{"id":"63.6.3.f","row":451,"stored":{"file":"master_catalog.json","row":451,"construction":null,"columns_sha256":null},"parameters":{"n":63,"k":6,"d":3,"N":16,"r":10,"level":3},"gate":{"string":"0+2+3+4+01+14+23+24+012+013+045+145+245+345","human":"T0\u00b7T2\u00b7T3\u00b7T4\u00b7CS01\u00b7CS14\u00b7CS23\u00b7CS24\u00b7CCZ012\u00b7CCZ013\u00b7CCZ045\u00b7CCZ145\u00b7CCZ245\u00b7CCZ345","monomials":[[0],[2],[3],[4],[0,1],[1,4],[2,3],[2,4],[0,1,2],[0,1,3],[0,4,5],[1,4,5],[2,4,5],[3,4,5]],"sk_key":[[0],[0,1],[0,1,2],[0,1,3],[0,4,5],[1,4],[1,4,5],[2],[2,3],[2,4],[2,4,5],[3],[3,4,5],[4]],"sk_fingerprint":"49b2d8187575c2dc","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,2,3,4,6],[0,2,3,4,7],[0,2,3,4,6,7],[0,2,3,4,8],[0,2,3,4,6,8],[0,2,3,4,7,8],[0,2,3,4,6,7,8],[9],[6,9],[7,9],[6,7,9],[8,9],[6,8,9],[7,8,9],[6,7,8,9],[1,2,5,14],[1,2,3,4,10,14],[0,11,14],[3,4,5,10,11,14],[0,2,12,14],[0,2,3,5,10,12,14],[0,1,4,5,11,12,14],[1,3,4,10,11,12,14],[0,3,4,5,13,14],[0,10,13,14],[2,11,13,14],[0,2,3,4,5,10,11,13,14],[0,2,12,13,14],[0,2,3,5,10,12,13,14],[0,3,5,11,12,13,14],[10,11,12,13,14],[0,3,4,5,15],[1,2,5,10,15],[1,4,5,11,15],[0,1,2,4,5,10,11,15],[3,5,12,15],[3,5,10,12,15],[1,2,5,11,12,15],[2,3,4,5,10,11,12,15],[0,1,2,3,4,13,15],[1,2,3,10,13,15],[0,11,13,15],[1,3,10,11,13,15],[0,1,2,3,12,13,15],[0,10,12,13,15],[2,4,11,12,13,15],[10,11,12,13,15],[0,1,2,3,4,14,15],[0,2,10,14,15],[0,1,2,3,4,11,14,15],[1,2,3,4,10,11,14,15],[1,3,4,12,14,15],[0,1,2,3,10,12,14,15],[1,2,3,11,12,14,15],[10,11,12,14,15],[13,14,15],[2,4,10,13,14,15],[0,1,2,3,11,13,14,15],[10,11,13,14,15],[0,1,3,4,12,13,14,15],[10,12,13,14,15],[11,12,13,14,15],[10,11,12,13,14,15]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,2],"A_d":283,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,2],[1,2],[2,1],[3,1]],"CZ":[[0,1],[0,12],[1,2],[1,3],[1,5],[1,11],[1,13],[2,3],[2,4],[2,11],[2,12],[2,13],[3,5],[3,11],[3,13],[4,11],[4,12],[4,13]]},"rotation_powers":null},"metrics":{"gamma":2.1403139955899646,"gamma_t":1.6753404748720375,"gamma_rho":null,"gamma_claim":2.1403139955899646,"gamma_t_claim":1.6753404748720375,"gamma_rho_claim":null,"v_ex":null,"rate":0.09523809523809523,"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 111","N":16,"d":3,"d_is_exact":true,"origin":"search_public_release_adam","provenance":"record 111 of the released catalogue, stored length 63","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"}]}