{"id":"111.9.3.a","row":690,"stored":{"file":"master_catalog.json","row":690,"construction":null,"columns_sha256":null},"parameters":{"n":111,"k":9,"d":3,"N":16,"r":7,"level":3},"gate":{"string":"0+1+2+345+678","human":"T0\u00b7T1\u00b7T2\u00b7CCZ345\u00b7CCZ678","monomials":[[0],[1],[2],[3,4,5],[6,7,8]],"sk_key":[[0],[1],[2],[3,4,5],[6,7,8]],"sk_fingerprint":"cda5109fc22ae3a2","sk_canonical_frame":true,"relabelled_into_canonical_frame":true},"circuit":{"columns":[[1,2,3,5,7,8,9],[0,5,6,8,10],[2,4,5,6,8,9,10],[0,7,11],[0,1,2,6,8,9,11],[0,1,3,5,10,11],[2,6,9,10,11],[0,2,3,5,8,12],[0,2,3,4,5,6,7,9,12],[0,1,3,4,5,6,8,10,12],[0,2,3,5,8,9,10,12],[1,6,7,8,11,12],[2,5,7,9,11,12],[0,1,3,7,10,11,12],[1,2,3,4,5,6,9,10,11,12],[1,3,4,5,6,13],[2,3,4,5,9,13],[0,1,2,3,4,5,7,8,10,13],[4,7,9,10,13],[0,1,2,3,4,5,6,7,11,13],[1,2,4,5,7,8,9,11,13],[0,1,2,3,4,5,7,10,11,13],[0,1,2,3,4,9,10,11,13],[6,12,13],[1,2,4,5,7,9,12,13],[0,1,2,3,4,10,12,13],[0,1,2,3,4,5,6,7,9,10,12,13],[6,8,11,12,13],[1,2,5,7,8,9,11,12,13],[0,3,7,10,11,12,13],[0,3,4,5,6,7,9,10,11,12,13],[6,14],[0,1,2,3,6,7,9,14],[0,2,5,6,7,10,14],[2,3,4,5,6,8,9,10,14],[6,8,11,14],[0,1,2,3,4,6,7,8,9,11,14],[0,1,4,5,10,11,14],[1,3,4,5,7,8,9,10,11,14],[6,7,8,12,14],[0,1,2,3,4,7,8,9,12,14],[0,1,4,7,10,12,14],[1,3,4,6,7,8,9,10,12,14],[11,12,14],[0,1,2,3,6,9,11,12,14],[0,2,7,10,11,12,14],[2,3,4,6,7,8,9,10,11,12,14],[7,13,14],[0,3,5,8,9,13,14],[2,3,6,8,10,13,14],[0,1,4,5,6,7,8,9,10,13,14],[11,13,14],[0,3,4,5,8,9,11,13,14],[1,3,4,7,10,11,13,14],[5,9,10,11,13,14],[7,12,13,14],[0,3,4,5,8,9,12,13,14],[1,3,4,5,6,7,8,10,12,13,14],[4,9,10,12,13,14],[2,3,5,8,11,12,13,14],[0,1,6,7,8,9,11,12,13,14],[6,7,8,10,11,12,13,14],[0,3,5,6,7,8,9,10,11,12,13,14],[6,7,8,15],[1,2,4,5,9,15],[0,3,5,9,10,15],[4,7,8,11,15],[1,2,4,5,6,7,9,11,15],[0,1,2,3,4,5,6,7,9,10,11,15],[0,2,6,7,12,15],[0,1,5,8,9,12,15],[1,3,6,7,9,10,12,15],[0,2,4,6,8,11,12,15],[0,1,5,6,7,8,9,11,12,15],[2,3,4,6,7,8,9,10,11,12,15],[0,1,3,4,5,8,13,15],[0,1,3,5,6,9,13,15],[0,2,3,4,7,8,9,10,13,15],[0,1,3,5,7,11,13,15],[0,1,3,5,9,11,13,15],[1,2,3,4,7,9,10,11,13,15],[1,2,3,4,5,6,7,8,12,13,15],[1,2,3,4,5,7,8,9,12,13,15],[0,1,3,4,5,8,9,10,12,13,15],[1,2,3,5,6,8,11,12,13,15],[3,4,5,6,7,9,11,12,13,15],[1,2,3,4,5,9,10,11,12,13,15],[0,1,4,5,6,7,14,15],[1,3,8,9,14,15],[4,5,6,8,9,10,14,15],[0,1,5,7,11,14,15],[1,3,6,7,8,9,11,14,15],[0,1,4,5,7,8,9,10,11,14,15],[1,2,4,5,7,8,12,14,15],[0,1,2,3,4,9,12,14,15],[0,3,5,6,7,8,9,10,12,14,15],[0,2,4,5,6,7,11,12,14,15],[0,2,4,6,7,9,11,12,14,15],[0,1,4,5,9,10,11,12,14,15],[3,6,7,8,13,14,15],[0,1,2,4,6,9,13,14,15],[0,4,6,7,9,10,13,14,15],[0,4,7,11,13,14,15],[1,2,3,4,5,8,9,11,13,14,15],[0,1,2,5,9,10,11,13,14,15],[0,1,2,5,7,12,13,14,15],[0,5,6,9,12,13,14,15],[2,9,10,12,13,14,15],[0,2,3,5,11,12,13,14,15],[2,9,11,12,13,14,15],[0,2,3,5,9,10,11,12,13,14,15]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,2],"A_d":1777,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,3],[2,2],[3,3],[5,1],[6,2],[7,2],[8,3]],"CZ":[[0,1],[0,3],[0,4],[0,5],[0,6],[0,8],[0,9],[0,11],[0,12],[0,14],[1,2],[1,5],[1,7],[1,8],[1,11],[1,12],[2,8],[2,10],[2,12],[2,13],[2,14],[3,4],[3,5],[3,6],[3,7],[3,8],[3,9],[3,10],[3,12],[3,13],[4,6],[4,7],[4,8],[4,9],[4,10],[4,11],[4,12],[4,13],[4,14],[4,15],[5,6],[5,7],[5,8],[5,11],[5,12],[5,13],[5,14],[5,15],[6,9],[6,10],[6,14],[6,15],[7,10],[7,14],[7,15],[8,9],[8,11],[8,12],[8,13],[8,14]]},"rotation_powers":null},"metrics":{"gamma":2.2867991282182727,"gamma_t":null,"gamma_rho":2.5155553790568503,"gamma_claim":2.2867991282182727,"gamma_t_claim":null,"gamma_rho_claim":2.5155553790568503,"v_ex":7,"rate":0.08108108108108109,"t_count":null,"poly_degree":null,"effective_width":9},"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_k9_d3_T3CCZ2.json","label":"8","N":16,"d":3,"d_is_exact":true,"origin":null,"provenance":"actor-2/found/n111_k6_d3_T3_T4_T5_CCZ012.json [[111,6,3]] V_ex 5 + addrows.greedy (unseeded, EXHAUSTED); actor-3 round 2 direction 2"}]},"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"}]}