{"id":"44.4.3.e","row":197,"stored":{"file":"master_catalog.json","row":197,"construction":null,"columns_sha256":null},"parameters":{"n":44,"k":4,"d":3,"N":11,"r":7,"level":3},"gate":{"string":"0+1+2+3","human":"T0\u00b7T1\u00b7T2\u00b7T3","monomials":[[0],[1],[2],[3]],"sk_key":[[0],[1],[2],[3]],"sk_fingerprint":"473e0903fa3e9dc7","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,1,4],[3,5,6],[3,5,8],[3,6,8],[2,5,6,8],[4,5,6,8],[1,7,9],[1,7,10],[1,9,10],[1,5,7,9],[1,6,7,10],[1,8,9,10],[4,5,7,9],[4,6,7,10],[4,8,9,10],[2,6,7,9],[2,7,8,10],[2,5,9,10],[0,1,4,6,7,9],[0,1,4,7,8,10],[0,1,4,5,9,10],[0,1,4,5,6,7,9],[0,1,4,6,7,8,10],[0,1,4,5,8,9,10],[2,5,7,8,9],[2,5,6,7,10],[2,6,8,9,10],[0,6,7,8,9],[0,5,7,8,10],[0,5,6,9,10],[1,5,6,7,8,9],[1,5,6,7,8,10],[1,5,6,8,9,10],[0,1,4,5,6,7,8,9],[0,1,4,5,6,7,8,10],[0,1,4,5,6,8,9,10],[3,7,9,10],[0,1,4,7,9,10],[3,5,6,7,9,10],[3,5,7,8,9,10],[3,6,7,8,9,10],[0,1,4,5,6,7,9,10],[0,1,4,5,7,8,9,10],[0,1,4,6,7,8,9,10]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,4,5],"A_d":132,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[1,1],[2,1],[3,1],[4,3],[7,2],[9,2],[10,2]],"CZ":[[0,1],[0,4],[0,5],[0,6],[0,8],[1,4],[4,5],[4,6],[4,8],[5,6],[5,7],[5,8],[5,10],[6,8],[6,9],[6,10],[7,8],[7,9],[7,10],[8,9],[9,10]]},"rotation_powers":[[0,5],[1,7],[2,7],[3,7],[4,5],[5,5],[6,7],[7,7],[8,7],[24,3],[25,3],[26,3],[27,3],[28,3],[29,3],[30,3],[31,3],[32,3],[33,3],[34,3],[35,3]]},"metrics":{"gamma":2.182658338644138,"gamma_t":2.182658338644138,"gamma_rho":2.182658338644138,"gamma_claim":2.182658338644138,"gamma_t_claim":2.182658338644138,"gamma_rho_claim":2.182658338644138,"v_ex":4,"rate":0.09090909090909091,"t_count":4,"poly_degree":1,"effective_width":4},"provenance":{"regimes":["exhaustive classification n<=54 (Pareto point)","symmetry-SAT search","AI search"],"discovery":"pre-existing","strongest_claim":"a Pareto point of the exhaustive classification of generalised triorthogonal protocols through length 54 (classification/length54/): no protocol with n <= 54, the same CNOT+S output class and the same exact distance has n and S both no larger and one of them smaller, where S counts every matrix row -- the N of this table","sources":[{"regime":"symmetry-SAT search","file":"symmetry_sat_search/catalog/factories.json","label":"T0 . T1 . T2 . T3","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"explicit circuit from ansatz-free SAT; archived result: beyond_cyclic_symmetric.json"},{"regime":"AI search","file":"master_catalog/AI results","label":"T0.T1.T2.T3","N":11,"d":3,"d_is_exact":true,"origin":"factory_records/reproductions","provenance":"factory_records/reproductions/n44_k4_d3_tau4_T0-T1-T2-T3.json"},{"regime":"AI search","file":"master_catalog/AI results","label":"T^4","N":11,"d":3,"d_is_exact":true,"origin":"ai_campaign/circuits","provenance":"ai_campaign/circuits/n44_k4_d3_tau4_P70_it01.json"},{"regime":"AI search","file":"master_catalog/AI results","label":"T0.T1.T2.T3","N":11,"d":3,"d_is_exact":true,"origin":"ai_campaign/circuits","provenance":"ai_campaign/circuits/n44_k4_d3_tau4_parent-target(n=44,kappa=12)_it11.json"},{"regime":"AI search","file":"master_catalog/AI results","label":"T^4","N":11,"d":3,"d_is_exact":true,"origin":"factory_records/findings_tm.jsonl","provenance":"factory_records/findings_tm.jsonl:4"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"T0.T1.T2.T3","N":11,"d":3,"d_is_exact":true,"origin":"factory_records/reproductions","provenance":"factory_records/reproductions \u00b7 catalogue.jsonl:126"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"T0.T1.T2.T3","N":11,"d":3,"d_is_exact":true,"origin":"ai_campaign/circuits","provenance":"ai_campaign/circuits \u00b7 catalogue.jsonl:127"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"T0.T1.T2.T3","N":11,"d":3,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:128"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"T0.T1.T2.T3","N":11,"d":3,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:129"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"T0.T1.T2.T3","N":11,"d":3,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:130"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"T0.T1.T2.T3","N":11,"d":3,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:131"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"T0.T1.T2.T3","N":11,"d":3,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:132"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"T0.T1.T2.T3","N":11,"d":3,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:133"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"T0.T1.T2.T3","N":11,"d":3,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:134"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"T0.T1.T2.T3","N":11,"d":3,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:135"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"T0.T1.T2.T3","N":11,"d":3,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:136"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"T0.T1.T2.T3","N":11,"d":3,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:137"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"T0.T1.T2.T3","N":11,"d":3,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:138"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"T0.T1.T2.T3","N":11,"d":3,"d_is_exact":true,"origin":"frontier_campaign","provenance":"frontier_campaign \u00b7 catalogue.jsonl:139"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+1+2+3","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+01+02+03+12+012+013+023+123","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+01+02+03+12+13+23+012+013+023+123","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+1+01+02+03+12+012+013+023","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+1+01+02+03+12+23+012+013+023+123","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+1+3+01+02+03+12+012+013+023+123","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+1+3+01+02+03+12+23+012+013+023","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+1+2+01+02+03+012+013+023","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+2+3+01+02+03+12+13+012+013","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+2+01+02+03+12+012+013","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+01+02+03+23+012+013+123","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+01+02+13+012+013+123","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+3+01+02+23+012+013","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+01+12+13+23+012+013+023+123","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+2+3+01+012+013+023","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+3+01+12+012+013+123","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+1+01+02+03+12+23+012","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+1+3+01+02+03+12+012","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+01+02+12+13+012","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+3+01+02+12+13+23+012","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+3+01+02+12+012","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+01+02+13+012+123","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+3+01+02+13+012","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+1+01+02+13+23+012+123","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+1+2+3+01+02+13+23+012+123","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+1+3+01+02+23+012+123","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+1+2+3+01+02+012+123","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+1+01+02+13+012","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+1+2+3+01+02+13+012","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+1+3+01+02+012","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+2+01+03+13+012+023+123","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+01+12+23+012+023","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+2+01+23+012+023","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+01+03+12+13+012","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+2+3+01+03+012","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+3+01+12+13+012","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+01+02+03+12+13+23+123","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+1+2+01+02+03","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+1+3+01+02+23","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+1+2+3+01+02","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+2+3+01+12+13+023","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+01+23+023+123","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+01+12+13+23+123","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+2+3+01+12+13","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+01+12+23","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+3+01+12","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+01+23+123","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+2+01+23","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+2+3+01","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+1+2+3+012+013+023+123","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/legacy/rank7_census/catalog/sk_classes_r7.json","label":"0+3+12+012","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"RM(3,7) orbit class 2633, origin 5; census_shard_07.json"},{"regime":"exhaustive classification n<=54 (Pareto point)","file":"classification/length54/pareto_frontier.json","label":"protocol 19","N":11,"d":3,"d_is_exact":true,"origin":"exhaustive classification of generalised triorthogonal protocols through length 54 (Wills, Jain and Singh)","provenance":"Pareto point 19 of the length-54 classification: output class Q4_00000000000001e0 (T^(tensor 4)), (n, S, d_Z) = (44, 11, 3), leading error coefficient 128; the outputs are its 4 logical rows"}]},"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"}]}