{"id":"70.8.3.a","row":501,"stored":{"file":"master_catalog.json","row":501,"construction":null,"columns_sha256":null},"parameters":{"n":70,"k":8,"d":3,"N":19,"r":11,"level":3},"gate":{"string":"0+1+2+3+4+5+6+7","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6\u00b7T7","monomials":[[0],[1],[2],[3],[4],[5],[6],[7]],"sk_key":[[0],[1],[2],[3],[4],[5],[6],[7]],"sk_fingerprint":"2daea1c2f1d6f117","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,8],[0,8,9],[0,8,9,10],[0,8,10],[0,9],[0,9,10],[0,10],[1,13,14,15,16,17,18],[1,13,14,15,16,18],[1,13,14,16],[1,13,14,16,17],[1,15,17,18],[1,15,18],[1,17],[2,12],[2,12,13,14,15,17],[2,12,13,16],[2,12,14,15,16,17],[2,13,14,15,17],[2,13,16],[2,14,15,16,17],[3,12,13,14,15,16],[3,12,13,14,17],[3,12,14,15,16,17,18],[3,12,14,18],[3,13,15,16,18],[3,13,17,18],[3,15,16,17],[4,12,13,14,15,16,17],[4,12,13,15,16,18],[4,12,14,16],[4,12,16,17,18],[4,13,14,15,18],[4,13,15,17],[4,14,17,18],[5,13,14,16,18],[5,13,14,17],[5,13,15,16,17],[5,13,15,18],[5,14,15,16],[5,14,15,17,18],[5,16,17,18],[6,12,13],[6,12,13,17,18],[6,12,14],[6,12,14,17,18],[6,13,14],[6,13,14,17,18],[6,17,18],[7,12,13,14],[7,12,13,14,15],[7,12,13,14,16],[7,12,13,14,18],[7,12,13,15],[7,12,13,15,16,17],[7,12,13,15,17],[7,12,13,16,17],[7,12,13,16,18],[7,12,13,17],[7,14,15,18],[7,14,16],[7,15,16,18],[8,9,10,11],[8,9,11],[8,10,11],[8,11],[9,10,11],[9,11],[10,11],[11]]},"distance":{"d":3,"is_exact":true,"upper":3,"witness":[0,1,4],"A_d":254,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,1],[1,1],[2,1],[3,1],[4,1],[5,1],[6,1],[7,2],[12,3],[13,3],[14,1],[15,3],[16,3],[17,2]],"CZ":[[7,12],[7,13],[7,14],[7,15],[7,16],[12,13],[12,14],[12,15],[13,14],[14,15],[14,16],[14,17],[15,16],[15,17],[16,18]]},"rotation_powers":null},"metrics":{"gamma":1.9743577627364344,"gamma_t":null,"gamma_rho":1.9743577627364344,"gamma_claim":1.9743577627364344,"gamma_t_claim":null,"gamma_rho_claim":1.9743577627364344,"v_ex":8,"rate":0.11428571428571428,"t_count":null,"poly_degree":null,"effective_width":8},"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":"/private/tmp/claude-501/-Users-shubhamjain-Documents-Claude-remote-magic-states-AI/25937cc1-0367-40c1-acc9-031067b831d4/scratchpad/msai_for_merge.jsonl","label":"msAI:58f85e58bf767d52","N":19,"d":3,"d_is_exact":true,"origin":"magic-states-AI/master_catalogue/master_catalogue.jsonl","provenance":"magic-states-AI/master_catalogue/master_catalogue.jsonl","notes":"gamma_campaign"}]},"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"}]}