{"id":"71.6.3.b","row":507,"stored":{"file":"master_catalog.json","row":507,"construction":null,"columns_sha256":null},"parameters":{"n":71,"k":6,"d":3,"N":13,"r":7,"level":3},"gate":{"string":"0+1+2+345","human":"T0\u00b7T1\u00b7T2\u00b7CCZ345","monomials":[[0],[1],[2],[3,4,5]],"sk_key":[[0],[1],[2],[3,4,5]],"sk_fingerprint":"7460afbf78dbd378","sk_canonical_frame":true,"relabelled_into_canonical_frame":true},"circuit":{"columns":[[5,7],[0,2,3,5,8],[0,7,8],[0,2,3,5,9],[0,1,2,7,9],[2,5,8,9],[1,2,3,5,7,8,9],[0,1,4,5,10],[1,3,5,7,10],[0,1,2,5,8,10],[0,2,3,4,5,7,8,10],[1,4,9,10],[1,2,4,5,7,9,10],[1,2,3,5,8,9,10],[1,5,7,8,9,10],[0,2,5,11],[1,3,4,7,11],[2,4,8,11],[0,1,3,4,7,8,11],[0,1,2,4,9,11],[5,7,9,11],[1,2,3,8,9,11],[1,5,7,8,9,11],[0,1,2,4,10,11],[3,4,7,10,11],[1,2,3,4,5,8,10,11],[0,3,7,8,10,11],[1,2,3,5,9,10,11],[0,3,4,7,9,10,11],[2,5,8,9,10,11],[7,8,9,10,11],[12],[0,1,2,5,6,12],[2,3,4,5,7,12],[0,1,4,6,7,12],[1,3,4,8,12],[0,1,2,3,6,8,12],[1,9,12],[0,2,5,6,9,12],[1,2,3,4,5,7,9,12],[0,4,6,7,9,12],[3,4,8,9,12],[1,2,5,6,8,9,12],[1,3,5,10,12],[0,2,3,6,10,12],[1,2,4,7,10,12],[0,3,4,5,6,7,10,12],[4,5,8,10,12],[0,2,3,5,6,8,10,12],[0,1,4,9,10,12],[0,1,2,3,6,9,10,12],[0,1,2,3,4,7,9,10,12],[0,1,3,4,5,6,7,9,10,12],[1,8,9,10,12],[2,6,8,9,10,12],[1,11,12],[5,7,11,12],[0,2,3,5,8,11,12],[0,3,5,6,7,8,11,12],[0,2,5,9,11,12],[1,7,9,11,12],[1,3,5,8,9,11,12],[6,7,8,9,11,12],[3,10,11,12],[2,5,7,10,11,12],[0,3,8,10,11,12],[0,1,3,6,7,8,10,11,12],[2,4,9,10,11,12],[0,2,3,7,9,10,11,12],[1,2,3,4,5,8,9,10,11,12],[1,5,6,7,8,9,10,11,12]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,2],"A_d":551,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,1],[1,2],[2,3],[3,3],[4,3],[5,2],[9,2],[10,2]],"CZ":[[0,1],[0,2],[0,3],[0,5],[0,7],[0,12],[1,2],[1,3],[1,5],[1,9],[1,11],[2,3],[2,5],[2,7],[2,10],[2,11],[2,12],[3,4],[3,5],[3,8],[3,9],[4,5],[4,7],[4,11],[4,12],[5,8],[5,9],[5,10],[5,11],[5,12],[9,10]]},"rotation_powers":null},"metrics":{"gamma":2.2491286810644118,"gamma_t":1.880058434635869,"gamma_rho":2.415084913917942,"gamma_claim":2.2491286810644118,"gamma_t_claim":1.880058434635869,"gamma_rho_claim":2.415084913917942,"v_ex":5,"rate":0.08450704225352113,"t_count":9,"poly_degree":3,"effective_width":6},"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/n71_k6_d3_T3_T4_T5_CCZ012.json","label":"39","N":13,"d":3,"d_is_exact":true,"origin":null,"provenance":"actor-2 sweep7b.py r=7 parent#0 n=71 target=CCZ,T,T,T tail=14 nodes=6170"}]},"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"}]}