{"id":"77.3.4.a","row":542,"stored":{"file":"master_catalog.json","row":542,"construction":null,"columns_sha256":null},"parameters":{"n":77,"k":3,"d":4,"N":13,"r":10,"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":[[0,2,3],[0,2,4],[0,5],[1,6],[0,2,7],[8],[2,5,6,7],[0,1,2,9],[1,10],[0,11],[0,1,3,4,10],[1,12],[6,8,10],[1,8,9,11],[4,6,9],[3,5,6,9,10],[0,3,4,8],[0,1,2,3,5,6,7,8,9,10,12],[2,3,6,7,8,9],[1,2,3,5,11],[0,3,9,10],[0,4,6,8,9,10,11],[1,2,3,5,6,10,12],[1,2,5,6,7,8,10],[0,1,4,5,6,7,8,12],[0,2,3,4,7,8,12],[2,3,5,6,7,9],[0,1,2,3,4,8,9,10],[0,5,6,12],[1,2,4,8,9,10,11,12],[2,3,4,5,8,9,12],[1,2,4,5,6,11,12],[0,3,4,6,7,8,9,10,12],[0,3,8,9],[0,1,4,5,7,8,10,12],[0,6,7,8,9,10,11],[3,4,7,9,10,11],[0,3,5,6,8,10,11,12],[0,1,2,3,6,8,9,11,12],[0,4,6,7,8,9,11],[0,3,5,6,11,12],[0,1,2,4,5,6,8,11],[0,1,3,4,6,10,12],[0,4,7,8,9,10,11],[0,1,2,4,5,7,8,9,10,11,12],[3,4,5,7,8,9,10,12],[0,3,5,7,8,9,10,11,12],[1,3,6,7,11,12],[0,1,4,6,9,10,11,12],[1,2,4,5,7,8,9,12],[0,4,5,6,9,12],[1,2,3,4,5,6,7,9,11],[2,5,8,9,10,11,12],[0,1,3,7,12],[0,1,2,4,5,6,7,8,10,11,12],[2,4,5,7,9,10,11],[0,2,3,7,9,10,12],[0,1,2,3,4,6,7,8,9,11,12],[2,5,6,7,8,11],[2,3,4,5,7,9,10,11,12],[2,3,5,6,7,11],[0,1,4,6,8,10,11,12],[3,8,9,10,11,12],[0,1,2,3,4,6,7,9,10,11,12],[2,3,4,5,7,8,10],[2,3,5,6,7,9,10,11,12],[3,4,8,9,11,12],[3,4,7,8,10,11],[3,4,7,8,9,10,11,12],[3,4,5,6,7,9,10,12],[3,4,6,7,8,10,11,12],[3,4,6,7,10,11],[4,10,11],[4,5,6,7,8,9,11,12],[4,6,7,9,11,12],[6,7,8,10,11,12],[3,6,7,8,9,10,11,12]]},"distance":{"d":4,"is_exact":true,"upper":4,"witness":[0,1,5,16],"A_d":1860,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,2],[1,2]],"CZ":[[0,2],[0,3],[0,6],[0,9],[0,10],[1,8],[1,10],[1,11],[1,12],[2,3],[2,9],[2,10]]},"rotation_powers":[[1,3],[2,3],[4,3],[5,3],[7,3],[10,3],[11,3],[30,3],[31,3],[33,3],[35,3],[39,3],[42,3],[45,3],[46,3],[49,3],[50,3],[51,3],[54,3],[55,3],[59,3],[61,3],[62,3],[63,3],[64,3],[66,3],[67,3],[70,3],[71,3],[76,3]]},"metrics":{"gamma":2.3409120199868725,"gamma_t":1.7297158093186489,"gamma_rho":2.633393270347451,"gamma_claim":2.3409120199868725,"gamma_t_claim":1.7297158093186489,"gamma_rho_claim":2.633393270347451,"v_ex":2,"rate":0.03896103896103896,"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":13,"d":4,"d_is_exact":true,"origin":"factory_records/findings_ccz.jsonl","provenance":"factory_records/findings_ccz.jsonl:29"},{"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:314"}]},"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"}]}