{"id":"68.5.3.a","row":493,"stored":{"file":"master_catalog.json","row":493,"construction":null,"columns_sha256":null},"parameters":{"n":68,"k":5,"d":3,"N":12,"r":7,"level":3},"gate":{"string":"01+234","human":"CS01\u00b7CCZ234","monomials":[[0,1],[2,3,4]],"sk_key":[[0,1],[2,3,4]],"sk_fingerprint":"c8110231103ed187","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[2,4,5,8],[0,2,3,4,5,6,8],[2,3,7,8],[1,3,6,7,8],[0,2,3,5,9],[0,2,4,5,6,9],[1,3,4,5,7,9],[1,2,5,6,7,9],[0,1,2,3,7,8,9],[1,3,5,7,8,9],[1,3,4,6,7,8,9],[2,4,5,6,7,8,9],[1,2,3,6,10],[2,3,4,5,6,10],[1,2,3,6,7,10],[0,2,3,4,5,6,7,10],[1,2,4,5,8,10],[0,2,6,8,10],[1,7,8,10],[0,1,2,3,4,5,6,7,8,10],[2,3,4,5,9,10],[1,2,3,4,6,9,10],[1,3,4,5,7,9,10],[0,2,3,4,6,7,9,10],[0,2,3,6,8,9,10],[0,1,2,3,4,5,6,8,9,10],[1,3,4,7,8,9,10],[1,5,7,8,9,10],[1,3,4,11],[1,5,11],[1,3,4,6,11],[1,5,6,11],[1,4,7,11],[4,5,7,11],[2,3,4,8,11],[2,3,4,5,8,11],[0,1,4,6,8,11],[0,2,5,6,8,11],[2,7,8,11],[0,1,2,3,4,5,7,8,11],[2,3,4,9,11],[0,1,3,5,9,11],[1,4,6,9,11],[2,5,6,9,11],[0,2,7,9,11],[1,5,7,9,11],[0,4,8,9,11],[0,2,5,8,9,11],[0,3,4,6,8,9,11],[0,1,3,5,6,8,9,11],[0,3,7,8,9,11],[1,2,5,7,8,9,11],[0,4,10,11],[0,1,6,10,11],[1,4,7,10,11],[0,1,5,6,7,10,11],[1,3,4,8,10,11],[1,2,4,6,8,10,11],[2,4,7,8,10,11],[2,4,5,6,7,8,10,11],[0,3,4,9,10,11],[1,6,9,10,11],[0,7,9,10,11],[0,2,3,4,5,6,7,9,10,11],[1,3,4,8,9,10,11],[1,2,3,6,8,9,10,11],[0,2,7,8,9,10,11],[0,3,4,5,6,7,8,9,10,11]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,6,8],"A_d":385,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,2],[1,2],[2,2],[3,2],[4,1],[8,2],[9,2]],"CZ":[[0,1],[0,4],[0,5],[0,9],[0,10],[0,11],[1,4],[1,6],[1,7],[1,8],[1,9],[1,10],[2,8],[2,9],[2,10],[3,6],[3,9],[3,10],[4,5],[4,6],[4,9],[4,11],[5,9],[6,10],[7,8],[7,9],[8,9]]},"rotation_powers":null},"metrics":{"gamma":2.3757879095875536,"gamma_t":1.8407614303054807,"gamma_rho":2.8407614303054807,"gamma_claim":2.3757879095875536,"gamma_t_claim":1.8407614303054807,"gamma_rho_claim":2.8407614303054807,"v_ex":3,"rate":0.07352941176470588,"t_count":9,"poly_degree":3,"effective_width":5},"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/n68_k5_d3_CS01_CCZ234.json","label":"35","N":12,"d":3,"d_is_exact":true,"origin":null,"provenance":"actor-2 round2.py r=7 DISTINCT parent#0 n=68 target=CS,CCZ tail=None nodes=4800"}]},"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"}]}