{"id":"60.5.3.f","row":379,"stored":{"file":"master_catalog.json","row":379,"construction":null,"columns_sha256":null},"parameters":{"n":60,"k":5,"d":3,"N":12,"r":7,"level":3},"gate":{"string":"0+01+012+034","human":"T0\u00b7CS01\u00b7CCZ012\u00b7CCZ034","monomials":[[0],[0,1],[0,1,2],[0,3,4]],"sk_key":[[0],[0,1],[0,1,2],[0,3,4]],"sk_fingerprint":"9d3d347091457f19","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[6],[0,1,2,5,6],[0,1,2,3,6,7],[3,6,8],[0,3,4,5,6,8],[2,4,5,7,8],[3,6,7,8],[3,5,6,7,8],[0,3,5,6,9],[3,5,8,9],[0,1,2,3,4,6,8,9],[0,1,2,3,5,6,8,9],[2,4,7,8,9],[0,3,5,7,8,9],[3,4,5,7,10],[1,2,6,8,10],[0,3,4,5,6,8,10],[1,2,4,7,8,10],[1,5,7,8,10],[0,1,2,3,4,5,6,7,8,10],[1,2,3,4,5,6,9,10],[3,7,9,10],[1,2,3,6,7,9,10],[0,1,2,5,8,9,10],[0,1,7,8,9,10],[4,6,7,8,9,10],[0,4,11],[0,4,5,11],[2,7,11],[1,2,3,4,5,7,11],[0,2,6,7,11],[0,1,2,4,5,8,11],[0,2,4,5,6,8,11],[0,4,6,7,8,11],[1,2,4,5,9,11],[1,2,3,6,9,11],[0,1,2,5,6,9,11],[0,2,5,7,9,11],[0,2,5,6,7,9,11],[3,4,5,8,9,11],[0,2,4,6,8,9,11],[1,2,4,5,6,8,9,11],[0,4,7,8,9,11],[0,1,2,4,5,7,8,9,11],[1,2,3,6,7,8,9,11],[5,6,7,8,9,11],[1,2,3,7,10,11],[0,1,5,8,10,11],[0,3,5,6,8,10,11],[0,3,4,5,7,8,10,11],[0,4,6,7,8,10,11],[5,6,7,8,10,11],[1,2,4,5,9,10,11],[3,4,6,9,10,11],[5,6,9,10,11],[1,8,9,10,11],[6,8,9,10,11],[5,6,8,9,10,11],[7,8,9,10,11],[5,6,7,8,9,10,11]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,5,7],"A_d":269,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,3],[2,2],[4,3],[5,3],[6,3],[7,1],[8,1],[10,3],[11,3]],"CZ":[[0,2],[0,3],[0,4],[0,5],[0,8],[1,3],[1,4],[1,5],[1,7],[1,8],[1,9],[2,3],[2,4],[2,7],[2,8],[3,4],[3,5],[3,8],[3,10],[4,8],[4,10],[5,6],[5,7],[5,8],[5,9],[5,10],[6,7],[6,8],[6,9],[6,10],[6,11],[7,9],[7,10],[8,10],[9,10],[10,11]]},"rotation_powers":null},"metrics":{"gamma":2.2618595071429146,"gamma_t":1.726833027860842,"gamma_rho":null,"gamma_claim":2.2618595071429146,"gamma_t_claim":1.726833027860842,"gamma_rho_claim":null,"v_ex":null,"rate":0.08333333333333333,"t_count":9,"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 59","N":12,"d":3,"d_is_exact":true,"origin":"search_public_release_adam","provenance":"record 59 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"}]}