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":2,"witness":[5020,11455],"A_d":19305,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,1],[1,1],[2,1],[3,2],[4,2],[5,2],[6,2],[7,2],[8,2],[9,2],[10,2],[11,2],[12,2],[13,2],[14,2],[15,2],[16,2],[17,2]],"CZ":[]},"rotation_powers":[[0,3],[1,3],[2,3],[3,3],[4,3],[5,3],[6,3],[7,3],[8,5],[10,3],[20,3],[66,3],[232,3],[728,3],[2016,3],[5020,3],[11455,3],[21321,3],[23037,3],[23829,3],[24159,3],[24279,3],[24315,3],[24316,3],[24317,3],[24318,3],[24319,3],[24320,3],[24321,3],[24322,3],[24325,7],[27328,3],[28608,3],[28609,3],[28610,3],[28611,3],[28612,3],[28613,3],[28614,3],[28615,3],[29104,3],[29105,3],[29106,3],[29107,3],[29108,3],[29109,3],[29110,3],[29111,3],[29270,3],[29271,3],[29272,3],[29273,3],[29274,3],[29275,3],[29276,3],[29277,3],[29316,3],[29317,3],[29318,3],[29319,3],[29320,3],[29321,3],[29322,3],[29323,3],[29326,3],[29327,3],[29328,3],[29329,3],[29330,3],[29331,3],[29332,3],[29333,3],[29335,3],[29336,3],[29337,3],[29338,3],[29339,3],[29340,3],[29341,3],[29342,3],[29343,3],[29344,3]]},"metrics":{"gamma":13.25586458694352,"gamma_t":13.25586458694352,"gamma_rho":13.25586458694352,"gamma_claim":13.25586458694352,"gamma_t_claim":13.25586458694352,"gamma_rho_claim":13.25586458694352,"v_ex":3,"rate":0.00010223206679161698,"t_count":3,"poly_degree":1,"effective_width":3},"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-0261","N":18,"d":2,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at ae9fbf8, outputs/large_unified_factories_l3.csv line 261","provenance":"larger unified search l=3, two-group s_total=8,s_O=2"}]},"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"}]}