{"id":"60.6.3.o","row":416,"stored":{"file":"master_catalog.json","row":416,"construction":null,"columns_sha256":null},"parameters":{"n":60,"k":6,"d":3,"N":13,"r":7,"level":3},"gate":{"string":"0+4+5+01+02+03+12+13+14+15+23+24+25+34+35+045","human":"T0\u00b7T4\u00b7T5\u00b7CS01\u00b7CS02\u00b7CS03\u00b7CS12\u00b7CS13\u00b7CS14\u00b7CS15\u00b7CS23\u00b7CS24\u00b7CS25\u00b7CS34\u00b7CS35\u00b7CCZ045","monomials":[[0],[4],[5],[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[0,4,5]],"sk_key":[[0],[0,1],[0,2],[0,3],[0,4,5],[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4],[5]],"sk_fingerprint":"49b0861881dda694","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[2,4,5,6],[0,1,2,3,5,6,7],[1,2,3,7,8],[3,6,9],[1,4,8,9],[0,1,4,6,8,9],[0,3,4,10],[0,2,4,7,10],[2,5,6,8,10],[0,3,5,7,8,10],[0,2,5,6,7,8,10],[2,3,4,9,10],[0,3,6,9,10],[2,3,4,6,7,9,10],[0,3,5,11],[0,1,2,3,5,6,7,11],[4,8,11],[0,1,2,3,4,6,8,11],[1,2,4,6,7,8,11],[1,4,5,7,9,11],[0,1,2,6,8,9,11],[0,1,2,7,8,9,11],[0,1,2,6,10,11],[0,7,10,11],[0,3,4,8,10,11],[0,2,4,6,9,10,11],[1,2,3,6,8,9,10,11],[0,3,5,6,7,8,9,10,11],[2,3,6,12],[1,7,12],[1,2,4,5,8,12],[0,4,6,8,12],[0,1,2,3,4,5,7,8,12],[0,2,3,4,9,12],[2,4,6,9,12],[0,1,3,4,6,7,9,12],[1,2,8,9,12],[0,1,2,3,5,7,8,9,12],[2,5,10,12],[0,1,3,5,6,10,12],[0,3,4,6,7,8,10,12],[2,4,5,6,7,9,10,12],[0,1,2,3,8,9,10,12],[6,8,9,10,12],[0,2,3,4,11,12],[0,1,2,4,7,11,12],[0,1,2,5,8,11,12],[0,1,4,5,6,8,11,12],[0,1,4,5,7,8,11,12],[6,9,11,12],[1,3,4,5,10,11,12],[0,1,2,4,6,10,11,12],[4,5,7,10,11,12],[4,5,6,7,10,11,12],[8,10,11,12],[6,8,10,11,12],[7,8,10,11,12],[9,10,11,12],[6,8,9,10,11,12],[7,8,9,10,11,12]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,4,5],"A_d":280,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,1],[1,3],[2,1],[4,2],[5,2],[6,1],[8,1],[10,1],[11,1]],"CZ":[[0,1],[0,2],[0,3],[0,7],[0,9],[0,10],[0,12],[1,2],[1,4],[1,9],[1,10],[1,11],[1,12],[2,3],[2,8],[2,12],[3,5],[3,7],[3,8],[3,9],[3,12],[4,5],[4,6],[4,9],[4,11],[5,6],[5,8],[5,10],[5,11],[6,7],[6,8],[6,9],[6,11],[6,12],[8,10],[9,11]]},"rotation_powers":null},"metrics":{"gamma":2.095903274289385,"gamma_t":1.8340437671464696,"gamma_rho":null,"gamma_claim":2.095903274289385,"gamma_t_claim":1.8340437671464696,"gamma_rho_claim":null,"v_ex":null,"rate":0.1,"t_count":8,"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 439","N":13,"d":3,"d_is_exact":true,"origin":"search_public_release_adam","provenance":"record 439 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"}]}