{"id":"176.3.5.a","row":804,"stored":{"file":"master_catalog.json","row":804,"construction":null,"columns_sha256":null},"parameters":{"n":176,"k":3,"d":5,"N":27,"r":24,"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],[1,2,4],[5],[0,2,6],[0,2,7],[0,2,8],[1,2,9],[2,10],[11],[0,2,12],[0,1,2,13],[2,14],[0,1,2,15],[1,16],[2,17],[18],[0,6,8,9,10,15],[1,2,19],[2,3,5,6,7,10,15,17],[1,20],[0,1,2,21],[0,1,2,4,6,8,10,12,13,17],[22],[0,3,4,5,6,7,11,13,14,18,19,20,21,22],[1,2,5,8,9,10,13],[2,3,5,6,8,11,12,16,17,22],[1,5,7,8,12,13,15,17],[0,1,11,16,18,19,22],[1,23],[3,4,5,6,10,12,15],[0,3,8,12,14,16,19,22],[1,4,5,6,7,10,12,15,17,18,21,22],[1,2,24],[0,1,2,3,5,6,8,11,12,14,17,18,19,22],[5,7,11,15,17,18,21],[1,2,8,10,12,14,19,20,24],[2,6,7,9,10,15,17,18,19,21],[0,3,10,11,12,13,15,17,19,20,21,22],[2,3,6,7,8,11,12,14,15,18,19,20],[0,1,2,3,5,7,10,11,12,13,14,20,21,22],[0,1,3,4,5,8,10,11,17,18,19,20,22],[2,3,5,7,8,11,19,21,22,23],[1,2,5,12,14,16,17,19,22],[1,2,7,8,10,12,14,19,20,21,23],[0,1,3,4,5,6,8,10,11,12,17,18,19,22,23],[0,2,25],[0,1,3,6,14,16,17,19,22],[1,5,7,8,10,13,14,16,19,20,23,24],[2,3,6,8,10,12,15,24],[0,1,2,5,7,8,9,13,17,18,20,21],[2,5,8,10,12,13,17,24],[1,26],[0,3,6,7,10,14,15,19,21,24],[3,5,7,8,13,14,18,20,21,22,24],[2,3,8,11,12,14,15,16,17,19,21,22,24,26],[0,1,3,8,9,10,12,14,17,18,19,20,22],[1,3,4,5,6,7,10,11,12,17,18,21,22,23],[0,3,8,11,12,14,15,16,17,19,20,21,24,25],[0,2,3,7,10,11,12,13,16,20,22,23,24],[0,1,2,3,4,5,6,7,8,11,14,19,20,21,22,23],[0,1,2,5,7,8,10,11,12,14,16,19,21,22,24,25],[0,3,5,6,7,9,10,11,15,17,22,23],[2,3,5,7,8,10,11,12,14,19,20,21,22,25],[0,2,4,5,6,7,8,9,12,14,15,17,18,22],[0,1,2,3,5,7,10,13,14,16,20,22,23,24],[0,2,3,7,8,9,10,14,16,18,20,21,22,23,24],[1,2,3,6,8,14,15,16,17,19,21,23,24,25,26],[0,2,3,6,8,11,14,17,19,22,26],[3,8,11,14,26],[2,9,12,20,21,26],[1,2,5,7,8,9,10,11,13,15,18,20,22,24,26],[0,1,2,4,5,6,7,9,10,15,17,18,19,20,22,25,26],[1,5,6,7,11,13,15,16,20,22,24,26],[0,12,16,19,20,21,24,26],[2,3,4,6,10,14,15,16,19,21,24,26],[0,1,2,3,7,9,10,16,18,21,22,23],[1,4,5,6,7,8,9,11,12,14,16,18,21,22,24,25,26],[0,2,6,9,10,15,18,21,23],[0,10,11,15,16,17,21,22,24,25],[1,6,9,12,14,15,18,20,21,23],[1,2,4,6,9,10,14,15,16,18,19,23,24,26],[0,1,2,3,5,7,8,9,11,12,16,17,21,22,23,24],[2,3,5,6,7,10,11,13,15,17,20,23,25,26],[2,10,16,22,24,25],[0,1,2,3,4,6,9,10,13,14,15,16,19,20,24,25],[0,3,4,6,7,9,11,12,13,16,18,20,21,22,23,24