{"id":"88.6.3.b","row":596,"stored":{"file":"master_catalog.json","row":596,"construction":null,"columns_sha256":null},"parameters":{"n":88,"k":6,"d":3,"N":13,"r":7,"level":3},"gate":{"string":"0+12+345","human":"T0\u00b7CS12\u00b7CCZ345","monomials":[[0],[1,2],[3,4,5]],"sk_key":[[0],[1,2],[3,4,5]],"sk_fingerprint":"b579cae9c850393f","sk_canonical_frame":true,"relabelled_into_canonical_frame":true},"circuit":{"columns":[[0,2,7,8],[0,2,3,4,5,6,7,8],[0,1,2,3,5,7,8,9],[1,2,3,4,6,7,8,9],[4,5,7,8,10],[0,5,6,7,8,10],[0,3,4,5,7,8,9,10],[5,6,7,8,9,10],[0,2,3,5,6,11],[1,2,3,4,5,6,7,11],[3,4,6,8,11],[2,3,4,7,8,11],[5,6,9,11],[1,2,3,6,7,9,11],[0,1,3,5,6,8,9,11],[1,3,4,7,8,9,11],[0,2,4,6,10,11],[0,3,4,5,6,7,10,11],[3,5,6,8,10,11],[0,1,3,4,5,7,8,10,11],[1,3,4,5,6,9,10,11],[1,3,5,6,7,9,10,11],[3,4,5,6,8,9,10,11],[0,1,2,3,4,7,8,9,10,11],[3,4,12],[2,4,5,6,12],[0,2,7,12],[0,3,6,7,12],[0,2,3,4,8,12],[0,3,4,5,6,8,12],[0,2,3,4,5,7,8,12],[1,3,4,5,6,7,8,12],[0,1,2,5,9,12],[3,4,5,6,9,12],[1,3,5,7,9,12],[1,2,4,5,6,7,9,12],[0,1,2,4,5,8,9,12],[0,1,2,6,8,9,12],[1,2,3,4,5,7,8,9,12],[1,2,6,7,8,9,12],[1,2,4,10,12],[2,3,4,5,6,10,12],[1,2,5,7,10,12],[1,3,6,7,10,12],[0,1,2,8,10,12],[0,1,4,5,6,8,10,12],[3,4,5,7,8,10,12],[0,5,6,7,8,10,12],[2,3,9,10,12],[0,6,9,10,12],[1,4,5,7,9,10,12],[0,1,3,4,6,7,9,10,12],[0,4,5,8,9,10,12],[2,6,8,9,10,12],[0,1,3,4,7,8,9,10,12],[0,3,5,6,7,8,9,10,12],[2,3,11,12],[0,2,3,5,6,11,12],[0,3,5,7,11,12],[3,4,5,6,7,11,12],[1,2,5,8,11,12],[1,4,5,6,8,11,12],[2,4,7,8,11,12],[0,2,3,4,6,7,8,11,12],[0,3,9,11,12],[1,2,3,6,9,11,12],[0,1,2,4,7,9,11,12],[0,1,2,3,4,5,6,7,9,11,12],[0,1,2,3,5,8,9,11,12],[0,2,6,8,9,11,12],[1,4,5,7,8,9,11,12],[1,4,6,7,8,9,11,12],[0,1,3,4,5,10,11,12],[0,2,6,10,11,12],[0,1,5,7,10,11,12],[0,2,4,5,6,7,10,11,12],[0,3,5,8,10,11,12],[0,2,3,4,5,6,8,10,11,12],[0,1,2,7,8,10,11,12],[1,2,3,4,5,6,7,8,10,11,12],[0,2,3,4,9,10,11,12],[1,4,5,6,9,10,11,12],[0,5,7,9,10,11,12],[3,4,5,6,7,9,10,11,12],[0,1,3,4,5,8,9,10,11,12],[0,1,2,5,6,8,9,10,11,12],[0,1,2,7,8,9,10,11,12],[5,6,7,8,9,10,11,12]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,9,10],"A_d":788,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,1],[1,3],[2,2],[3,3],[5,1],[9,2],[10,2]],"CZ":[[0,2],[0,3],[0,4],[0,6],[0,9],[0,10],[0,11],[1,3],[1,5],[1,7],[2,3],[2,4],[2,6],[2,7],[2,12],[3,8],[3,10],[3,11],[4,6],[4,9],[4,11],[4,12],[5,7],[5,8],[5,9],[5,10],[5,11],[5,12],[9,10]]},"rotation_powers":null},"metrics":{"gamma":2.4445178457870527,"gamma_t":1.9795443250691258,"gamma_rho":2.8135880922155954,"gamma_claim":2.4445178457870527,"gamma_t_claim":1.9795443250691258,"gamma_rho_claim":2.8135880922155954,"v_ex":4,"rate":0.06818181818181818,"t_count":10,"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/n88_k6_d3_T5_CS34_CCZ012.json","label":"76","N":13,"d":3,"d_is_exact":true,"origin":null,"provenance":"actor-2 sweep7cs.py r=7 parent#0 n=88 target=CCZ,CS,T tail=None nodes=7"}]},"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"}]}