{"id":"92.6.4.a","row":622,"stored":{"file":"master_catalog.json","row":622,"construction":null,"columns_sha256":null},"parameters":{"n":92,"k":6,"d":4,"N":14,"r":8,"level":3},"gate":{"string":"012+345","human":"CCZ012\u00b7CCZ345","monomials":[[0,1,2],[3,4,5]],"sk_key":[[0,1,2],[3,4,5]],"sk_fingerprint":"7c05f5a651b43d16","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,3,4,6,9,13],[0,2,6,7,9,13],[2,3,4,5,8,9,13],[5,7,8,9,13],[1,2,5,6,10,13],[3,6,7,10,13],[2,4,5,6,8,10,13],[1,2,6,7,8,10,13],[0,2,8,9,10,13],[0,6,8,9,10,13],[1,7,8,9,10,13],[1,3,4,6,7,8,9,10,13],[1,2,7,11,13],[0,2,4,5,6,7,11,13],[0,1,3,4,5,7,8,11,13],[0,1,3,6,7,8,11,13],[1,6,9,11,13],[0,2,7,9,11,13],[0,5,8,9,11,13],[0,2,5,6,7,8,9,11,13],[3,5,6,10,11,13],[0,2,3,4,7,10,11,13],[2,4,6,8,10,11,13],[1,2,3,4,5,7,8,10,11,13],[0,7,9,10,11,13],[1,4,5,6,7,9,10,11,13],[5,8,9,10,11,13],[2,3,6,8,9,10,11,13],[2,3,4,5,12,13],[5,6,12,13],[0,4,5,7,12,13],[0,1,4,6,7,12,13],[1,2,3,5,8,12,13],[0,3,5,6,8,12,13],[0,3,5,7,8,12,13],[6,7,8,12,13],[1,2,3,9,12,13],[0,2,3,5,6,9,12,13],[0,1,2,7,9,12,13],[0,2,6,7,9,12,13],[0,2,3,4,5,8,9,12,13],[1,2,3,4,6,8,9,12,13],[2,3,5,7,8,9,12,13],[1,2,3,4,5,6,7,8,9,12,13],[3,5,10,12,13],[0,1,4,6,10,12,13],[2,3,7,10,12,13],[0,1,2,3,4,5,6,7,10,12,13],[2,5,8,10,12,13],[1,2,3,5,6,8,10,12,13],[1,2,4,5,7,8,10,12,13],[3,4,5,6,7,8,10,12,13],[1,9,10,12,13],[1,3,4,6,9,10,12,13],[4,5,7,9,10,12,13],[0,2,3,6,7,9,10,12,13],[0,3,8,9,10,12,13],[3,6,8,9,10,12,13],[2,7,8,9,10,12,13],[2,3,5,6,7,8,9,10,12,13],[4,5,11,12,13],[0,1,2,5,6,11,12,13],[2,3,4,5,7,11,12,13],[2,3,6,7,11,12,13],[0,1,3,8,11,12,13],[2,3,5,6,8,11,12,13],[0,1,2,3,4,5,7,8,11,12,13],[2,3,5,6,7,8,11,12,13],[0,2,4,5,9,11,12,13],[4,6,9,11,12,13],[0,2,3,4,5,7,9,11,12,13],[3,6,7,9,11,12,13],[0,1,2,4,8,9,11,12,13],[0,1,2,3,4,6,8,9,11,12,13],[4,5,7,8,9,11,12,13],[0,1,3,4,5,6,7,8,9,11,12,13],[0,4,5,10,11,12,13],[1,4,5,6,10,11,12,13],[0,1,4,7,10,11,12,13],[0,3,5,6,7,10,11,12,13],[1,4,8,10,11,12,13],[0,2,5,6,8,10,11,12,13],[1,3,5,7,8,10,11,12,13],[0,1,3,5,6,7,8,10,11,12,13],[0,1,2,5,9,10,11,12,13],[0,1,2,3,4,6,9,10,11,12,13],[2,3,7,9,10,11,12,13],[3,6,7,9,10,11,12,13],[0,1,8,9,10,11,12,13],[0,5,6,8,9,10,11,12,13],[1,2,3,4,5,7,8,9,10,11,12,13],[0,1,2,3,5,6,7,8,9,10,11,12,13]]},"distance":{"d":4,"is_exact":true,"upper":4,"witness":[0,1,4,5],"A_d":22462,"certified":null},"clifford":{"kind":"required","correction":{"S":[[0,3],[1,1],[4,1],[5,3],[13,2]],"CZ":[[0,1],[0,2],[0,4],[0,5],[0,6],[0,7],[0,10],[0,11],[0,12],[0,13],[1,5],[1,8],[1,9],[1,10],[1,11],[1,13],[2,7],[2,8],[2,9],[2,10],[2,12],[3,12],[4,6],[4,8],[4,9],[4,10],[4,11],[4,13],[5,7],[5,8],[5,12],[5,13],[6,10],[7,11],[8,9],[8,10]]},"rotation_powers":null},"metrics":{"gamma":1.9692997276679285,"gamma_t":1.4115611189579604,"gamma_rho":2.2617809780285065,"gamma_claim":1.9692997276679285,"gamma_t_claim":1.4115611189579604,"gamma_rho_claim":2.2617809780285065,"v_ex":4,"rate":0.06521739130434782,"t_count":13,"poly_degree":3,"effective_width":6},"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/n92_k6_d4_CCZ012_CCZ345_lift.json","label":"87","N":14,"d":4,"d_is_exact":true,"origin":null,"provenance":"REVIEWER-DERIVED (round 3 review, both reviewers): all-ones check lift of actor 2 raw hit work/actor-2/raw8/n92_k6_CCZCCZ_tNone_p0.json (the CCZ^2 frame folded into [[92,7,3]] T.CCZ^2): every column gets the new check wire 13; every odd-weight fault is then detected, so d>=3 becomes d>=4 (2026-08-31 RESULTS.md s11/s16d; actor 3 tools/affine.py). Legal because n is even and the gate is pure CCZ. Ve"}]},"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"}]}