,7],[13,7],[14,7],[15,7],[16,7],[17,7],[18,7],[19,7],[20,7],[21,7],[22,7],[23,7],[24,7],[25,7],[26,7],[27,7],[28,7],[29,7],[30,7],[31,7],[32,7],[33,7],[34,7],[35,7],[36,7],[37,7],[38,7],[39,7],[40,7],[41,7],[42,7],[43,7],[44,7],[45,7],[46,7],[47,7],[48,7],[49,7],[50,7],[51,7],[52,7],[53,7],[54,7],[55,7]]},"metrics":{"gamma":2.807354922057604,"gamma_t":null,"gamma_rho":2.807354922057604,"gamma_claim":2.807354922057604,"gamma_t_claim":null,"gamma_rho_claim":2.807354922057604,"v_ex":8,"rate":0.14285714285714285,"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":"k78-0019","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 19","provenance":"unified search l=3, gluing blocks=1+1+1+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"}]}