{"id":"55.4.3.a","row":315,"stored":{"file":"master_catalog.json","row":315,"construction":null,"columns_sha256":null},"parameters":{"n":55,"k":4,"d":3,"N":11,"r":7,"level":3},"gate":{"string":"0+123","human":"T0\u00b7CCZ123","monomials":[[0],[1,2,3]],"sk_key":[[0],[1,2,3]],"sk_fingerprint":"8297f0773a61313f","sk_canonical_frame":true,"relabelled_into_canonical_frame":true},"circuit":{"columns":[[1,2,3,4],[1,2,3,5],[0,1,2,3,6],[1,2,4,8,9],[1,2,5,7,9],[0,1,2,6,7,8],[0,1,3,4,10],[0,1,3,5,10],[1,3,6,10],[0,1,3,7,8],[1,3,7,8,10],[1,3,7,9],[0,1,3,7,9,10],[1,3,8,9],[0,1,3,8,9,10],[0,1,4,5,8,9],[1,4,5,8,9,10],[0,1,4,6,7,8],[1,4,6,7,8,10],[0,1,4,8,9,10],[0,1,5,6,7,9],[1,5,6,7,9,10],[0,1,5,7,9,10],[1,6,7,8,10],[0,2,3,4,5,6],[0,2,4,5,6,7,8],[0,2,4,5,6,7,9],[0,2,4,5,6,8,9],[0,2,4,5,7],[0,2,4,5,8],[2,4,6,7],[2,4,6,9],[2,5,6,8],[2,5,6,9],[3,4,5,6,10],[0,3,4,5,7,9],[3,4,5,7,9,10],[0,3,4,6,8,9],[3,4,6,8,9,10],[0,3,5,6,7,8],[3,5,6,7,8,10],[4,5,6,7,8,10],[4,5,6,7,9,10],[4,5,6,8,9,10],[0,4,5,7,8,9],[0,4,5,9],[4,6,7,8,9],[4,6,8],[5,6,7],[5,6,7,8,9],[7,8,9,10],[7,10],[8,10],[9,10],[10]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,3,13],"A_d":207,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,1],[3,2],[4,2],[5,2],[6,2],[7,2],[8,2],[9,2]],"CZ":[[0,3],[0,4],[0,5],[0,6],[0,10],[1,2],[2,4],[2,5],[2,6],[2,7],[2,8],[2,9],[3,10],[4,10],[5,10],[6,10],[7,8],[7,9],[8,9]]},"rotation_powers":null},"metrics":{"gamma":2.38577235221915,"gamma_t":1.876388110200643,"gamma_rho":2.647631859362065,"gamma_claim":2.38577235221915,"gamma_t_claim":1.876388110200643,"gamma_rho_claim":2.647631859362065,"v_ex":3,"rate":0.07272727272727272,"t_count":7,"poly_degree":3,"effective_width":4},"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/n55_k4_d3_T1CCZ1.json","label":"22","N":11,"d":3,"d_is_exact":true,"origin":null,"provenance":"master_catalogue [[55,3,3]] + campaigns/2026-08-31_48to128/tools/census.py --grow (addrows.py, unseeded); actor-3 round 1; new_point=True, gate_new_at_n=True"}]},"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"}]}