{"id":"43.3.3.e","row":164,"stored":{"file":"master_catalog.json","row":164,"construction":null,"columns_sha256":null},"parameters":{"n":43,"k":3,"d":3,"N":10,"r":7,"level":3},"gate":{"string":"0+1+2+01","human":"T0\u00b7T1\u00b7T2\u00b7CS01","monomials":[[0],[1],[2],[0,1]],"sk_key":[[0],[0,1],[1],[2]],"sk_fingerprint":"d3a1ad1584fffcc0","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[1,3,4],[0,3,5],[0,2,4,5],[1,2,3,6],[1,4,6],[2,3,4,6],[0,1,2,5,6],[3,7],[0,2,4,7],[0,5,7],[0,1,4,5,7],[1,2,6,7],[0,1,2,3,5,6,7],[2,3,8],[2,4,8],[0,1,5,8],[0,2,3,4,5,8],[0,1,6,8],[0,1,5,6,8],[2,7,8],[2,3,7,8],[0,2,4,6,7,8],[0,1,3,4,5,6,7,8],[1,2,3,9],[0,1,2,4,9],[1,2,5,9],[3,5,9],[0,6,9],[4,5,6,9],[0,7,9],[3,4,7,9],[0,1,2,6,7,9],[3,4,5,6,7,9],[0,1,2,8,9],[0,1,2,4,8,9],[1,2,3,6,8,9],[3,4,5,6,8,9],[1,2,5,7,8,9],[3,4,5,7,8,9],[3,4,6,7,8,9],[3,5,6,7,8,9],[4,5,6,7,8,9],[3,4,5,6,7,8,9]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,2],"A_d":109,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,3],[1,3],[2,2],[3,2],[4,2],[5,2],[6,2],[7,2],[8,2],[9,2]],"CZ":[[0,2],[0,5],[0,9],[1,3],[1,4],[1,6],[1,7],[2,5],[2,8],[3,4],[3,5],[3,6],[3,7],[3,8],[3,9],[4,5],[4,6],[4,7],[4,8],[4,9],[5,6],[5,7],[5,8],[5,9],[6,7],[6,8],[6,9],[7,8],[7,9],[8,9]]},"rotation_powers":null},"metrics":{"gamma":2.4235918844976796,"gamma_t":2.792662130926222,"gamma_rho":null,"gamma_claim":2.4235918844976796,"gamma_t_claim":2.792662130926222,"gamma_rho_claim":null,"v_ex":null,"rate":0.06976744186046512,"t_count":2,"poly_degree":1,"effective_width":3},"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+2+01","N":10,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2936, origin 0; census_shard_06.json"},{"regime":"exhaustive classification n<=54","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+01+02+012","N":10,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2936, origin 0; census_shard_06.json"},{"regime":"exhaustive classification n<=54","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+1+01+02+12+012","N":10,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2936, origin 0; census_shard_06.json"},{"regime":"exhaustive classification n<=54","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+2+01+12","N":10,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2936, origin 0; census_shard_06.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"}]}