{"id":"60.5.3.t","row":393,"stored":{"file":"master_catalog.json","row":393,"construction":null,"columns_sha256":null},"parameters":{"n":60,"k":5,"d":3,"N":12,"r":7,"level":3},"gate":{"string":"0+13+012+034+123","human":"T0\u00b7CS13\u00b7CCZ012\u00b7CCZ034\u00b7CCZ123","monomials":[[0],[1,3],[0,1,2],[0,3,4],[1,2,3]],"sk_key":[[0],[0,1,2],[0,3,4],[1,2,3],[1,3]],"sk_fingerprint":"96da93cbefdac07a","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[1,2,3,5],[1,2,6,7],[0,3,6,8],[5,7,8],[0,3,4,9],[4,6,9],[0,1,3,5,6,9],[0,2,7,9],[0,5,8,9],[2,4,6,8,9],[0,2,5,6,8,9],[0,1,2,4,5,7,8,9],[3,4,5,10],[0,1,2,3,4,5,6,10],[0,2,4,7,10],[1,3,5,7,10],[2,5,8,10],[2,3,4,6,8,10],[0,1,3,5,9,10],[1,2,4,5,6,9,10],[0,1,3,4,5,7,9,10],[4,6,7,9,10],[0,1,2,3,8,9,10],[0,3,4,5,8,9,10],[0,11],[0,2,3,5,11],[3,5,6,11],[0,1,4,5,7,11],[2,3,4,5,6,8,11],[1,3,5,7,8,11],[0,1,2,3,6,7,8,11],[1,2,3,5,6,7,8,11],[1,3,4,9,11],[3,4,5,9,11],[2,3,6,9,11],[0,1,2,4,6,7,9,11],[1,8,9,11],[4,7,8,9,11],[0,1,3,6,7,8,9,11],[5,6,7,8,9,11],[0,3,4,10,11],[1,2,3,5,10,11],[1,3,4,5,7,10,11],[0,1,3,5,6,7,10,11],[2,5,8,10,11],[1,4,5,6,8,10,11],[4,7,8,10,11],[5,7,8,10,11],[0,2,3,9,10,11],[0,1,3,4,5,9,10,11],[3,4,6,9,10,11],[2,5,6,9,10,11],[1,7,9,10,11],[5,7,9,10,11],[0,1,2,3,4,8,9,10,11],[5,8,9,10,11],[0,1,2,4,7,8,9,10,11],[5,7,8,9,10,11],[6,7,8,9,10,11],[5,6,7,8,9,10,11]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,5,6],"A_d":270,"certified":null},"clifford":{"kind":"required","correction":{"S":[[1,3],[3,1],[4,3],[5,3],[7,3],[8,2],[9,3],[11,2]],"CZ":[[0,1],[0,7],[0,8],[1,3],[1,6],[1,7],[1,8],[1,9],[1,10],[2,4],[3,4],[3,5],[3,8],[3,9],[3,11],[4,6],[4,7],[4,8],[4,11],[5,7],[6,7],[6,9],[6,10],[6,11],[7,8],[7,9],[7,10],[7,11],[8,10],[8,11],[9,10]]},"rotation_powers":null},"metrics":{"gamma":2.2618595071429146,"gamma_t":1.6309297535714573,"gamma_rho":null,"gamma_claim":2.2618595071429146,"gamma_t_claim":1.6309297535714573,"gamma_rho_claim":null,"v_ex":null,"rate":0.08333333333333333,"t_count":10,"poly_degree":2,"effective_width":5},"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 56","N":12,"d":3,"d_is_exact":true,"origin":"search_public_release_adam","provenance":"record 56 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"}]}