,26],[2,7,17,18,21,25],[0,2,4,5,6,7,9,10,15,16,17,18,19,24],[5,7,8,12,13,16,17,18,19,24],[0,1,2,9,14,16,18,19,23,24],[0,3,5,6,7,10,12,15,17,20,21,23,25,26],[0,4,5,7,12,14,16,17,19,21,23,24],[0,11,12,16,18,20,21,22,23,24,25,26],[0,1,3,4,5,6,7,8,10,15,16,17,23,25],[0,1,4,5,7,9,14,16,17,19,21,23,24,26],[0,1,3,8,9,11,14,15,18,21,26],[0,1,4,6,7,9,10,12,15,17,18,20,25,26],[1,3,5,6,7,9,11,12,13,14,15,18,19,20,22,26],[0,1,2,7,8,9,10,11,15,16,18,20,21,22,24,26],[1,4,5,7,9,10,11,14,15,18,19,20,22,25,26],[0,1,4,6,7,8,13,15,18,19,20,22,26],[6,8,9,10,15,19,21,24,26],[1,2,5,7,8,9,13,17,20,21,25,26],[0,2,9,10,11,12,18,20,21,24,26],[0,3,7,8,9,14,17,18,24,25,26],[0,3,4,5,6,8,10,12,15,25,26],[2,3,4,5,6,7,10,12,15,17,18,20,21,22,24,26],[1,4,5,6,7,8,10,13,15,16,17,18,19,20,24,26],[0,3,4,5,6,8,9,10,14,15,16,17,18,19,24,25,26],[4,10,12,16,18,20,21,24,26],[0,2,4,5,7,8,9,13,16,17,18,20,21,24,25,26],[0,1,3,7,8,9,10,11,14,16,18,21,22,24,26],[1,2,9,10,16,18,23],[0,2,3,4,6,8,10,14,15,16,17,19,21,24,25,26],[1,3,5,7,8,9,11,16,17,19,20,21,22,23],[0,1,2,3,10,15,17,18,19,23,24,25],[0,3,4,5,6,8,15,16,18,20,21,23],[0,3,7,8,9,10,11,14,16,19,21,22,24,25,26],[0,2,7,8,10,11,12,14,15,16,18,19,22,24,25],[3,4,5,6,7,8,9,10,11,12,17,18,21,22,23,26],[0,1,3,7,8,12,14,16,17,18,19,20,21,24,25],[1,3,6,7,9,15,16,17,23,24,25],[1,5,7,8,11,12,13,15,16,17,20,22,23,24,25,26],[0,2,4,11,16,18,19,23,24],[0,1,8,10,11,14,15,17,18,19,21,22,23,25,26],[0,1,4,5,7,10,12,14,16,18,19,20,21,23,24],[0,1,2,3,4,5,7,8,9,11,12,15,22,23,25,26],[1,3,4,6,14,15,17,19,24,25,26],[0,3,4,5,7,8,9,11,12,17,22,23,26],[0,1,2,3,4,6,8,9,10,12,13,15,16,20,24,25],[4,5,6,8,9,12,14,15,17,18,19,22,23,26],[0,1,5,7,9,10,14,15,19,22,23,25],[4,6,9,10,16,18,19,24],[0,1,5,10,12,14,17,18,19,20,23,26],[0,2,3,6,10,11,12,20,23,26],[2,8,10,12,13,14,18,19,20,23,25,26],[4,5,7,10,12,14,19,21,22,24,25,26],[0,1,4,5,7,8,9,10,13,17,20,21,23,26],[0,1,4,5,10,12,14,17,19,22,23,25],[0,4,5,6,7,9,12,14,15,16,18,22,23,25],[0,9,10,16,17,23,25],[0,1,3,4,5,6,8,11,14,17,19,20,21,22,26],[1,2,3,5,7,8,9,17,18,21,25,26],[4,5,7,8,13,17,19,20,21,22,25,26],[3,4,5,6,8,11,12,14,15,17,18,19,21,22,26],[0,2,5,8,9,10,13,16,20,24,26],[2,3,8,9,10,11,14,15,17,25,26],[0,1,5,7,8,9,10,11,13,16,17,18,20,21,22,24,25,26],[3,4,5,6,7,8,11,14,18,19,21,22,25,26],[0,1,3,8,9,10,11,14,15,19,21,24,25,26],[0,2,3,4,5,6,7,8,10,11,12,17,18,21,22,24,26],[1,3,6,8,9,10,13,14,15,19,20