{"id":"128.15.4.a","row":744,"stored":{"file":"master_catalog.json","row":744,"construction":null,"columns_sha256":null},"parameters":{"n":128,"k":15,"d":4,"N":23,"r":8,"level":3},"gate":{"string":"0,1,2+3,4,5+6,7,8+9,10,11+12,13,14","human":"CCZ0,1,2\u00b7CCZ3,4,5\u00b7CCZ6,7,8\u00b7CCZ9,10,11\u00b7CCZ12,13,14","monomials":[[0,1,2],[3,4,5],[6,7,8],[9,10,11],[12,13,14]],"sk_key":[[0,1,2],[3,4,5],[6,7,8],[9,10,11],[12,13,14]],"sk_fingerprint":"80b5a926a0d82cef","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[14,22],[12,15,22],[14,16,22],[0,12,15,16,22],[13,17,22],[3,13,14,15,17,22],[12,14,16,17,22],[0,3,13,15,16,17,22],[12,18,22],[12,13,14,15,18,22],[16,18,22],[0,12,14,15,16,18,22],[1,12,14,17,18,22],[1,3,13,15,17,18,22],[1,12,16,17,18,22],[0,1,3,13,14,15,16,17,18,22],[12,13,19,22],[13,15,19,22],[4,14,16,19,22],[0,4,12,13,15,16,19,22],[13,14,17,19,22],[3,14,15,17,19,22],[4,12,13,14,16,17,19,22],[0,3,4,15,16,17,19,22],[13,18,19,22],[12,14,15,18,19,22],[4,16,18,19,22],[0,4,14,15,16,18,19,22],[1,12,13,14,17,18,19,22],[1,3,12,13,15,17,18,19,22],[1,4,12,13,16,17,18,19,22],[0,1,3,4,12,13,14,15,16,17,18,19,22],[13,20,22],[12,13,14,15,20,22],[13,16,20,22],[0,12,15,16,20,22],[12,13,17,20,22],[3,13,14,15,17,20,22],[13,16,17,20,22],[0,3,12,15,16,17,20,22],[5,13,14,18,20,22],[5,12,15,18,20,22],[5,13,16,18,20,22],[0,5,12,14,15,16,18,20,22],[1,5,12,14,17,18,20,22],[1,3,5,13,15,17,18,20,22],[1,5,13,16,17,18,20,22],[0,1,3,5,12,14,15,16,17,18,20,22],[2,19,20,22],[2,12,13,14,15,19,20,22],[2,4,14,16,19,20,22],[0,2,4,12,13,15,16,19,20,22],[2,12,13,17,19,20,22],[2,3,14,15,17,19,20,22],[2,4,14,16,17,19,20,22],[0,2,3,4,12,13,15,16,17,19,20,22],[2,5,14,18,19,20,22],[2,5,15,18,19,20,22],[2,4,5,16,18,19,20,22],[0,2,4,5,14,15,16,18,19,20,22],[1,2,5,12,13,14,17,18,19,20,22],[1,2,3,5,12,13,15,17,18,19,20,22],[1,2,4,5,16,17,18,19,20,22],[0,1,2,3,4,5,14,15,16,17,18,19,20,22],[12,13,21,22],[12,13,14,15,21,22],[13,16,21,22],[6,13,14,15,16,21,22],[12,13,17,21,22],[9,13,14,15,17,21,22],[16,17,21,22],[6,9,13,14,15,16,17,21,22],[14,18,21,22],[13,14,15,18,21,22],[14,16,18,21,22],[6,12,14,15,16,18,21,22],[7,13,14,17,18,21,22],[7,9,12,14,15,17,18,21,22],[7,13,14,16,17,18,21,22],[6,7,9,12,14,15,16,17,18,21,22],[12,14,19,21,22],[12,13,14,15,19,21,22],[10,12,13,16,19,21,22],[6,10,12,13,14,15,16,19,21,22],[13,14,17,19,21,22],[9,12,13,14,15,17,19,21,22],[10,12,13,16,17,19,21,22],[6,9,10,12,13,14,15,16,17,19,21,22],[14,18,19,21,22],[14,15,18,19,21,22],[10,12,13,14,16,18,19,21,22],[6,10,14,15,16,18,19,21,22],[7,12,13,14,17,18,19,21,22],[7,9,14,15,17,18,19,21,22],[7,10,12,13,14,16,17,18,19,21,22],[6,7,9,10,14,15,16,17,18,19,21,22],[14,20,21,22],[15,20,21,22],[13,14,16,20,21,22],[6,14,15,16,20,21,22],[12,17,20,21,22],[9,12,14,15,17,20,21,22],[13,14,16,17,20,21,22],[6,9,14,15,16,17,20,21,22],[11,13,18,20,21,22],[11,12,15,18,20,21,22],[11,14,16,18,20,21,22],[6,11,12,13,14,15,16,18,20,21,22],[7,11,12,14,17,18,20,21,22],[7,9,11,13,14,15,17,18,20,21,22],[7,11,14,16,17,18,20,21,22],[6,7,9,11,12,13,14,15,16,17,18,20,21,22],[8,12,13,14,19,20,21,22],[8,12,13,15,19,20,21,22],[8,10,12,16,19,20,21,22],[6,8,10,12,14,15,16,19,20,21,22],[8,17,19,20,21,22],[8,9,14,15,17,19,20,21,22],[8,10,12,16,17,19,20,21,22],[6,8,9,10,12,14,15,16,17,19,20,21,22],[8,11,12,13,18,19,20,21,22],[8,11,15,18,19,20,21,22],[8,10,11,12,14,16,18,19,20,21,22],[6,8,10,11,13,14,15,16,18,19,20,21,22],[7,8,11,14,17,18,19,20,21,22],[7,8,9,11,12,13,14,15,17,18,19,20,21,22],[7,8,10,11,12,14,16,17,18,19,20,21,22],[6,7,8,9,10,11,13,14,15,16,17,18,19,20,21,22]]},"distance":{"d":4,"is_exact":true,"upper":4,"witness":[0,1,2,3],"A_d":84984,"certified":null},"clifford":{"kind":"required","correction":{"S":[[12,1],[14,1]],"CZ":[[0,12],[0,13],[1,12],[1,13],[2,12],[2,13],[3,12],[3,13],[4,12],[4,13],[5,12],[5,13],[8,12],[8,13],[8,14],[12,13],[12,15],[12,16],[12,18],[12,19],[12,20],[12,22],[14,17],[14,22]]},"rotation_powers":null},"metrics":{"gamma":1.5465547021957409,"gamma_t":null,"gamma_rho":1.839035952556319,"gamma_claim":1.5465547021957409,"gamma_t_claim":null,"gamma_rho_claim":1.839035952556319,"v_ex":10,"rate":0.1171875,"t_count":null,"poly_degree":null,"effective_width":15},"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/n128_ccz5_OUTSIDE_window.json","label":"10","N":23,"d":4,"d_is_exact":true,"origin":null,"provenance":"n128_ccz5_OUTSIDE_window.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"}]}