{"id":"111.4.3.a","row":687,"stored":{"file":"master_catalog.json","row":687,"construction":null,"columns_sha256":null},"parameters":{"n":111,"k":4,"d":3,"N":11,"r":7,"level":3},"gate":{"string":"0+1+23","human":"T0\u00b7T1\u00b7CS23","monomials":[[0],[1],[2,3]],"sk_key":[[0],[1],[2,3]],"sk_fingerprint":"8189cc6effced12b","sk_canonical_frame":true,"relabelled_into_canonical_frame":true},"circuit":{"columns":[[4],[1,2,3,5],[0,1,2,4,5],[0,2,3,6],[0,1,3,4,6],[1,2,5,6],[0,4,5,6],[0,7],[4,7],[0,1,5,7],[0,1,4,5,7],[0,1,3,6,7],[0,1,3,4,6,7],[1,5,6,7],[2,4,5,6,7],[0,1,8],[0,3,4,8],[1,2,3,5,8],[0,4,5,8],[3,6,8],[4,6,8],[0,1,5,6,8],[1,3,4,5,6,8],[0,1,2,7,8],[4,7,8],[1,3,5,7,8],[2,3,4,5,7,8],[1,2,3,6,7,8],[3,4,6,7,8],[1,2,5,6,7,8],[0,3,4,5,6,7,8],[0,2,9],[0,1,2,4,9],[0,1,2,3,5,9],[0,2,3,4,5,9],[0,1,2,6,9],[0,2,4,6,9],[0,1,3,5,6,9],[1,2,3,4,5,6,9],[0,1,2,7,9],[1,2,3,4,7,9],[5,7,9],[0,1,3,4,5,7,9],[0,6,7,9],[2,4,6,7,9],[0,3,5,6,7,9],[0,2,4,5,6,7,9],[8,9],[3,4,8,9],[0,3,5,8,9],[0,3,4,5,8,9],[1,2,3,6,8,9],[0,1,3,4,6,8,9],[2,3,5,6,8,9],[0,3,4,5,6,8,9],[0,1,3,7,8,9],[4,7,8,9],[5,7,8,9],[1,2,3,4,5,7,8,9],[0,1,2,6,7,8,9],[1,3,4,6,7,8,9],[5,6,7,8,9],[2,3,4,5,6,7,8,9],[0,2,10],[0,1,2,4,10],[3,4,5,10],[0,3,6,10],[0,1,2,4,6,10],[2,4,5,6,10],[0,7,10],[1,4,7,10],[4,5,7,10],[6,7,10],[0,1,4,6,7,10],[2,3,4,5,6,7,10],[3,8,10],[0,1,4,8,10],[0,1,2,3,4,5,8,10],[6,8,10],[0,3,4,6,8,10],[1,4,5,6,8,10],[1,2,7,8,10],[4,7,8,10],[2,4,5,7,8,10],[0,2,3,6,7,8,10],[1,4,6,7,8,10],[1,2,3,4,5,6,7,8,10],[1,9,10],[2,4,9,10],[4,5,9,10],[0,1,6,9,10],[0,2,4,6,9,10],[2,3,4,5,6,9,10],[3,7,9,10],[1,2,3,4,7,9,10],[4,5,7,9,10],[6,7,9,10],[1,4,6,7,9,10],[2,4,5,6,7,9,10],[0,2,8,9,10],[3,4,8,9,10],[1,4,5,8,9,10],[0,2,3,6,8,9,10],[2,4,6,8,9,10],[0,2,4,5,6,8,9,10],[0,2,7,8,9,10],[0,1,4,7,8,9,10],[1,2,4,5,7,8,9,10],[1,3,6,7,8,9,10],[0,1,3,4,6,7,8,9,10],[1,2,3,4,5,6,7,8,9,10]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,2],"A_d":1668,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,3],[1,3]],"CZ":[[0,1],[0,2],[0,3],[0,4],[0,5],[0,6],[0,8],[0,9],[0,10],[1,5],[1,6],[1,8],[2,3],[2,6],[2,7],[2,8],[2,10],[3,7],[3,8],[3,9]]},"rotation_powers":[[1,7],[2,5],[3,3],[6,5],[15,5],[31,5],[58,3],[59,3],[61,3],[62,3],[63,7],[67,3],[68,3],[71,3],[72,3],[74,3],[75,3],[79,3],[80,3],[81,3],[83,3],[85,3],[87,3],[89,3],[91,3],[95,3],[96,3],[97,3],[99,3],[100,3],[101,3],[103,3],[104,3],[107,3],[108,3],[109,3]]},"metrics":{"gamma":3.0249396210753576,"gamma_t":2.8218256075003456,"gamma_rho":3.2867991282182727,"gamma_claim":3.0249396210753576,"gamma_t_claim":2.8218256075003456,"gamma_rho_claim":3.2867991282182727,"v_ex":3,"rate":0.036036036036036036,"t_count":5,"poly_degree":2,"effective_width":4},"provenance":{"regimes":["AI search: multi-agent campaign 39<=n<=127"],"discovery":"AI search","strongest_claim":"found by the 39 <= n <= 127 multi-actor AI campaign (three Opus 5 actors, two conferring Fable 5 reviewers, three rounds, 2026-09-01); a verified witness, not a maximum","sources":[{"regime":"AI search: multi-agent campaign 39<=n<=127","file":"magic-states-AI/campaigns/2026-09-01_39to127_broad/found/n111_k4_d3_T2_T3_CS01.json","label":"6","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"actor-2 sweep7cs.py r=7 parent#0 n=111 target=CS,T,T tail=None nodes=4"}]},"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"}]}