{"id":"60.6.3.d","row":405,"stored":{"file":"master_catalog.json","row":405,"construction":null,"columns_sha256":null},"parameters":{"n":60,"k":6,"d":3,"N":13,"r":7,"level":3},"gate":{"string":"0+3+4+01+02+03+04+13+14+23+24+34+35+45+012+013+014+015+023+024+035+045+123+124+134+234+235+245","human":"T0\u00b7T3\u00b7T4\u00b7CS01\u00b7CS02\u00b7CS03\u00b7CS04\u00b7CS13\u00b7CS14\u00b7CS23\u00b7CS24\u00b7CS34\u00b7CS35\u00b7CS45\u00b7CCZ012\u00b7CCZ013\u00b7CCZ014\u00b7CCZ015\u00b7CCZ023\u00b7CCZ024\u00b7CCZ035\u00b7CCZ045\u00b7CCZ123\u00b7CCZ124\u00b7CCZ134\u00b7CCZ234\u00b7CCZ235\u00b7CCZ245","monomials":[[0],[3],[4],[0,1],[0,2],[0,3],[0,4],[1,3],[1,4],[2,3],[2,4],[3,4],[3,5],[4,5],[0,1,2],[0,1,3],[0,1,4],[0,1,5],[0,2,3],[0,2,4],[0,3,5],[0,4,5],[1,2,3],[1,2,4],[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],[0,2,3],[0,2,4],[0,3],[0,3,5],[0,4],[0,4,5],[1,2,3],[1,2,4],[1,3],[1,3,4],[1,4],[2,3],[2,3,4],[2,3,5],[2,4],[2,4,5],[3],[3,4],[3,5],[4],[4,5]],"sk_fingerprint":"0b3ed6e5dc063e42","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,2,5,7,8],[2,6,8,9],[1,2,4,10],[0,2,4,7,10],[0,1,2,3,6,7,10],[1,2,9,10],[0,2,4,5,6,9,10],[0,1,2,6,7,9,10],[0,1,2,3,5,6,11],[0,2,5,6,8,11],[0,2,3,4,5,6,7,8,11],[2,9,11],[0,2,3,4,6,9,11],[1,2,3,4,5,6,7,9,11],[2,3,5,6,8,9,11],[2,6,7,8,9,11],[2,4,10,11],[1,2,6,10,11],[0,2,4,6,8,10,11],[0,2,3,5,7,9,10,11],[1,2,4,6,7,9,10,11],[2,7,8,9,10,11],[0,1,12],[0,1,3,6,12],[0,1,3,7,12],[0,1,8,12],[3,6,7,8,12],[0,4,5,7,9,12],[0,4,5,7,8,9,12],[4,5,6,7,8,9,12],[0,1,3,6,10,12],[3,4,6,7,10,12],[3,4,5,8,10,12],[1,3,7,8,10,12],[0,3,4,6,7,8,10,12],[8,9,10,12],[3,5,11,12],[0,3,5,6,11,12],[1,3,4,5,7,11,12],[1,5,6,7,11,12],[1,8,11,12],[0,1,7,8,11,12],[0,1,3,4,6,7,8,11,12],[0,4,5,9,11,12],[0,1,3,7,9,11,12],[0,1,3,4,6,8,9,11,12],[1,3,4,7,8,9,11,12],[6,7,8,9,11,12],[0,1,3,5,6,10,11,12],[0,1,4,7,10,11,12],[0,3,4,6,7,10,11,12],[1,4,8,10,11,12],[7,8,10,11,12],[9,10,11,12],[0,1,5,7,9,10,11,12],[6,7,9,10,11,12],[3,5,8,9,10,11,12],[6,8,9,10,11,12],[7,8,9,10,11,12],[6,7,8,9,10,11,12]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,8,10],"A_d":268,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,2],[1,3],[2,1],[4,1],[5,2],[6,1],[8,2],[9,2],[10,1],[11,1],[12,1]],"CZ":[[0,4],[0,8],[0,9],[0,12],[1,3],[1,4],[1,5],[1,7],[1,12],[2,4],[2,6],[2,7],[2,11],[3,7],[3,8],[3,10],[3,12],[4,5],[4,7],[4,8],[4,9],[4,11],[4,12],[5,6],[5,7],[5,9],[5,10],[5,11],[6,8],[6,9],[6,10],[7,12],[8,9],[8,11],[9,10],[10,11],[10,12]]},"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 619","N":13,"d":3,"d_is_exact":true,"origin":"search_public_release_adam","provenance":"record 619 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"}]}