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2569,3],[2570,3],[2571,3],[2572,3],[2573,3]]},"metrics":{"gamma":9.329796338220703,"gamma_t":9.329796338220703,"gamma_rho":9.329796338220703,"gamma_claim":9.329796338220703,"gamma_t_claim":9.329796338220703,"gamma_rho_claim":9.329796338220703,"v_ex":4,"rate":0.001554001554001554,"t_count":4,"poly_degree":1,"effective_width":4},"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-0365","N":15,"d":2,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at ae9fbf8, outputs/large_unified_factories_l3.csv line 365","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"}]}