{"id":"38.10.2.a","row":118,"stored":{"file":"master_catalog.json","row":118,"construction":null,"columns_sha256":null},"parameters":{"n":38,"k":10,"d":2,"N":13,"r":3,"level":3},"gate":{"string":"0+1+2+3+4+5+6+7+8+9","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6\u00b7T7\u00b7T8\u00b7T9","monomials":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9]],"sk_key":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9]],"sk_fingerprint":"97115137a69484d8","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,11],[0,1,2,3,4,5,6,7,8,9,12],[0,10,11],[0,10,12],[0,11,12],[1,10,11],[1,10,12],[1,11,12],[2,10,11],[2,10,12],[2,11,12],[3,10,11],[3,10,12],[3,11,12],[4,10,11],[4,10,12],[4,11,12],[5,10,11],[5,10,12],[5,11,12],[6,10,11],[6,10,12],[6,11,12],[7,10,11],[7,10,12],[7,11,12],[8,10,11],[8,10,12],[8,11,12],[9,10,11],[9,10,12],[9,11,12],[10],[10,11,12],[11],[12]]},"distance":{"d":2,"is_exact":true,"upper":2,"witness":[0,34],"A_d":139,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,1],[1,1],[2,1],[3,1],[4,1],[5,1],[6,1],[7,1],[8,1],[9,1]],"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]]},"metrics":{"gamma":1.925999418556223,"gamma_t":null,"gamma_rho":1.925999418556223,"gamma_claim":1.925999418556223,"gamma_t_claim":null,"gamma_rho_claim":1.925999418556223,"v_ex":10,"rate":0.2631578947368421,"t_count":null,"poly_degree":null,"effective_width":10},"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.json","label":"lu-1066","N":13,"d":2,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at ae9fbf8, outputs/large_unified_factories_l3.csv line 1066","provenance":"larger unified search l=3, two-group s_total=2,s_O=9"}]},"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"}]}