{"id":"18.3.2.a","row":11,"stored":{"file":"master_catalog.json","row":11,"construction":null,"columns_sha256":null},"parameters":{"n":18,"k":3,"d":2,"N":6,"r":3,"level":3},"gate":{"string":"0+012","human":"T0\u00b7CCZ012","monomials":[[0],[0,1,2]],"sk_key":[[0],[0,1,2]],"sk_fingerprint":"9a0284062e26f60f","sk_canonical_frame":true,"relabelled_into_canonical_frame":true},"circuit":{"columns":[[1,2,3],[0,1,2,3],[1,2,4],[0,1,2,4],[1,3,4],[2,3,4],[1,2,3,4],[0,1,3,4],[0,2,3,4],[0,1,2,3,4],[1,2,5],[0,1,2,5],[3,5],[0,3,5],[4,5],[0,4,5],[1,2,3,4,5],[0,1,2,3,4,5]]},"distance":{"d":2,"is_exact":true,"upper":2,"witness":[0,1],"A_d":21,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[1,2],[2,2],[3,2],[4,2]],"CZ":[[0,1],[0,2],[0,3],[0,4],[1,2]]},"rotation_powers":[[1,3],[2,3],[4,3],[5,3],[9,3],[10,3],[12,3],[15,3],[17,3]]},"metrics":{"gamma":2.584962500721156,"gamma_t":1.5849625007211563,"gamma_rho":null,"gamma_claim":2.584962500721156,"gamma_t_claim":1.5849625007211563,"gamma_rho_claim":null,"v_ex":null,"rate":0.16666666666666666,"t_count":6,"poly_degree":2,"effective_width":3},"provenance":{"regimes":["symmetry-SAT search"],"discovery":"pre-existing","strongest_claim":"found by the symmetry-slot or ansatz-free SAT search (symmetry_sat_search/); a verified witness, not a maximum","sources":[{"regime":"symmetry-SAT search","file":"symmetry_sat_search/catalog/factories.json","label":"T3_CCZ123 (N=6)","N":6,"d":2,"d_is_exact":true,"origin":null,"provenance":"archived symmetry-reduced CP-SAT binary-matrix export"}]},"references":[{"key":"jain2026symmetry","short":"Jain et al. (2026)","full":"S. P. Jain, A. Wills, and S. Singh, \"Symmetry and AI-assisted discovery of magic-state factories,\" arXiv:2610.06535 (2026).","url":"https://arxiv.org/abs/2610.06535","date":"2026-10-05"}]}