{"id":"36.2.3.b","row":95,"stored":{"file":"master_catalog.json","row":95,"construction":null,"columns_sha256":null},"parameters":{"n":36,"k":2,"d":3,"N":9,"r":7,"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":[[0,1,2],[4],[0,1,2,5],[0,4,5],[6],[4,6],[0,5,6],[0,1,4,5,6],[0,1,2,7],[0,4,7],[0,1,5,7],[0,1,2,5,7],[3,5,7],[3,4,5,7],[0,6,7],[0,1,4,6,7],[3,5,6,7],[3,4,5,6,7],[2,8],[4,8],[2,5,8],[1,4,5,8],[6,8],[4,6,8],[1,5,6,8],[4,5,6,8],[2,7,8],[1,4,7,8],[5,7,8],[2,5,7,8],[3,5,7,8],[3,4,5,7,8],[1,6,7,8],[4,6,7,8],[3,5,6,7,8],[3,4,5,6,7,8]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,10,11],"A_d":40,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,3],[1,3],[5,2],[7,2],[8,3]],"CZ":[[0,5],[0,7],[1,5],[1,7],[5,8],[7,8]]},"rotation_powers":null},"metrics":{"gamma":2.630929753571457,"gamma_t":3.2618595071429146,"gamma_rho":null,"gamma_claim":2.630929753571457,"gamma_t_claim":3.2618595071429146,"gamma_rho_claim":null,"v_ex":null,"rate":0.05555555555555555,"t_count":1,"poly_degree":1,"effective_width":2},"provenance":{"regimes":["exhaustive classification n<=54","AI search"],"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/exhaustive_n38/catalog/classification_n38.json","label":"0+1+01","N":9,"d":3,"d_is_exact":true,"origin":null,"provenance":"quotient_catalog_k3"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"T0.T1.CS01","N":9,"d":3,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:102"},{"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 1350, origin 11; census_shard_09.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"}]}