{"id":"39.2.3.b","row":121,"stored":{"file":"master_catalog.json","row":121,"construction":null,"columns_sha256":null},"parameters":{"n":39,"k":2,"d":3,"N":8,"r":6,"level":3},"gate":{"string":"0+1+01","human":"T0\u00b7T1\u00b7CS01","monomials":[[0],[1],[0,1]],"sk_key":[[0],[0,1],[1]],"sk_fingerprint":"3ecc49b933f7ac91","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[1,2],[0,3],[4],[2,4],[3,4],[5],[2,5],[3,5],[2,3,4,5],[6],[2,6],[3,6],[4,6],[2,4,6],[3,4,6],[0,1,5,6],[1,2,5,6],[0,3,5,6],[2,3,4,5,6],[7],[2,7],[3,7],[4,7],[2,4,7],[3,4,7],[0,1,5,7],[1,2,5,7],[0,3,5,7],[2,3,4,5,7],[0,1,6,7],[1,2,6,7],[0,3,6,7],[4,6,7],[2,4,6,7],[3,4,6,7],[5,6,7],[2,5,6,7],[3,5,6,7],[2,3,4,5,6,7]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,2,3],"A_d":103,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,1],[1,1],[6,2],[7,2]],"CZ":[[6,7]]},"rotation_powers":null},"metrics":{"gamma":2.703787765901335,"gamma_t":3.3347175194727923,"gamma_rho":null,"gamma_claim":2.703787765901335,"gamma_t_claim":3.3347175194727923,"gamma_rho_claim":null,"v_ex":null,"rate":0.05128205128205128,"t_count":1,"poly_degree":1,"effective_width":2},"provenance":{"regimes":["exhaustive classification n<=54"],"discovery":"pre-existing","strongest_claim":"found within the exhaustive classification through length 54 but not one of its Pareto points: a Pareto point with the same output class (after removing spectator outputs) and the same exact distance strictly dominates it, which tests/test_master_catalog.py checks -- a verified witness, not an optimum","sources":[{"regime":"exhaustive classification n<=54","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+1+01","N":9,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2600, origin 7; census_shard_08.json"},{"regime":"exhaustive classification n<=54","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+1+01","N":8,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 3386, origin 1; rep_3386_1.json"}]},"references":[{"key":"wills2026classification","short":"Wills et al. (2026)","full":"A. Wills, S. P. Jain, and S. Singh, \"Classification of Generalised Triorthogonal Codes through Length 54,\" arXiv:2609.30860 (2026).","url":"https://arxiv.org/abs/2609.30860","date":"2026-09-25"},{"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"}]}