{"id":"32.9.2.a","row":76,"stored":{"file":"master_catalog.json","row":76,"construction":null,"columns_sha256":null},"parameters":{"n":32,"k":9,"d":2,"N":12,"r":3,"level":3},"gate":{"string":"0+12+345+678","human":"T0\u00b7CS12\u00b7CCZ345\u00b7CCZ678","monomials":[[0],[1,2],[3,4,5],[6,7,8]],"sk_key":[[0],[1,2],[3,4,5],[6,7,8]],"sk_fingerprint":"9d9237e0a747b82e","sk_canonical_frame":true,"relabelled_into_canonical_frame":true},"circuit":{"columns":[[3,4,5,11],[3,4,11],[3,5,11],[3,11],[4,5,11],[4,11],[5,11],[6,7,8,10],[6,7,10],[6,8,10],[6,10],[7,8,10],[7,10],[8,10],[0,1,2,9],[0,1,2,10],[1,2,9,10],[0,1,9],[0,1,10],[1,9,10],[0,2,9],[0,2,10],[2,9,10],[0,9,10],[0,9,10,11],[0,9,11],[0,10,11],[0,11],[9],[9,10,11],[9,11],[10,11]]},"distance":{"d":2,"is_exact":true,"upper":2,"witness":[0,1],"A_d":88,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,3],[1,1],[2,1],[3,2],[4,2],[5,2],[6,2],[7,2],[8,2],[9,2],[10,3],[11,1]],"CZ":[[0,9],[0,10],[3,4],[3,5],[4,5],[6,7],[6,8],[7,8],[9,10]]},"rotation_powers":[[1,7],[2,7],[4,7],[8,3],[9,3],[11,3],[15,7],[16,3],[17,3],[20,3],[24,3],[26,3],[28,3],[29,3],[31,3]]},"metrics":{"gamma":1.8300749985576878,"gamma_t":null,"gamma_rho":2.415037499278844,"gamma_claim":1.8300749985576878,"gamma_t_claim":null,"gamma_rho_claim":2.415037499278844,"v_ex":6,"rate":0.28125,"t_count":null,"poly_degree":null,"effective_width":9},"provenance":{"regimes":["borrowed-identity search: symmetry-free"],"discovery":"pre-existing","strongest_claim":"found by the symmetry-free, targeted-output borrowed-identity search of Singh, Gidney and Jones (arXiv:2606.28518; borrowed_identities/), which solves for the check couplings of a chosen output; a verified witness, not a maximum","sources":[{"regime":"borrowed-identity search: symmetry-free","file":"borrowed_identities/circuits/large_unified_l3.json","label":"lu-0948","N":12,"d":2,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at ae9fbf8, outputs/large_unified_factories_l3.csv line 948","provenance":"larger unified search l=3, gluing blocks=3+3+2+1"}]},"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"}]}