{"id":"60.6.3.b","row":403,"stored":{"file":"master_catalog.json","row":403,"construction":null,"columns_sha256":null},"parameters":{"n":60,"k":6,"d":3,"N":13,"r":7,"level":3},"gate":{"string":"01+02+03+04+05+012+013+014+123+124+134+235+245+345","human":"CS01\u00b7CS02\u00b7CS03\u00b7CS04\u00b7CS05\u00b7CCZ012\u00b7CCZ013\u00b7CCZ014\u00b7CCZ123\u00b7CCZ124\u00b7CCZ134\u00b7CCZ235\u00b7CCZ245\u00b7CCZ345","monomials":[[0,1],[0,2],[0,3],[0,4],[0,5],[0,1,2],[0,1,3],[0,1,4],[1,2,3],[1,2,4],[1,3,4],[2,3,5],[2,4,5],[3,4,5]],"sk_key":[[0,1],[0,1,2],[0,1,3],[0,1,4],[0,2],[0,3],[0,4],[0,5],[1,2,3],[1,2,4],[1,3,4],[2,3,5],[2,4,5],[3,4,5]],"sk_fingerprint":"08e4d52068f8d135","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[1,2,4,6],[1,2,3,7],[0,3,4,5,6,7],[0,3,5,6,8],[0,2,4,5,7,8],[3,4,5,6,7,8],[5,9],[1,2,3,4,6,7,9],[5,6,8,9],[0,4,5,7,8,9],[0,3,5,6,10],[4,5,6,8,10],[1,4,9,10],[0,1,2,6,9,10],[0,1,3,8,9,10],[0,2,3,5,6,8,9,10],[1,7,11],[0,2,3,5,6,7,8,11],[0,3,4,5,6,9,11],[0,5,6,7,9,11],[0,2,4,5,6,8,9,11],[3,5,7,8,9,11],[0,1,3,10,11],[0,3,5,6,10,11],[2,5,7,10,11],[0,2,4,5,7,8,10,11],[1,3,9,10,11],[0,1,2,4,6,9,10,11],[0,3,5,7,9,10,11],[0,1,3,6,7,9,10,11],[5,8,9,10,11],[1,2,6,8,9,10,11],[3,6,12],[1,2,3,4,5,7,12],[3,4,7,8,12],[1,4,5,6,7,8,12],[0,1,4,5,9,12],[0,1,3,4,5,6,9,12],[1,4,5,6,7,9,12],[2,3,8,9,12],[0,1,4,5,10,12],[1,2,4,5,6,10,12],[2,3,4,6,8,10,12],[0,3,4,7,8,10,12],[1,3,5,6,7,9,10,12],[6,8,9,10,12],[1,2,3,4,5,11,12],[0,2,3,4,6,11,12],[2,7,11,12],[1,4,5,6,7,11,12],[2,3,4,6,8,11,12],[0,1,2,3,4,5,7,8,11,12],[2,3,4,7,9,11,12],[6,8,9,11,12],[1,3,5,10,11,12],[7,10,11,12],[7,8,10,11,12],[6,7,8,10,11,12],[6,7,9,10,11,12],[8,9,10,11,12]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,2],"A_d":272,"certified":null},"clifford":{"kind":"required","correction":{"S":[[2,1],[3,1],[4,2],[7,2],[8,3],[9,2],[10,2],[11,1],[12,2]],"CZ":[[0,1],[0,2],[0,4],[0,5],[0,6],[0,7],[0,8],[0,12],[1,2],[1,4],[1,7],[1,11],[2,4],[2,5],[2,7],[2,8],[2,12],[3,4],[3,7],[3,11],[3,12],[4,5],[4,7],[4,9],[4,11],[5,6],[5,8],[5,9],[5,11],[6,8],[6,10],[6,11],[6,12],[7,9],[7,10],[7,12],[9,10],[9,11],[9,12],[11,12]]},"rotation_powers":null},"metrics":{"gamma":2.095903274289385,"gamma_t":1.6309297535714573,"gamma_rho":null,"gamma_claim":2.095903274289385,"gamma_t_claim":1.6309297535714573,"gamma_rho_claim":null,"v_ex":null,"rate":0.1,"t_count":10,"poly_degree":3,"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 138","N":13,"d":3,"d_is_exact":true,"origin":"search_public_release_adam","provenance":"record 138 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"}]}