{"id":"127.5.5.a","row":732,"stored":{"file":"master_catalog.json","row":732,"construction":null,"columns_sha256":null},"parameters":{"n":127,"k":5,"d":5,"N":19,"r":14,"level":3},"gate":{"string":"0+1+2+3+4","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4","monomials":[[0],[1],[2],[3],[4]],"sk_key":[[0],[1],[2],[3],[4]],"sk_fingerprint":"65a2b287ec4a80f7","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,1,4,5,12],[1,2,4,8,13],[2,3,4,5,6,7,8,12,13],[1,11,14],[0,1,3,5,7,9,11,12,14],[0,1,3,8,9,10,11,13,14],[0,5,6,8,10,11,12,13,14],[2,7,8,15],[1,2,3,5,7,11,12,15],[2,3,4,5,6,7,10,13,15],[4,8,10,11,12,13,15],[1,3,4,5,8,11,14,15],[0,1,2,3,4,7,9,12,14,15],[2,6,9,11,13,14,15],[1,2,3,5,8,12,13,14,15],[0,2,4,10,11,16],[2,3,4,5,6,7,9,10,11,12,16],[0,1,2,7,10,13,16],[0,5,7,9,10,12,13,16],[3,6,7,8,9,10,14,16],[0,1,4,5,7,8,9,10,12,14,16],[4,6,8,11,13,14,16],[0,5,6,7,8,11,12,13,14,16],[1,2,3,7,11,15,16],[0,1,2,5,6,8,9,12,15,16],[0,1,2,5,6,10,13,15,16],[1,3,4,6,8,9,10,11,12,13,15,16],[1,2,4,5,6,7,8,9,14,15,16],[3,7,9,11,12,14,15,16],[4,8,11,13,14,15,16],[0,1,4,5,7,12,13,14,15,16],[1,3,4,6,8,17],[3,5,6,9,10,12,17],[0,1,4,5,9,10,13,17],[0,3,4,6,7,8,12,13,17],[0,6,7,10,14,17],[0,1,2,5,6,8,12,14,17],[4,5,7,8,10,13,14,17],[1,3,4,6,7,12,13,14,17],[2,3,4,5,7,9,10,11,15,17],[0,3,4,7,12,15,17],[0,1,2,5,7,8,10,11,13,15,17],[2,6,8,9,12,13,15,17],[2,7,8,9,11,14,15,17],[1,2,4,5,8,9,10,12,14,15,17],[2,7,9,10,11,13,14,15,17],[3,5,6,7,9,12,13,14,15,17],[2,3,4,7,8,10,16,17],[1,2,4,5,6,12,16,17],[0,3,4,5,6,8,9,11,13,16,17],[1,2,3,6,9,10,11,12,13,16,17],[0,3,4,6,7,8,9,14,16,17],[0,1,4,5,7,10,12,14,16,17],[4,5,8,9,11,13,14,16,17],[0,1,4,7,10,11,12,13,14,16,17],[0,1,4,5,6,8,9,10,11,15,16,17],[0,2,3,7,8,9,12,15,16,17],[2,3,4,5,6,7,8,10,13,15,16,17],[1,3,4,6,7,8,11,12,13,15,16,17],[3,7,8,11,14,15,16,17],[1,3,4,5,6,7,8,9,10,12,14,15,16,17],[0,1,3,8,10,13,14,15,16,17],[0,3,4,5,7,8,9,11,12,13,14,15,16,17],[0,3,9,11,18],[2,4,5,9,10,11,12,18],[0,1,5,7,8,9,13,18],[0,1,6,8,9,10,12,13,18],[0,1,5,7,8,14,18],[0,1,2,3,8,9,10,12,14,18],[1,2,3,4,9,10,11,13,14,18],[3,4,5,6,11,12,13,14,18],[1,3,6,7,9,10,15,18],[0,1,3,4,5,6,7,8,9,11,12,15,18],[0,4,8,9,11,13,15,18],[0,1,3,4,5,6,7,9,10,12,13,15,18],[0,4,6,7,8,10,11,14,15,18],[5,6,9,12,14,15,18],[1,4,9,10,13,14,15,18],[0,1,5,6,8,11,12,13,14,15,18],[0,1,2,3,5,10,16,18],[0,1,6,7,9,12,16,18],[0,1,2,4,10,13,16,18],[0,3,5,9,12,13,16,18],[3,4,6,10,11,14,16,18],[2,3,5,11,12,14,16,18],[0,3,5,6,9,11,13,14,16,18],[3,4,6,7,9,10,11,12,13,14,16,18],[0,1,3,4,5,6,7,8,10,11,15,16,