{"id":"65.1.3.a","row":478,"stored":{"file":"master_catalog.json","row":478,"construction":null,"columns_sha256":null},"parameters":{"n":65,"k":1,"d":3,"N":11,"r":10,"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":[[0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,9],[0,1,2,3,4,5,6,7,10],[0,1,2,3,4,5,6,8,9],[0,1,2,3,4,5,6,8,10],[0,1,2,3,4,5,6,9,10],[0,1,2,3,4,5,7,8,9],[0,1,2,3,4,5,7,8,10],[0,1,2,3,4,5,7,9,10],[0,1,2,3,4,5,8,9,10],[0,1,2,3,4,6,7,8,9],[0,1,2,3,4,6,7,8,10],[0,1,2,3,4,6,7,9,10],[0,1,2,3,4,6,8,9,10],[0,1,2,3,4,7,8,9,10],[0,1,2,3,5,6,7,8,9],[0,1,2,3,5,6,7,8,10],[0,1,2,3,5,6,7,9,10],[0,1,2,3,5,6,8,9,10],[0,1,2,3,5,7,8,9,10],[0,1,2,3,6,7,8,9,10],[0,1,2,4,5,6,7,8,9],[0,1,2,4,5,6,7,8,10],[0,1,2,4,5,6,7,9,10],[0,1,2,4,5,6,8,9,10],[0,1,2,4,5,7,8,9,10],[0,1,2,4,6,7,8,9,10],[0,1,2,5,6,7,8,9,10],[0,1,3,4,5,6,7,8,9],[0,1,3,4,5,6,7,8,10],[0,1,3,4,5,6,7,9,10],[0,1,3,4,5,6,8,9,10],[0,1,3,4,5,7,8,9,10],[0,1,3,4,6,7,8,9,10],[0,1,3,5,6,7,8,9,10],[0,1,4,5,6,7,8,9,10],[0,2,3,4,5,6,7,8,9],[0,2,3,4,5,6,7,8,10],[0,2,3,4,5,6,7,9,10],[0,2,3,4,5,6,8,9,10],[0,2,3,4,5,7,8,9,10],[0,2,3,4,6,7,8,9,10],[0,2,3,5,6,7,8,9,10],[0,2,4,5,6,7,8,9,10],[0,3,4,5,6,7,8,9,10],[1],[1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,10],[1,2,3,4,5,6,7,9,10],[1,2,3,4,5,6,8,9,10],[1,2,3,4,5,7,8,9,10],[1,2,3,4,6,7,8,9,10],[1,2,3,5,6,7,8,9,10],[1,2,4,5,6,7,8,9,10],[1,3,4,5,6,7,8,9,10],[2],[2,3,4,5,6,7,8,9,10],[3],[4],[5],[6],[7],[8],[9],[10]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,46,63],"A_d":90,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,2],[1,1],[2,1],[3,1],[4,1],[5,1],[6,1],[7,1],[8,1],[9,1],[10,1]],"CZ":[]},"rotation_powers":[[0,5],[1,5],[3,5],[6,5],[10,5],[15,5],[21,5],[28,5],[36,5],[45,3],[55,3],[57,3],[58,3],[59,3],[60,3],[61,3],[62,3],[63,3],[64,3]]},"metrics":{"gamma":3.7996910401907193,"gamma_t":3.7996910401907193,"gamma_rho":3.7996910401907193,"gamma_claim":3.7996910401907193,"gamma_t_claim":3.7996910401907193,"gamma_rho_claim":3.7996910401907193,"v_ex":1,"rate":0.015384615384615385,"t_count":1,"poly_degree":1,"effective_width":1},"provenance":{"regimes":["borrowed-identity search: two-group"],"discovery":"pre-existing","strongest_claim":"found by the two-group borrowed-identity search of Singh, Gidney and Jones (arXiv:2606.28518; borrowed_identities/): an identity circuit symmetric within its output and check blocks, with its output-only gates removed; a verified witness, not a maximum","sources":[{"regime":"borrowed-identity search: two-group","file":"borrowed_identities/circuits/large_unified_l3_d3.json","label":"lu-0010","N":11,"d":3,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at ae9fbf8, outputs/large_unified_factories_l3.csv line 10","provenance":"larger unified search l=3, two-group s_total=8,s_O=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"}]}