{"id":"127.17.3.a","row":736,"stored":{"file":"master_catalog.json","row":736,"construction":null,"columns_sha256":null},"parameters":{"n":127,"k":17,"d":3,"N":24,"r":7,"level":3},"gate":{"string":"0+1+2+3+4+5,6,7+8,9,10+11,12,13+14,15,16","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7CCZ5,6,7\u00b7CCZ8,9,10\u00b7CCZ11,12,13\u00b7CCZ14,15,16","monomials":[[0],[1],[2],[3],[4],[5,6,7],[8,9,10],[11,12,13],[14,15,16]],"sk_key":[[0],[1],[2],[3],[4],[5,6,7],[8,9,10],[11,12,13],[14,15,16]],"sk_fingerprint":"1c6e8134f9e28f35","sk_canonical_frame":true,"relabelled_into_canonical_frame":true},"circuit":{"columns":[[0,1,17],[0,1,3,18],[0,1,2,3,5,17,18],[1,2,3,4,19],[0,1,3,8,17,19],[0,1,18,19],[2,3,4,5,8,17,18,19],[20],[0,2,4,17,20],[1,3,18,20],[0,2,3,5,17,18,20],[0,1,3,6,19,20],[0,3,6,8,17,19,20],[2,3,4,6,18,19,20],[1,2,3,4,5,6,8,17,18,19,20],[0,1,2,21],[2,4,17,21],[1,2,3,9,18,21],[2,3,5,9,17,18,21],[0,3,19,21],[3,8,17,19,21],[0,2,3,4,9,18,19,21],[0,1,2,3,4,5,8,9,17,18,19,21],[1,4,20,21],[1,17,20,21],[0,4,9,18,20,21],[0,1,4,5,9,17,18,20,21],[0,2,4,6,19,20,21],[0,1,2,4,6,8,17,19,20,21],[1,6,9,18,19,20,21],[5,6,8,9,17,18,19,20,21],[0,2,22],[0,2,4,17,22],[0,1,18,22],[1,3,4,5,17,18,22],[4,19,22],[1,2,3,4,8,17,19,22],[1,2,3,18,19,22],[0,3,5,8,17,18,19,22],[3,10,20,22],[1,3,10,17,20,22],[1,3,4,10,18,20,22],[3,4,5,10,17,18,20,22],[1,2,3,4,6,10,19,20,22],[2,3,4,6,8,10,17,19,20,22],[0,3,6,10,18,19,20,22],[0,1,3,5,6,8,10,17,18,19,20,22],[0,3,7,21,22],[0,1,3,7,17,21,22],[0,1,3,4,7,9,18,21,22],[0,3,4,5,7,9,17,18,21,22],[0,1,2,3,4,7,19,21,22],[0,2,3,4,7,8,17,19,21,22],[3,7,9,18,19,21,22],[1,3,5,7,8,9,17,18,19,21,22],[1,2,4,7,10,20,21,22],[2,4,7,10,17,20,21,22],[2,7,9,10,18,20,21,22],[1,2,5,7,9,10,17,18,20,21,22],[6,7,10,19,20,21,22],[1,6,7,8,10,17,19,20,21,22],[0,1,2,4,6,7,9,10,18,19,20,21,22],[0,2,4,5,6,7,8,9,10,17,18,19,20,21,22],[0,1,2,3,4,23],[3,4,17,23],[0,3,4,18,23],[1,2,11,17,18,23],[0,2,3,4,19,23],[0,1,4,14,17,19,23],[1,4,18,19,23],[1,2,4,11,14,17,18,19,23],[2,3,20,23],[0,2,3,17,20,23],[2,4,18,20,23],[0,1,2,11,17,18,20,23],[2,12,19,20,23],[1,4,12,14,17,19,20,23],[0,12,18,19,20,23],[0,1,2,4,11,12,14,17,18,19,20,23],[2,3,4,21,23],[2,4,17,21,23],[0,1,2,15,18,21,23],[1,2,3,4,11,15,17,18,21,23],[0,4,19,21,23],[0,1,3,14,17,19,21,23],[0,1,2,4,15,18,19,21,23],[1,2,3,11,14,15,17,18,19,21,23],[1,4,20,21,23],[0,3,4,17,20,21,23],[0,1,15,18,20,21,23],[1,3,4,11,15,17,18,20,21,23],[1,2,4,12,19,20,21,23],[0,1,2,3,12,14,17,19,20,21,23],[0,1,4,12,15,18,19,20,21,23],[1,3,11,12,14,15,17,18,19,20,21,23],[1,4,22,23],[0,3,4,17,22,23],[2,3,18,22,23],[1,2,3,11,17,18,22,23],[0,1,3,19,22,23],[1,2,3,4,14,17,19,22,23],[0,1,2,18,19,22,23],[0,1,3,4,11,14,17,18,19,22,23],[0,1,4,16,20,22,23],[0,2,16,17,20,22,23],[0,3,4,16,18,20,22,23],[0,1,2,3,11,16,17,18,20,22,23],[0,3,12,16,19,20,22,23],[0,1,2,3,4,12,14,16,17,19,20,22,23],[2,3,12,16,18,19,20,22,23],[1,3,4,11,12,14,16,17,18,19,20,22,23],[0,2,13,21,22,23],[2,3,4,13,17,21,22,23],[0,1,2,3,13,15,18,21,22,23],[1,2,4,11,13,15,17,18,21,22,23],[0,1,2,3,4,13,19,21,22,23],[1,2,13,14,17,19,21,22,23],[1,3,4,13,15,18,19,21,22,23],[0,1,11,13,14,15,17,18,19,21,22,23],[0,13,16,20,21,22,23],[3,4,13,16,17,20,21,22,23],[0,1,3,13,15,16,18,20,21,22,23],[1,4,11,13,15,16,17,18,20,21,22,23],[0,1,3,4,12,13,16,19,20,21,22,23],[1,12,13,14,16,17,19,20,21,22,23],[1,2,3,4,12,13,15,16,18,19,20,21,22,23],[0,1,2,11,12,13,14,15,16,17,18,19,20,21,22,23]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,2],"A_d":2667,"certified":null},"clifford":{"kind":"required","correction":{"S":[[1,3],[2,1],[3,1]],"CZ":[[0,1],[0,2],[0,4],[0,11],[0,16],[0,17],[0,19],[0,20],[0,23],[1,4],[1,16],[1,19],[1,22],[1,23],[2,3],[2,11],[2,16],[2,17],[2,22],[2,23],[3,16],[3,17],[3,18],[3,19],[3,20],[3,21],[3,23],[4,17],[4,18],[4,19],[4,21]]},"rotation_powers":null},"metrics":{"gamma":1.8304671840512146,"gamma_t":null,"gamma_rho":2.0746515877409877,"gamma_claim":1.8304671840512146,"gamma_t_claim":null,"gamma_rho_claim":2.0746515877409877,"v_ex":13,"rate":0.13385826771653545,"t_count":null,"poly_degree":null,"effective_width":17},"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/n127_ccz4t5.json","label":"6","N":24,"d":3,"d_is_exact":true,"origin":null,"provenance":"n127_ccz4t5.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"}]}