{"id":"63.6.3.a","row":446,"stored":{"file":"master_catalog.json","row":446,"construction":null,"columns_sha256":null},"parameters":{"n":63,"k":6,"d":3,"N":12,"r":6,"level":3},"gate":{"string":"01+23+45","human":"CS01\u00b7CS23\u00b7CS45","monomials":[[0,1],[2,3],[4,5]],"sk_key":[[0,1],[2,3],[4,5]],"sk_fingerprint":"538b9963091189c1","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[6],[7],[0,1,6,7],[8],[1,2,3,4,6,8],[2,4,5,7,8],[2,5,6,7,8],[9],[0,1,2,3,6,9],[2,7,9],[5,6,7,9],[1,8,9],[2,3,4,5,6,8,9],[3,4,7,8,9],[6,7,8,9],[10],[0,1,2,5,6,10],[0,1,2,3,4,7,10],[0,1,2,3,5,6,7,10],[1,8,10],[5,6,8,10],[1,3,4,5,7,8,10],[1,6,7,8,10],[0,3,9,10],[4,6,9,10],[0,7,9,10],[0,1,2,5,6,7,9,10],[3,5,8,9,10],[0,1,3,4,6,8,9,10],[0,2,3,5,7,8,9,10],[2,3,5,6,7,8,9,10],[11],[2,5,6,11],[0,2,4,7,11],[0,1,2,4,6,7,11],[0,1,3,4,8,11],[0,1,2,5,6,8,11],[1,2,3,4,5,7,8,11],[0,3,5,6,7,8,11],[0,2,4,5,9,11],[2,4,6,9,11],[0,2,3,4,5,7,9,11],[1,4,6,7,9,11],[0,2,4,8,9,11],[0,1,6,8,9,11],[0,1,2,7,8,9,11],[1,4,6,7,8,9,11],[1,2,4,5,10,11],[0,1,3,4,6,10,11],[1,2,5,7,10,11],[0,3,4,5,6,7,10,11],[4,8,10,11],[1,2,3,4,5,6,8,10,11],[0,1,5,7,8,10,11],[1,4,5,6,7,8,10,11],[0,2,3,5,9,10,11],[2,4,5,6,9,10,11],[0,1,4,5,7,9,10,11],[4,5,6,7,9,10,11],[0,4,8,9,10,11],[2,5,6,8,9,10,11],[1,2,7,8,9,10,11],[2,5,6,7,8,9,10,11]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,2],"A_d":644,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,3],[1,2],[2,1],[3,2],[4,2],[5,1]],"CZ":[[0,2],[0,7],[0,8],[0,9],[0,10],[1,2],[1,3],[1,4],[1,9],[2,4],[2,8],[2,10],[2,11],[3,6],[3,7],[3,9],[4,5],[4,6],[4,7],[4,8],[4,9],[4,10],[5,6],[5,7],[5,9],[5,11]]},"rotation_powers":null},"metrics":{"gamma":2.1403139955899646,"gamma_t":1.7712437491614221,"gamma_rho":2.771243749161422,"gamma_claim":2.1403139955899646,"gamma_t_claim":1.7712437491614221,"gamma_rho_claim":2.771243749161422,"v_ex":3,"rate":0.09523809523809523,"t_count":9,"poly_degree":2,"effective_width":6},"provenance":{"regimes":["AI search: punctured r=7 simplex parents"],"discovery":"AI search","strongest_claim":"found by the 48 < n < 128 AI campaigns, from punctured r=7 simplex parents with free-row appending; a verified witness, not a maximum","sources":[{"regime":"AI search: punctured r=7 simplex parents","file":"magic-states-AI/campaign_48to128/found/n63_cs3.json","label":"14","N":12,"d":3,"d_is_exact":true,"origin":null,"provenance":"n63_cs3.json[0]"}]},"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"}]}