{"id":"60.6.3.k","row":412,"stored":{"file":"master_catalog.json","row":412,"construction":null,"columns_sha256":null},"parameters":{"n":60,"k":6,"d":3,"N":13,"r":7,"level":3},"gate":{"string":"0+1+2+01+02+03+14+24+34+35+45+012+013+014+023+025+045+135+234+245","human":"T0\u00b7T1\u00b7T2\u00b7CS01\u00b7CS02\u00b7CS03\u00b7CS14\u00b7CS24\u00b7CS34\u00b7CS35\u00b7CS45\u00b7CCZ012\u00b7CCZ013\u00b7CCZ014\u00b7CCZ023\u00b7CCZ025\u00b7CCZ045\u00b7CCZ135\u00b7CCZ234\u00b7CCZ245","monomials":[[0],[1],[2],[0,1],[0,2],[0,3],[1,4],[2,4],[3,4],[3,5],[4,5],[0,1,2],[0,1,3],[0,1,4],[0,2,3],[0,2,5],[0,4,5],[1,3,5],[2,3,4],[2,4,5]],"sk_key":[[0],[0,1],[0,1,2],[0,1,3],[0,1,4],[0,2],[0,2,3],[0,2,5],[0,3],[0,4,5],[1],[1,3,5],[1,4],[2],[2,3,4],[2,4],[2,4,5],[3,4],[3,5],[4,5]],"sk_fingerprint":"68f49fa2024cc4d4","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[3,7],[0,1,3,5,8],[1,4,5,6,8],[0,1,3,6,9],[0,1,2,4,7,9],[1,2,3,4,5,6,7,9],[0,2,3,4,6,8,9],[1,2,3,4,7,8,9],[1,2,3,4,10],[0,2,3,5,6,7,9,10],[0,1,3,4,5,6,8,9,10],[0,1,2,3,4,5,7,8,9,10],[5,6,11],[1,4,5,7,11],[0,1,2,4,5,7,8,11],[1,4,9,11],[0,2,3,5,7,9,11],[0,2,3,5,6,7,8,9,11],[0,1,3,4,5,6,10,11],[1,4,6,7,10,11],[2,8,10,11],[1,4,5,6,9,10,11],[3,5,6,7,9,10,11],[1,4,6,8,9,10,11],[1,4,5,7,8,9,10,11],[5,6,7,8,9,10,11],[5,6,12],[0,3,6,7,12],[0,3,5,7,8,12],[2,3,5,9,12],[0,1,4,5,6,7,9,12],[0,1,2,3,4,5,8,9,12],[1,2,3,4,6,8,9,12],[0,3,7,8,9,12],[1,3,10,12],[1,2,3,4,6,7,10,12],[2,3,4,8,10,12],[2,3,4,5,6,9,10,12],[7,9,10,12],[1,3,5,6,8,9,10,12],[0,3,5,7,8,9,10,12],[6,7,8,9,10,12],[0,1,4,5,6,11,12],[5,6,8,11,12],[5,7,8,11,12],[0,2,9,11,12],[6,9,11,12],[7,9,11,12],[0,8,9,11,12],[6,8,9,11,12],[0,2,5,10,11,12],[6,10,11,12],[0,7,10,11,12],[0,1,2,3,4,6,8,10,11,12],[6,7,8,10,11,12],[6,9,10,11,12],[2,3,7,9,10,11,12],[6,7,9,10,11,12],[8,9,10,11,12],[6,8,9,10,11,12]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,3,5],"A_d":273,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,1],[2,2],[3,2],[5,2],[7,2],[8,2],[9,2],[10,1],[12,3]],"CZ":[[0,4],[0,5],[0,6],[0,9],[0,11],[1,2],[1,3],[1,4],[1,5],[1,6],[1,7],[1,9],[1,11],[2,4],[2,5],[2,7],[2,8],[2,9],[2,10],[2,12],[3,4],[3,6],[3,7],[3,8],[3,9],[3,10],[3,11],[3,12],[4,5],[4,6],[4,7],[4,9],[4,11],[5,7],[5,8],[5,11],[6,8],[6,10],[6,11],[6,12],[7,9],[7,10],[7,11],[7,12],[8,9],[8,10],[8,11],[9,10],[9,11],[10,11],[10,12],[11,12]]},"rotation_powers":null},"metrics":{"gamma":2.095903274289385,"gamma_t":1.8340437671464696,"gamma_rho":null,"gamma_claim":2.095903274289385,"gamma_t_claim":1.8340437671464696,"gamma_rho_claim":null,"v_ex":null,"rate":0.1,"t_count":8,"poly_degree":2,"effective_width":6},"provenance":{"regimes":["AI search: generalised triorthogonal search 55<=n<=64"],"discovery":"AI search","strongest_claim":"found by the AI-assisted public search for generalised triorthogonal protocols at lengths 55-64; a verified witness, not a maximum","sources":[{"regime":"AI search: generalised triorthogonal search 55<=n<=64","file":"data/protocols/index.json","label":"release record 523","N":13,"d":3,"d_is_exact":true,"origin":"search_public_release_adam","provenance":"record 523 of the released catalogue, stored length 60","notes":"re-verified against factorylib/verification.py in audit_ours/results/audit_report.json; declared d_Z=3"}]},"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"}]}