{"id":"20.4.2.c","row":19,"stored":{"file":"master_catalog.json","row":19,"construction":null,"columns_sha256":null},"parameters":{"n":20,"k":4,"d":2,"N":6,"r":2,"level":3},"gate":{"string":"01+02+03+012","human":"CS01\u00b7CS02\u00b7CS03\u00b7CCZ012","monomials":[[0,1],[0,2],[0,3],[0,1,2]],"sk_key":[[0,1],[0,1,2],[0,2],[0,3]],"sk_fingerprint":"4417624584fcbdb4","sk_canonical_frame":true,"relabelled_into_canonical_frame":true},"circuit":{"columns":[[1,3,4],[0,1,3,4],[2,4],[0,2,4],[1,3,5],[0,5],[0,3,5],[0,1,5],[2,5],[0,2,3,5],[0,1,2,5],[0,1,2,3,5],[4,5],[1,4,5],[1,3,4,5],[0,3,4,5],[2,4,5],[2,3,4,5],[1,2,3,4,5],[0,1,2,4,5]]},"distance":{"d":2,"is_exact":true,"upper":2,"witness":[0,1],"A_d":62,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,3],[1,3],[2,3],[3,3],[4,2]],"CZ":[[0,1],[0,2],[0,3],[1,3],[1,4],[2,4],[3,4]]},"rotation_powers":null},"metrics":{"gamma":2.321928094887362,"gamma_t":2.321928094887362,"gamma_rho":null,"gamma_claim":2.321928094887362,"gamma_t_claim":2.321928094887362,"gamma_rho_claim":null,"v_ex":null,"rate":0.2,"t_count":4,"poly_degree":2,"effective_width":4},"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":"CS13_CS23_CS34_CCZ234 (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"}]}