{"id":"64.3.4.a","row":471,"stored":{"file":"master_catalog.json","row":471,"construction":null,"columns_sha256":null},"parameters":{"n":64,"k":3,"d":4,"N":10,"r":7,"level":3},"gate":{"string":"012","human":"CCZ012","monomials":[[0,1,2]],"sk_key":[[0,1,2]],"sk_fingerprint":"d0c21becf7c06e56","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[2,3],[0,4],[1,5],[1,2,3,4,5],[0,2,6],[0,1,2,3,4,6],[0,1,4,5,6],[2,3,5,6],[1,2,7],[0,2,3,4,7],[0,1,3,5,7],[1,4,5,7],[1,3,6,7],[1,2,4,6,7],[0,1,3,4,5,6,7],[0,5,6,7],[0,1,2,8],[3,4,8],[2,3,5,8],[0,2,4,5,8],[0,3,6,8],[0,1,4,6,8],[3,4,5,6,8],[5,6,8],[0,3,7,8],[4,7,8],[2,5,7,8],[3,4,5,7,8],[1,2,6,7,8],[1,3,4,6,7,8],[0,2,4,5,6,7,8],[3,5,6,7,8],[1,2,9],[0,3,4,9],[3,5,9],[0,1,2,4,5,9],[0,1,3,6,9],[1,4,6,9],[0,3,4,5,6,9],[2,5,6,9],[0,1,3,7,9],[0,1,4,7,9],[0,5,7,9],[1,3,4,5,7,9],[1,6,7,9],[2,3,4,6,7,9],[0,4,5,6,7,9],[3,5,6,7,9],[0,1,2,7,8,9],[0,1,2,3,4,7,8,9],[0,3,5,7,8,9],[0,2,4,5,7,8,9],[0,1,3,6,7,8,9],[0,1,2,4,6,7,8,9],[2,3,4,5,6,7,8,9],[5,6,7,8,9],[0,1,2,3,8,9],[4,8,9],[5,8,9],[3,4,5,8,9],[0,1,6,8,9],[3,4,6,8,9],[4,5,6,8,9],[3,5,6,8,9]]},"distance":{"d":4,"is_exact":true,"upper":4,"witness":[0,1,2,3],"A_d":9104,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,1],[1,2]],"CZ":[[0,3],[0,6],[0,8],[1,4],[1,6],[1,8],[1,9],[2,3],[2,5],[2,6],[2,9]]},"rotation_powers":[[0,5],[1,7],[3,7],[5,3],[6,7],[24,3],[25,3],[30,3],[31,3],[36,3],[38,3],[44,3],[46,3],[52,3],[54,3],[57,3],[58,3]]},"metrics":{"gamma":2.207518749639422,"gamma_t":1.596322538971198,"gamma_rho":2.5,"gamma_claim":2.207518749639422,"gamma_t_claim":1.596322538971198,"gamma_rho_claim":2.5,"v_ex":2,"rate":0.046875,"t_count":7,"poly_degree":3,"effective_width":3},"provenance":{"regimes":["AI search"],"discovery":"AI search","strongest_claim":"found by an AI search campaign; a verified witness, not a maximum","sources":[{"regime":"AI search","file":"master_catalog/AI results","label":"CCZ012","N":10,"d":4,"d_is_exact":true,"origin":"factory_records/findings_ccz.jsonl","provenance":"factory_records/findings_ccz.jsonl:27"},{"regime":"AI search","file":"master_catalog/AI results","label":"CCZ012","N":11,"d":4,"d_is_exact":true,"origin":"factory_records/findings_ccz.jsonl","provenance":"factory_records/findings_ccz.jsonl:25"},{"regime":"AI search","file":"master_catalog/AI results","label":"CCZ","N":12,"d":4,"d_is_exact":true,"origin":"ai_campaign/circuits","provenance":"ai_campaign/circuits/n64_k3_d4_tau7_C7_S2_it02.json"},{"regime":"AI search","file":"master_catalog/AI results","label":"CCZ","N":12,"d":4,"d_is_exact":true,"origin":"ai_campaign/circuits","provenance":"ai_campaign/circuits/n64_k3_d4_tau7_P90_it02.json"},{"regime":"AI search","file":"master_catalog/AI results","label":"CCZ","N":12,"d":4,"d_is_exact":true,"origin":"ai_campaign/circuits","provenance":"ai_campaign/circuits/n64_k3_d4_tau7_S3_S3_S3_it02.json"},{"regime":"AI search","file":"master_catalog/AI results","label":"CCZ","N":13,"d":4,"d_is_exact":true,"origin":"ai_campaign/circuits","provenance":"ai_campaign/circuits/n64_k3_d4_tau7_C7_S3_it02.json"},{"regime":"AI search","file":"master_catalog/AI results","label":"CCZ012","N":13,"d":4,"d_is_exact":true,"origin":"factory_records/findings_ccz.jsonl","provenance":"factory_records/findings_ccz.jsonl:23"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"CCZ012","N":10,"d":4,"d_is_exact":true,"origin":"factory_records/findings_ccz","provenance":"factory_records/findings_ccz \u00b7 catalogue.jsonl:272"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"CCZ012","N":11,"d":4,"d_is_exact":true,"origin":"factory_records/findings_ccz","provenance":"factory_records/findings_ccz \u00b7 catalogue.jsonl:271"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"CCZ012","N":12,"d":4,"d_is_exact":true,"origin":"ai_campaign/circuits","provenance":"ai_campaign/circuits \u00b7 catalogue.jsonl:274"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"CCZ012","N":12,"d":4,"d_is_exact":true,"origin":"ai_campaign/circuits","provenance":"ai_campaign/circuits \u00b7 catalogue.jsonl:276"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"CCZ012","N":12,"d":4,"d_is_exact":true,"origin":"ai_campaign/circuits","provenance":"ai_campaign/circuits \u00b7 catalogue.jsonl:277"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"CCZ012","N":12,"d":4,"d_is_exact":true,"origin":"ai_campaign/circuits","provenance":"ai_campaign/circuits \u00b7 catalogue.jsonl:278"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"CCZ012","N":12,"d":4,"d_is_exact":true,"origin":"ai_campaign/circuits","provenance":"ai_campaign/circuits \u00b7 catalogue.jsonl:279"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"CCZ012","N":13,"d":4,"d_is_exact":true,"origin":"factory_records/findings_ccz","provenance":"factory_records/findings_ccz \u00b7 catalogue.jsonl:270"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"CCZ012","N":13,"d":4,"d_is_exact":true,"origin":"ai_campaign/circuits","provenance":"ai_campaign/circuits \u00b7 catalogue.jsonl:275"}]},"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"}]}