{"id":"56.6.3.a","row":333,"stored":{"file":"master_catalog.json","row":333,"construction":null,"columns_sha256":null},"parameters":{"n":56,"k":6,"d":3,"N":13,"r":7,"level":3},"gate":{"string":"0+3+4+5+01+02+23+24+25+34+35+45+012+013+014+015+034+134+234+235+245","human":"T0\u00b7T3\u00b7T4\u00b7T5\u00b7CS01\u00b7CS02\u00b7CS23\u00b7CS24\u00b7CS25\u00b7CS34\u00b7CS35\u00b7CS45\u00b7CCZ012\u00b7CCZ013\u00b7CCZ014\u00b7CCZ015\u00b7CCZ034\u00b7CCZ134\u00b7CCZ234\u00b7CCZ235\u00b7CCZ245","monomials":[[0],[3],[4],[5],[0,1],[0,2],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5],[0,1,2],[0,1,3],[0,1,4],[0,1,5],[0,3,4],[1,3,4],[2,3,4],[2,3,5],[2,4,5]],"sk_key":[[0],[0,1],[0,1,2],[0,1,3],[0,1,4],[0,1,5],[0,2],[0,3,4],[1,3,4],[2,3],[2,3,4],[2,3,5],[2,4],[2,4,5],[2,5],[3],[3,4],[3,5],[4],[4,5],[5]],"sk_fingerprint":"c1bdd65609c256c4","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[2,4,9,10],[2,6,9,10],[1,2,3,4,5,7,9,10],[1,2,3,5,6,7,9,10],[0,2,5,8,9,10],[1,2,4,5,6,8,9,10],[0,2,4,5,7,8,9,10],[0,1,2,3,4,6,7,8,9,10],[1,2,4,5,11],[1,2,3,5,6,11],[2,3,5,7,11],[0,2,3,6,7,11],[0,2,3,5,8,9,11],[1,2,3,6,8,9,11],[2,4,5,7,8,9,11],[0,1,2,4,6,7,8,9,11],[0,1,2,3,4,8,10,11],[2,4,5,6,8,10,11],[1,2,7,8,10,11],[0,2,3,5,6,7,8,10,11],[0,2,3,5,8,9,10,11],[0,1,2,6,8,9,10,11],[2,4,5,7,8,9,10,11],[0,1,2,5,6,7,8,9,10,11],[4,5,12],[0,1,6,12],[1,3,4,8,12],[1,3,5,6,8,12],[3,4,5,9,12],[1,3,6,9,12],[0,1,5,8,9,12],[0,1,3,5,6,8,9,12],[1,4,7,10,12],[1,4,6,7,10,12],[1,4,5,7,8,10,12],[3,6,7,8,10,12],[0,3,5,9,10,12],[0,4,6,9,10,12],[0,1,3,4,5,8,9,10,12],[6,8,9,10,12],[4,5,11,12],[3,4,5,6,11,12],[0,1,3,7,8,11,12],[6,7,8,11,12],[0,1,7,9,11,12],[1,3,6,7,9,11,12],[0,1,4,5,8,9,11,12],[6,8,9,11,12],[1,3,7,10,11,12],[0,4,5,6,7,10,11,12],[0,8,10,11,12],[6,8,10,11,12],[0,1,7,9,10,11,12],[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":[0,12,16],"A_d":224,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,1],[1,2],[3,1],[4,1],[5,3],[6,2]],"CZ":[[0,1],[0,3],[0,6],[0,7],[0,10],[0,11],[1,3],[1,6],[1,7],[1,10],[1,11],[3,5],[3,7],[3,10],[4,7],[4,10],[4,11],[5,6],[5,7],[5,10],[5,11]]},"rotation_powers":null},"metrics":{"gamma":2.033103256304337,"gamma_t":1.7712437491614221,"gamma_rho":null,"gamma_claim":2.033103256304337,"gamma_t_claim":1.7712437491614221,"gamma_rho_claim":null,"v_ex":null,"rate":0.10714285714285714,"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 750","N":13,"d":3,"d_is_exact":true,"origin":"search_public_release_adam","provenance":"record 750 of the released catalogue, stored length 56","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"}]}