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:true,"upper":2,"witness":[3004,6007],"A_d":9009,"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]],"CZ":[]},"rotation_powers":[[0,5],[1,5],[2,5],[3,7],[10,7],[46,7],[166,7],[496,7],[1288,7],[3004,3],[6007,3],[10725,3],[11517,3],[11847,3],[11967,3],[12003,3],[12004,3],[12005,3],[12006,3],[12007,3],[12008,3],[12009,3],[12011,3],[12012,3],[12013,7],[13298,3],[13299,3],[13300,3],[13788,3],[13789,3],[13790,3],[13791,3],[13792,3],[13793,3],[13954,3],[13955,3],[13956,3],[13957,3],[13958,3],[13959,3],[14000,3],[14001,3],[14002,3],[14003,3],[14004,3],[14005,3],[14010,3],[14011,3],[14012,3],[14013,3],[14014,3],[14015,3],[14023,3],[14024,3],[14025,3],[14026,3],[14027,3],[14028,3]]},"metrics":{"gamma":12.191162054824026,"gamma_t":12.191162054824026,"gamma_rho":12.191162054824026,"gamma_claim":12.191162054824026,"gamma_t_claim":12.191162054824026,"gamma_rho_claim":12.191162054824026,"v_ex":3,"rate":0.0002138427542946753,"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-0248","N":17,"d":2,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at ae9fbf8, outputs/large_unified_factories_l3.csv line 248","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"}]}