{"id":"77.7.4.a","row":546,"stored":{"file":"master_catalog.json","row":546,"construction":null,"columns_sha256":null},"parameters":{"n":77,"k":7,"d":4,"N":17,"r":10,"level":3},"gate":{"string":"0+123+456","human":"T0\u00b7CCZ123\u00b7CCZ456","monomials":[[0],[1,2,3],[4,5,6]],"sk_key":[[0],[1,2,3],[4,5,6]],"sk_fingerprint":"441b01c40d2c0316","sk_canonical_frame":true,"relabelled_into_canonical_frame":true},"circuit":{"columns":[[1,2,3,4,5,6,8,9,10,12,15],[0,1,2,3,4,5,7,10,12,13,15,16],[1,2,3,4,5,8,9,11,12,13,14,15,16],[1,2,3,4,6,7,9,10,11,12,13,14,16],[0,1,2,3,4,7,8,12,13,14],[1,2,3,5,6,7,8,10,11,12,13,15,16],[0,1,2,3,5,6,7,8,10,11,13,14,15,16],[0,1,2,3,5,6,8,9,10,11,12,14,15,16],[0,1,2,3,5,13],[1,2,4,5,6,8,9,10,11,12,16],[1,2,5,6,7,8,14],[1,2,5,6,8,10,12,14,15,16],[0,1,2,6,7,8,10,14,16],[1,2,6,7,11,16],[0,1,2,6,8,9,11,12,14,16],[0,1,2,6,8,10,13,14,15,16],[0,1,3,4,5,6,7,11,13,14,16],[0,1,3,4,5,11],[0,1,3,4,6,8],[1,3,5,6,7],[1,3,7,8,11,12,16],[0,1,4,5,7,9,10,12,14,15,16],[0,1,4,5,7,9,11,12,13,14,15,16],[1,4,5,8,10,11,12,13,15],[1,4,5,15],[1,4,6,7,12,13],[0,1,4,7,8,10,11,12,13,14,16],[1,4,8,10,12,13,14,15],[0,1,5,6,7,13,14],[1,5,7,8,12],[0,1,5,10,11,12,13,14,15],[1,6,8,9,10,13,16],[0,1,7,9,10,15,16],[1,8,11,12,13,14,15],[1,9],[0,1,9,10,16],[2,3,4,5,7,9,10,14,16],[0,2,3,4,5,8,12,13,14,15,16],[2,3,4,8,9,11,12,13,16],[0,2,3,5,8,9,10,15,16],[0,2,3,6,9,10,11,12,14],[2,3,7,8,9,10,11,13,15],[2,3,7,9,15],[2,4,5,6,14],[2,4,5,16],[0,2,4,10],[2,5,7,10,11,15,16],[2,12,13,15],[3,4,5,7,8,9,11,12,14],[3,4,5,7,9,10,11,15],[3,4,5,9,12,13,14,15,16],[3,4,6,7,8,9,11,13,14,15,16],[3,4,6,7,8,9,12,13,16],[3,4,6,7,9,10,11,13],[3,4,6,8,9,11,13,14,15],[3,6,7,9,10,11,13,14,15,16],[3,6,7,10,11,12,13],[0,3,6,9,10,11,12,15],[3,9,10,11],[4,5,6,7,9,10,13,14],[4,6,7,8,12,13,15,16],[4,6,8,10,13],[5,6,7,8,11,13,14,15],[5,6,10,12,14],[0,7,8,9,10,11,13,14,16],[7,8,9,11,12,13,14,16],[0,7,8,10,11,12,14,15,16],[7,8,10,11,14,15],[7,8,11,12,13,14,15,16],[7,8,11,12,14,15],[7,10,11,12,13,14,15,16],[7,12,13,14,15,16],[8,9,10,11,12,13,15,16],[8,10,11,13,15,16],[8,14,15],[10,11,12,14,15,16],[12]]},"distance":{"d":4,"is_exact":true,"upper":4,"witness":[0,1,5,57],"A_d":2270,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[1,2],[2,2]],"CZ":[[0,1],[0,4],[0,6],[0,9],[1,3],[1,6],[1,7],[1,10],[1,13],[1,14],[2,6],[2,12],[2,14],[2,15],[2,16],[3,4],[3,7],[3,13],[3,14],[4,5],[4,6],[4,10],[4,11],[4,12],[4,15],[5,6],[5,8],[5,11],[5,13],[5,14],[5,15],[6,7],[6,8],[6,9],[6,10],[6,12],[6,13],[6,14]]},"rotation_powers":[[1,3],[4,3],[5,3],[8,3],[10,3],[11,3],[12,3],[13,3],[20,3],[30,3],[36,3],[38,3],[39,3],[41,3],[44,3],[45,3],[48,3],[51,3],[52,3],[53,3],[54,3],[56,3],[58,3],[59,3],[63,3],[65,3],[66,3],[69,3],[70,3],[71,3]]},"metrics":{"gamma":1.7297158093186489,"gamma_t":null,"gamma_rho":1.9724292229037697,"gamma_claim":1.7297158093186489,"gamma_t_claim":null,"gamma_rho_claim":1.9724292229037697,"v_ex":5,"rate":0.09090909090909091,"t_count":null,"poly_degree":null,"effective_width":7},"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/n77_k7_d4_T1CCZ2.json","label":"50","N":17,"d":4,"d_is_exact":true,"origin":null,"provenance":"master_catalogue [[77,6,4]] + tools/census.py --grow; new [[77,7,4]]; no catalogued d=4 row at n=77 has this gate or a superset of it; a second, non-isomorphic class with the identical A_d 2270 is in logs/assessed_d4.json [6]"}]},"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"}]}