{"id":"100.15.3.a","row":666,"stored":{"file":"master_catalog.json","row":666,"construction":null,"columns_sha256":null},"parameters":{"n":100,"k":15,"d":3,"N":23,"r":8,"level":3},"gate":{"string":"0+1+2+3+4+5+6+7+8+9+10+11+12,13,14","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6\u00b7T7\u00b7T8\u00b7T9\u00b7T10\u00b7T11\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":"010ace333efd5ebc","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,13,14,15,16],[0,12,15,16,17,18,21,22],[0,13,14,15,17,19,20],[0,12,15,18,19,20,21,22],[0,16,17,19,20],[0,12,13,14,16,18,19,20,21,22],[0,12,13,14,17,18,21,22],[1,13,15,16,18,22],[1,12,13,14,15,16,19,20,21,22],[1,12,13,15,17],[1,13,14,15,17,18,19,20,21],[1,12,16,17,18,22],[1,14,16,17,19,20,21,22],[1,12,14,18,19,20,21],[2,13,14,15,16,18,19,22],[2,12,13,14,15,16,19,22],[2,12,13,15,17,18,19,21,22],[2,13,15,17,19,21,22],[2,14,16,17,18,21],[2,12,14,16,17,21],[2,12,18],[3,12,15,16,17,18,20,21],[3,12,13,15,16,17,19,21],[3,12,14,15,18],[3,12,13,14,15,19,20],[3,13,14,16,17,18,19,21],[3,14,16,17,20,21],[3,13,18,19,20],[4,14,15,16,17,18,21],[4,15,16,17,21,22],[4,12,14,15,17,18,21,22],[4,12,15,17,21],[4,12,14,16,18],[4,12,16,22],[4,14,18,22],[5,12,13,15,16,18],[5,13,14,15,16,18,21],[5,12,14,15,18,19,21,22],[5,15,18,19,22],[5,13,14,16,19,21,22],[5,12,13,16,19,22],[5,12,14,21],[6,12,13,15,16,17,21],[6,13,15,16,20,22],[6,12,15,17,19,20,21,22],[6,15,19],[6,12,13,16,17,19,21],[6,13,16,19,20,22],[6,12,17,20,21,22],[7,13,14,15,16,17,19,20,22],[7,12,13,14,15,16,18,20],[7,14,15,17,18,19,20],[7,12,14,15,20,22],[7,12,13,16,17,19],[7,13,16,18,22],[7,12,17,18,19,22],[8,13,15,16,17,18,22],[8,13,15,16,17,19],[8,12,13,14,15,16,18,21,22],[8,12,13,14,15,16,19,21],[8,12,14,17,18,19,21,22],[8,12,14,17,21],[8,18,19,22],[9,13,14,16,17,18,19,20,21],[9,13,16,17,20,22],[9,13,16,18,19,20,22],[9,13,14,16,20,21],[9,17,18,19],[9,14,17,21,22],[9,14,18,19,21,22],[10,12,14,15,17,18,20,22],[10,14,15,17,21,22],[10,12,13,14,15,18,20],[10,13,14,15,21],[10,12,13,17,18,20,21,22],[10,13,17,22],[10,12,18,20,21],[11,12,15,16,19,20,21],[11,12,15,16,22],[11,15,17,18,19,20,22],[11,15,17,18,21],[11,12,16,17,18,19,20],[11,12,16,17,18,21,22],[11,19,20,21,22],[13,15,16,17],[15,16,17,18,19],[13,15,16,17,18,19,22],[15,16,18,19,21],[13,15,16,18,19,21,22],[13,15,16,21,22],[15,17,18,22],[13,15,17,19],[13,15,17,19,22],[15,18,21,22],[16,17,22],[16,21],[17,18],[18,21],[19,21],[19,21,22]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,6],"A_d":744,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,1],[1,1],[2,1],[3,1],[4,1],[5,1],[6,1],[7,1],[8,1],[9,1],[10,1],[11,1],[12,2],[13,1],[15,1],[16,2],[17,2],[18,2],[21,2],[22,2]],"CZ":[[12,13],[12,16],[12,17],[12,19],[12,21],[12,22],[13,15],[13,17],[13,19],[14,15],[14,17],[14,18],[14,19],[14,21],[14,22],[15,19],[15,21],[16,17],[16,21],[16,22],[17,18],[17,22],[18,21],[19,22],[21,22]]},"rotation_powers":null},"metrics":{"gamma":1.726833027860842,"gamma_t":null,"gamma_rho":1.7896330458458893,"gamma_claim":1.726833027860842,"gamma_t_claim":null,"gamma_rho_claim":1.7896330458458893,"v_ex":14,"rate":0.15,"t_count":null,"poly_degree":null,"effective_width":15},"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/n100_k15_d3_T12CCZ1_v2.json","label":"0","N":23,"d":3,"d_is_exact":true,"origin":null,"provenance":"master_catalogue [[100,12,3]] + campaigns/2026-08-31_48to128/tools/census.py --grow (addrows.py, unseeded); actor-3 round 1; new_point=True, gate_new_at_n=True"}]},"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"}]}