{"id":"64.5.4.a","row":473,"stored":{"file":"master_catalog.json","row":473,"construction":null,"columns_sha256":null},"parameters":{"n":64,"k":5,"d":4,"N":12,"r":7,"level":3},"gate":{"string":"012+034","human":"CCZ012\u00b7CCZ034","monomials":[[0,1,2],[0,3,4]],"sk_key":[[0,1,2],[0,3,4]],"sk_fingerprint":"a45e77c944711548","sk_canonical_frame":true,"relabelled_into_canonical_frame":true},"circuit":{"columns":[[0,3,5],[1,6],[2,3,4,7],[0,2,4,5,6,7],[0,1,4,8],[0,1,2,5,6,8],[1,2,3,4,6,7,8],[0,3,5,7,8],[0,2,3,9],[0,1,3,4,5,6,9],[1,2,3,5,7,9],[2,3,6,7,9],[2,3,5,8,9],[0,2,4,6,8,9],[1,2,5,6,7,8,9],[1,3,7,8,9],[0,1,2,4,10],[5,6,10],[0,3,4,5,7,10],[0,1,4,6,7,10],[1,3,5,8,10],[1,2,3,4,6,8,10],[3,4,5,6,7,8,10],[4,7,8,10],[1,5,9,10],[3,4,6,9,10],[0,3,4,7,9,10],[3,5,6,7,9,10],[0,2,8,9,10],[2,3,5,6,8,9,10],[0,1,6,7,8,9,10],[5,7,8,9,10],[0,2,3,4,11],[1,5,6,11],[5,7,11],[0,1,2,4,6,7,11],[1,2,3,4,5,8,11],[2,6,8,11],[1,3,4,5,6,7,8,11],[0,3,7,8,11],[1,2,3,5,9,11],[1,2,3,4,6,9,11],[1,3,7,9,11],[2,5,6,7,9,11],[2,8,9,11],[0,5,6,8,9,11],[1,3,4,6,7,8,9,11],[5,7,8,9,11],[0,1,2,9,10,11],[0,1,2,4,5,6,9,10,11],[1,3,4,5,7,9,10,11],[0,1,3,6,7,9,10,11],[1,2,5,8,9,10,11],[0,1,2,3,4,6,8,9,10,11],[0,3,4,5,6,7,8,9,10,11],[7,8,9,10,11],[0,1,2,3,4,5,10,11],[4,6,10,11],[3,4,7,10,11],[5,6,7,10,11],[1,2,4,8,10,11],[5,6,8,10,11],[6,7,8,10,11],[5,7,8,10,11]]},"distance":{"d":4,"is_exact":true,"upper":4,"witness":[0,1,2,3],"A_d":10088,"certified":null},"clifford":{"kind":"required","correction":{"S":[[1,1],[2,2],[4,2]],"CZ":[[0,4],[0,5],[0,7],[0,8],[0,11],[1,5],[1,8],[1,10],[2,3],[2,4],[2,6],[2,8],[2,10],[2,11],[3,4],[3,6],[3,7],[3,8],[3,9],[3,10],[3,11],[4,5],[4,7],[4,9],[4,11]]},"rotation_powers":null},"metrics":{"gamma":1.839035952556319,"gamma_t":1.2702841906813513,"gamma_rho":null,"gamma_claim":1.839035952556319,"gamma_t_claim":1.2702841906813513,"gamma_rho_claim":null,"v_ex":null,"rate":0.078125,"t_count":11,"poly_degree":3,"effective_width":5},"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.CCZ234","N":12,"d":4,"d_is_exact":true,"origin":"factory_records/findings_ccz.jsonl","provenance":"factory_records/findings_ccz.jsonl:28"},{"regime":"AI search","file":"master_catalog/AI results","label":"CCZ012.CCZ234","N":13,"d":4,"d_is_exact":true,"origin":"factory_records/findings_ccz.jsonl","provenance":"factory_records/findings_ccz.jsonl:26"},{"regime":"AI search","file":"master_catalog/AI results","label":"CCZ012.CCZ234","N":15,"d":4,"d_is_exact":true,"origin":"factory_records/findings_ccz.jsonl","provenance":"factory_records/findings_ccz.jsonl:24"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"CCZ012.CCZ234","N":12,"d":4,"d_is_exact":true,"origin":"factory_records/findings_ccz","provenance":"factory_records/findings_ccz \u00b7 catalogue.jsonl:267"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"CCZ012.CCZ234","N":13,"d":4,"d_is_exact":true,"origin":"factory_records/findings_ccz","provenance":"factory_records/findings_ccz \u00b7 catalogue.jsonl:266"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"CCZ012.CCZ234","N":15,"d":4,"d_is_exact":true,"origin":"factory_records/findings_ccz","provenance":"factory_records/findings_ccz \u00b7 catalogue.jsonl:265"}]},"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"}]}