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n":{"S":[[0,3],[1,3],[2,3],[3,3],[4,3],[5,3],[6,3],[7,2],[8,2],[9,2],[10,2],[11,2],[12,2],[13,2]],"CZ":[[7,8],[7,9],[7,10],[7,11],[7,12],[7,13],[8,9],[8,10],[8,11],[8,12],[8,13],[9,10],[9,11],[9,12],[9,13],[10,11],[10,12],[10,13],[11,12],[11,13],[12,13]]},"rotation_powers":null},"metrics":{"gamma":6.22881869049588,"gamma_t":null,"gamma_rho":6.22881869049588,"gamma_claim":6.22881869049588,"gamma_t_claim":null,"gamma_rho_claim":6.22881869049588,"v_ex":7,"rate":0.013333333333333334,"t_count":null,"poly_degree":null,"effective_width":7},"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-0751","N":14,"d":2,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at ae9fbf8, outputs/large_unified_factories_l3.csv line 751","provenance":"larger unified search l=3, two-group s_total=4,s_O=5"}]},"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"}]}