,21,24,25,26],[3,4,10,11,12,13,19,20,22,24,26],[3,4,6,7,10,11,12,13,14,18,20,21,22,24,25,26],[3,4,5,6,7,8,11,12,14,16,18,19,22,24,25,26],[6,8,9,11,14,15,16,17,22,24,25,26],[3,4,6,8,10,13,15,16,19,20,21,24,25,26],[1,2,18,19,23,24,25],[3,4,5,6,7,10,15,16,17,19,23],[3,10,12,13,18,19,23,24,25],[3,4,6,8,10,11,15,16,18,21,23],[3,5,7,11,13,14,17,19,20,21,23,24,25],[3,4,6,8,9,10,11,13,15,18,20,21,23,26],[10,12,18,20,23,26],[5,7,10,12,14,19,21,22,23,25,26],[3,4,5,6,9,10,11,13,14,15,16,17,18,19,20,24,25],[3,4,5,6,8,9,10,11,12,14,15,17,18,19,21,22,23,26],[3,4,6,8,9,12,13,15,16,23,24,25],[4,5,6,7,8,9,11,12,14,15,19,22,23,25,26],[3,4,5,6,7,12,15,16,17,23,24,25],[10,12,14,19,20,21,23,25,26],[4,5,6,7,9,14,15,18,19,22,23,25,26],[4,5,6,7,9,12,14,15,19,22,23,25],[3,4,5,6,7,9,15,16,17,23,25],[10,12,14,17,19,20,23,24,25],[5,7,10,11,12,14,15,19,21,22,23,24,25]]},"distance":{"d":5,"is_exact":true,"upper":5,"witness":[1,28,40,58,88],"A_d":1292,"certified":null},"clifford":{"kind":"required","correction":{"S":[[1,3],[2,3]],"CZ":[[0,2],[0,4],[0,5],[0,6],[0,7],[0,9],[0,14],[0,15],[0,22],[0,23],[0,24],[0,26],[1,2],[2,3],[2,5],[2,7],[2,8],[2,9],[2,10],[2,11],[2,12],[2,17],[2,18],[2,19],[2,21],[2,24],[2,26]]},"rotation_powers":null},"metrics":{"gamma":2.5299961402125652,"gamma_t":2.003540379576383,"gamma_rho":2.7819257766251577,"gamma_claim":2.5299961402125652,"gamma_t_claim":2.003540379576383,"gamma_rho_claim":2.7819257766251577,"v_ex":2,"rate":0.017045454545454544,"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":27,"d":5,"d_is_exact":true,"origin":"factory_records/findings_ccz.jsonl","provenance":"factory_records/findings_ccz.jsonl:2"},{"regime":"AI search","file":"master_catalog/AI results","label":"CCZ012","N":28,"d":6,"d_is_exact":true,"origin":"factory_records/findings_ccz.jsonl","provenance":"factory_records/findings_ccz.jsonl:1","notes":["source stored d=5, the exact distance is 6"]},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"CCZ012","N":27,"d":5,"d_is_exact":true,"origin":"factory_records/findings_ccz","provenance":"factory_records/findings_ccz \u00b7 catalogue.jsonl:353"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"CCZ012","N":28,"d":6,"d_is_exact":true,"origin":"factory_records/findings_ccz","provenance":"factory_records/findings_ccz \u00b7 catalogue.jsonl:352"}]},"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"}]}