{"id":"18.5.2.a","row":14,"stored":{"file":"master_catalog.json","row":14,"construction":null,"columns_sha256":null},"parameters":{"n":18,"k":5,"d":2,"N":7,"r":2,"level":3},"gate":{"string":"01+234","human":"CS01\u00b7CCZ234","monomials":[[0,1],[2,3,4]],"sk_key":[[0,1],[2,3,4]],"sk_fingerprint":"c8110231103ed187","sk_canonical_frame":true,"relabelled_into_canonical_frame":true},"circuit":{"columns":[[5],[2,6],[3,6],[4,6],[0,5],[0,6],[1,5],[1,6],[5,6],[2,3,6],[2,4,6],[3,4,6],[0,1,5],[0,1,6],[0,5,6],[1,5,6],[2,3,4,6],[0,1,5,6]]},"distance":{"d":2,"is_exact":true,"upper":2,"witness":[0,4],"A_d":57,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,1],[1,1],[2,2],[3,2],[4,2],[6,1]],"CZ":[[2,3],[2,4],[3,4]]},"rotation_powers":[[0,7],[1,3],[2,3],[3,3],[5,5],[6,5],[12,3],[13,3],[14,3],[15,3],[16,3]]},"metrics":{"gamma":1.84799690655495,"gamma_t":1.0,"gamma_rho":2.584962500721156,"gamma_claim":1.84799690655495,"gamma_t_claim":1.0,"gamma_rho_claim":2.584962500721156,"v_ex":3,"rate":0.2777777777777778,"t_count":9,"poly_degree":3,"effective_width":5},"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/circuits_l3.json","label":"l3-row123-symmetry-free","N":7,"d":2,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at cae4982, outputs/factory_catalogue_l3.csv row 123","provenance":"symmetry-free l=3 parts=3+2 checks=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"}]}