{"id":"26.5.2.a","row":40,"stored":{"file":"master_catalog.json","row":40,"construction":null,"columns_sha256":null},"parameters":{"n":26,"k":5,"d":2,"N":8,"r":3,"level":3},"gate":{"string":"0+12+34","human":"T0\u00b7CS12\u00b7CS34","monomials":[[0],[1,2],[3,4]],"sk_key":[[0],[1,2],[3,4]],"sk_fingerprint":"bc3a4bbecad4d0d5","sk_canonical_frame":true,"relabelled_into_canonical_frame":true},"circuit":{"columns":[[6],[4,5],[4,7],[0,5],[6,7],[1,3,5],[1,3,6],[1,5,6],[2,3,5],[2,3,6],[2,5,6],[3,4,5],[3,4,6],[3,5,6],[0,4,6],[0,4,7],[4,5,7],[0,6,7],[5,6,7],[1,2,3,5],[1,2,3,6],[1,2,5,6],[3,4,5,6],[0,4,5,6],[0,4,5,7],[0,5,6,7]]},"distance":{"d":2,"is_exact":true,"upper":2,"witness":[0,6],"A_d":49,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,1],[1,1],[2,1],[3,3],[4,3]],"CZ":[[3,5],[3,6],[4,5]]},"rotation_powers":null},"metrics":{"gamma":2.37851162325373,"gamma_t":1.893084796083488,"gamma_rho":3.1154772174199357,"gamma_claim":2.37851162325373,"gamma_t_claim":1.893084796083488,"gamma_rho_claim":3.1154772174199357,"v_ex":3,"rate":0.19230769230769232,"t_count":7,"poly_degree":2,"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-row125-symmetry-free","N":8,"d":2,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at cae4982, outputs/factory_catalogue_l3.csv row 125","provenance":"symmetry-free l=3 parts=2+2+1 checks=3"}]},"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"}]}