{"id":"45.2.3.a","row":209,"stored":{"file":"master_catalog.json","row":209,"construction":null,"columns_sha256":null},"parameters":{"n":45,"k":2,"d":3,"N":10,"r":8,"level":3},"gate":{"string":"01","human":"CS01","monomials":[[0,1]],"sk_key":[[0,1]],"sk_fingerprint":"f076b3dc759b1665","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[1,2],[3],[0,4],[1,3,4],[3,5],[6],[0,1,2,6],[0,3,4,6],[1,2,3,4,6],[2,3,4,7],[0,1,3,5,7],[0,6,7],[1,3,6,7],[2,3,6,7],[0,1,4,6,7],[1,2,4,6,7],[3,4,6,7],[8],[1,3,5,8],[4,6,8],[0,1,2,4,6,8],[0,3,4,7,8],[0,3,5,7,8],[1,2,3,6,7,8],[0,1,4,6,7,8],[1,9],[3,5,9],[0,1,6,9],[0,1,2,3,6,9],[0,4,6,9],[1,3,4,6,9],[1,7,9],[0,2,3,7,9],[2,4,7,9],[0,1,3,5,7,9],[0,1,2,3,6,7,9],[1,4,6,7,9],[0,1,2,8,9],[1,3,5,8,9],[7,8,9],[2,7,8,9],[1,3,4,7,8,9],[0,3,5,7,8,9],[0,2,3,6,7,8,9],[0,1,2,4,6,7,8,9]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,5,6],"A_d":71,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,2],[4,3],[6,1],[9,2]],"CZ":[[0,3],[0,9],[1,2],[1,4],[1,6],[2,4],[2,6],[2,7],[2,8],[3,6],[3,7],[3,9],[4,7],[4,8],[4,9],[6,8],[7,8]]},"rotation_powers":null},"metrics":{"gamma":2.8340437671464693,"gamma_t":2.464973520717927,"gamma_rho":3.4649735207179266,"gamma_claim":2.8340437671464693,"gamma_t_claim":2.464973520717927,"gamma_rho_claim":3.4649735207179266,"v_ex":1,"rate":0.044444444444444446,"t_count":3,"poly_degree":2,"effective_width":2},"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/n45_k2_d3_CS.json","label":"14","N":10,"d":3,"d_is_exact":true,"origin":null,"provenance":"actor-1, round 3, campaigns/2026-09-01_39to127_broad. n = 45 is unreachable at r <= 7 (the mod-4 obstruction), so the parent is a check-rank-8 one recovered from a CATALOGUED row by work/actor-1/tools/parent_from_record.py: reduce the check block of a d >= 3 class to independent rows and read each column's syndrome in that basis. Six such parents at n = 45 (ids 2010c75a, 0ee8fb2e, cfebf4b2, 7c64e1"}]},"references":[{"key":"wills2026classification","short":"Wills et al. (2026)","full":"A. Wills, S. P. Jain, and S. Singh, \"Classification of Generalised Triorthogonal Codes through Length 54,\" arXiv:2609.30860 (2026).","url":"https://arxiv.org/abs/2609.30860","date":"2026-09-25"},{"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"}]}