18],[1,4,9,12,15,16,18],[0,1,2,3,5,7,8,11,13,15,16,18],[0,3,7,9,10,12,13,15,16,18],[1,3,5,8,10,14,15,16,18],[0,2,6,11,12,14,15,16,18],[0,1,3,4,5,6,8,9,10,13,14,15,16,18],[6,7,9,11,12,13,14,15,16,18],[0,1,6,7,10,11,17,18],[0,1,2,3,5,6,7,8,9,10,11,12,17,18],[1,3,8,9,13,17,18],[2,3,5,6,7,12,13,17,18],[0,4,5,6,7,9,11,14,17,18],[1,3,6,8,9,11,12,14,17,18],[0,1,3,4,5,8,9,13,14,17,18],[2,3,6,9,12,13,14,17,18],[1,3,5,6,9,10,11,15,17,18],[1,4,6,10,12,15,17,18],[1,3,6,7,8,10,13,15,17,18],[5,8,9,10,11,12,13,15,17,18],[1,2,5,6,7,11,14,15,17,18],[0,4,6,12,14,15,17,18],[0,1,2,3,6,8,10,13,14,15,17,18],[5,8,10,11,12,13,14,15,17,18],[0,1,2,4,5,9,11,16,17,18],[0,2,6,7,8,9,11,12,16,17,18],[0,1,3,4,5,6,10,11,13,16,17,18],[6,8,10,11,12,13,16,17,18],[0,1,2,3,6,7,8,9,10,11,14,16,17,18],[5,7,10,11,12,14,16,17,18],[7,8,9,10,11,13,14,16,17,18],[5,10,11,12,13,14,16,17,18],[1,3,7,8,10,11,15,16,17,18],[5,6,8,10,12,15,16,17,18],[5,7,8,9,10,11,13,15,16,17,18],[7,8,9,10,12,13,15,16,17,18],[6,7,11,14,15,16,17,18],[5,7,9,12,14,15,16,17,18],[5,6,7,10,11,13,14,15,16,17,18],[6,9,10,12,13,14,15,16,17,18]]},"distance":{"d":5,"is_exact":true,"upper":5,"witness":[13,72,86,97,113],"A_d":16002,"certified":null},"clifford":{"kind":"required","correction":{"S":[[1,1],[2,3],[3,2],[4,1]],"CZ":[[0,2],[0,3],[0,4],[0,7],[0,8],[0,9],[0,11],[0,14],[0,15],[0,16],[0,18],[1,3],[1,4],[1,5],[1,6],[1,8],[1,9],[1,10],[1,11],[2,3],[2,5],[2,7],[2,13],[2,15],[3,5],[3,6],[3,7],[3,9],[3,10],[3,11],[3,12],[3,13],[3,15],[3,16],[3,17],[3,18],[4,5],[4,7],[4,9],[4,11],[4,12],[4,14],[4,15],[4,17]]},"rotation_powers":null},"metrics":{"gamma":2.0098626663592656,"gamma_t":2.0098626663592656,"gamma_rho":2.0098626663592656,"gamma_claim":2.0098626663592656,"gamma_t_claim":2.0098626663592656,"gamma_rho_claim":2.0098626663592656,"v_ex":5,"rate":0.03937007874015748,"t_count":5,"poly_degree":1,"effective_width":5},"provenance":{"regimes":["AI search"],"discovery":"AI search","strongest_claim":"found by an AI search campaign; a verified witness, not a maximum","sources":[{"regime":"AI search","file":"master_catalog/AI results","label":"T0.T1.T2.T3.T4","N":19,"d":5,"d_is_exact":true,"origin":"factory_records/headline","provenance":"factory_records/headline/n127_k5_d5_T5.json"},{"regime":"AI search","file":"master_catalog/catalogue_new","label":"T0.T1.T2.T3.T4","N":19,"d":5,"d_is_exact":true,"origin":"factory_records/headline","provenance":"factory_records/headline \u00b7 catalogue.jsonl:350"}]},"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"}]}