{"id":"63.7.3.a","row":452,"stored":{"file":"master_catalog.json","row":452,"construction":null,"columns_sha256":null},"parameters":{"n":63,"k":7,"d":3,"N":17,"r":10,"level":3},"gate":{"string":"0+12+13+14+15+26+36+46+56+123+124+125+126+134+135+146+235+256+345+346+456","human":"T0\u00b7CS12\u00b7CS13\u00b7CS14\u00b7CS15\u00b7CS26\u00b7CS36\u00b7CS46\u00b7CS56\u00b7CCZ123\u00b7CCZ124\u00b7CCZ125\u00b7CCZ126\u00b7CCZ134\u00b7CCZ135\u00b7CCZ146\u00b7CCZ235\u00b7CCZ256\u00b7CCZ345\u00b7CCZ346\u00b7CCZ456","monomials":[[0],[1,2],[1,3],[1,4],[1,5],[2,6],[3,6],[4,6],[5,6],[1,2,3],[1,2,4],[1,2,5],[1,2,6],[1,3,4],[1,3,5],[1,4,6],[2,3,5],[2,5,6],[3,4,5],[3,4,6],[4,5,6]],"sk_key":[[0],[1,2],[1,2,3],[1,2,4],[1,2,5],[1,2,6],[1,3],[1,3,4],[1,3,5],[1,4],[1,4,6],[1,5],[2,3,5],[2,5,6],[2,6],[3,4,5],[3,4,6],[3,6],[4,5,6],[4,6],[5,6]],"sk_fingerprint":"978c7da0230ea9ef","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,7],[0,8],[0,7,8],[0,9],[0,7,9],[0,8,9],[0,7,8,9],[10],[7,10],[8,10],[7,8,10],[9,10],[7,9,10],[8,9,10],[7,8,9,10],[1,5,6,15],[4,11,15],[2,4,12,15],[2,5,11,12,15],[1,5,13,15],[1,2,3,5,11,13,15],[3,5,6,12,13,15],[1,2,5,11,12,13,15],[1,14,15],[2,3,6,11,14,15],[1,2,4,5,12,14,15],[1,3,4,5,11,12,14,15],[1,6,13,14,15],[1,4,5,6,11,13,14,15],[1,3,6,12,13,14,15],[3,4,5,11,12,13,14,15],[1,2,3,6,16],[1,2,5,6,11,16],[1,2,4,12,16],[6,11,12,16],[4,6,13,16],[2,6,11,13,16],[1,3,6,12,13,16],[5,11,12,13,16],[1,4,6,14,16],[3,4,5,11,14,16],[2,4,5,6,12,14,16],[5,6,11,12,14,16],[2,3,6,13,14,16],[1,3,4,11,13,14,16],[3,5,12,13,14,16],[11,12,13,14,16],[1,6,15,16],[1,6,11,15,16],[2,3,4,5,12,15,16],[11,12,15,16],[1,2,3,4,5,6,13,15,16],[2,3,4,5,11,13,15,16],[1,2,3,4,5,6,12,13,15,16],[11,12,13,15,16],[14,15,16],[1,2,3,4,5,6,11,14,15,16],[1,6,12,14,15,16],[11,12,14,15,16],[2,3,4,5,13,14,15,16],[11,13,14,15,16],[12,13,14,15,16],[11,12,13,14,15,16]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,2],"A_d":287,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,1],[1,1],[2,3],[3,3],[4,3],[5,1],[6,1]],"CZ":[[1,2],[1,3],[1,4],[1,6],[1,13],[1,14],[2,3],[2,4],[2,6],[2,14],[3,4],[3,6],[3,14],[4,14],[5,6],[5,14],[6,13],[6,14]]},"rotation_powers":null},"metrics":{"gamma":2.0,"gamma_t":null,"gamma_rho":null,"gamma_claim":2.0,"gamma_t_claim":null,"gamma_rho_claim":null,"v_ex":null,"rate":0.1111111111111111,"t_count":null,"poly_degree":null,"effective_width":7},"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 80612","N":17,"d":3,"d_is_exact":true,"origin":"search_public_release_adam","provenance":"record 80612 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"}]}