{"id":"273.7.2.a","row":937,"stored":{"file":"master_catalog.json","row":937,"construction":null,"columns_sha256":null},"parameters":{"n":273,"k":7,"d":2,"N":14,"r":7,"level":3},"gate":{"string":"0+1+2+3+4+5+6","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6","monomials":[[0],[1],[2],[3],[4],[5],[6]],"sk_key":[[0],[1],[2],[3],[4],[5],[6]],"sk_fingerprint":"4227720e4bdc2b66","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,7,8,9,10],[0,7,8,9,11],[0,7,8,9,12],[0,7,8,9,13],[0,7,8,10,11],[0,7,8,10,12],[0,7,8,10,13],[0,7,8,11,12],[0,7,8,11,13],[0,7,8,12,13],[0,7,9,10,11],[0,7,9,10,12],[0,7,9,10,13],[0,7,9,11,12],[0,7,9,11,13],[0,7,9,12,13],[0,7,10,11,12],[0,7,10,11,13],[0,7,10,12,13],[0,7,11,12,13],[0,8,9,10,11],[0,8,9,10,12],[0,8,9,10,13],[0,8,9,11,12],[0,8,9,11,13],[0,8,9,12,13],[0,8,10,11,12],[0,8,10,11,13],[0,8,10,12,13],[0,8,11,12,13],[0,9,10,11,12],[0,9,10,11,13],[0,9,10,12,13],[0,9,11,12,13],[0,10,11,12,13],[1,7,8,9,10],[1,7,8,9,11],[1,7,8,9,12],[1,7,8,9,13],[1,7,8,10,11],[1,7,8,10,12],[1,7,8,10,13],[1,7,8,11,12],[1,7,8,11,13],[1,7,8,12,13],[1,7,9,10,11],[1,7,9,10,12],[1,7,9,10,13],[1,7,9,11,12],[1,7,9,11,13],[1,7,9,12,13],[1,7,10,11,12],[1,7,10,11,13],[1,7,10,12,13],[1,7,11,12,13],[1,8,9,10,11],[1,8,9,10,12],[1,8,9,10,13],[1,8,9,11,12],[1,8,9,11,13],[1,8,9,12,13],[1,8,10,11,12],[1,8,10,11,13],[1,8,10,12,13],[1,8,11,12,13],[1,9,10,11,12],[1,9,10,11,13],[1,9,10,12,13],[1,9,11,12,13],[1,10,11,12,13],[2,7,8,9,10],[2,7,8,9,11],[2,7,8,9,12],[2,7,8,9,13],[2,7,8,10,11],[2,7,8,10,12],[2,7,8,10,13],[2,7,8,11,12],[2,7,8,11,13],[2,7,8,12,13],[2,7,9,10,11],[2,7,9,10,12],[2,7,9,10,13],[2,7,9,11,12],[2,7,9,11,13],[2,7,9,12,13],[2,7,10,11,12],[2,7,10,11,13],[2,7,10,12,13],[2,7,11,12,13],[2,8,9,10,11],[2,8,9,10,12],[2,8,9,10,13],[2,8,9,11,12],[2,8,9,11,13],[2,8,9,12,13],[2,8,10,11,12],[2,8,10,11,13],[2,8,10,12,13],[2,8,11,12,13],[2,9,10,11,12],[2,9,10,11,13],[2,9,10,12,13],[2,9,11,12,13],[2,10,11,12,13],[3,7,8,9,10],[3,7,8,9,11],[3,7,8,9,12],[3,7,8,9,13],[3,7,8,10,11],[3,7,8,10,12],[3,7,8,10,13],[3,7,8,11,12],[3,7,8,11,13],[3,7,8,12,13],[3,7,9,10,11],[3,7,9,10,12],[3,7,9,10,13],[3,7,9,11,12],[3,7,9,11,13],[3,7,9,12,13],[3,7,10,11,12],[3,7,10,11,13],[3,7,10,12,13],[3,7,11,12,13],[3,8,9,10,11],[3,8,9,10,12],[3,8,9,10,13],[3,8,9,11,12],[3,8,9,11,13],[3,8,9,12,13],[3,8,10,11,12],[3,8,10,11,13],[3,8,10,12,13],[3,8,11,12,13],[3,9,10,11,12],[3,9,10,11,13],[3,9,10,12,13],[3,9,11,12,13],[3,10,11,12,13],[4,7,8,9,10],[4,7,8,9,11],[4,7,8,9,12],[4,7,8,9,13],[4,7,8,10,11],[4,7,8,10,12],[4,7,8,10,13],[4,7,8,11,12],[4,7,8,11,13],[4,7,8,12,13],[4,7,9,10,11],[4,7,9,10,12],[4,7,9,10,13],[4,7,9,11,12],[4,7,9,11,13],[4,7,9,12,13],[4,7,10,11,12],[4,7,10,11,13],[4,7,10,12,13],[4,7,11,12,13],[4,8,9,10,11],[4,8,9,10,12],[4,8,9,10,13],[4,8,9,11,12],[4,8,9,11,13],[4,8,9,12,13],[4,8,10,11,12],[4,8,10,11,13],[4,8,10,12,13],[4,8,11,12,13],[4,9,10,11,12],[4,9,10,11,13],[4,9,10,12,13],[4,9,11,12,13],[4,10,11,12,13],[5,7,8,9,10],[5,7,8,9,11],[5,7,8,9,12],[5,7,8,9,13],[5,7,8,10,11],[5,7,8,10,12],[5,7,8,10,13],[5,7,8,11,12],[5,7,8,11,13],[5,7,8,12,13],[5,7,9,10,11],[5,7,9,10,12],[5,7,9,10,13],[5,7,9,11,12],[5,7,9,11,13],[5,7,9,12,13],[5,7,10,11,12],[5,7,10,11,13],[5,7,10,12,13],[5,7,11,12,13],[5,8,9,10,11],[5,8,9,10,12],[5,8,9,10,13],[5,8,9,11,12],[5,8,9,11,13],[5,8,9,12,13],[5,8,10,11,12],[5,8,10,11,13],[5,8,10,12,13],[5,8,11,12,13],[5,9,10,11,12],[5,9,10,11,13],[5,9,10,12,13],[5,9,11,12,13],[5,10,11,12,13],[6,7,8,9,10],[6,7,8,9,11],[6,7,8,9,12],[6,7,8,9,13],[6,7,8,10,11],[6,7,8,10,12],[6,7,8,10,13],[6,7,8,11,12],[6,7,8,11,13],[6,7,8,12,13],[6,7,9,10,11],[6,7,9,10,12],[6,7,9,10,13],[6,7,9,11,12],[6,7,9,11,13],[6,7,9,12,13],[6,7,10,11,12],[6,7,10,11,13],[6,7,10,12,13],[6,7,11,12,13],[6,8,9,10,11],[6,8,9,10,12],[6,8,9,10,13],[6,8,9,11,12],[6,8,9,11,13],[6,8,9,12,13],[6,8,10,11,12],[6,8,10,11,13],[6,8,10,12,13],[6,8,11,12,13],[6,9,10,11,12],[6,9,10,11,13],[6,9,10,12,13],[6,9,11,12,13],[6,10,11,12,13],[7],[7,8,9,10,11],[7,8,9,10,12],[7,8,9,10,13],[7,8,9,11,12],[7,8,9,11,13],[7,8,9,12,13],[7,8,10,11,12],[7,8,10,11,13],[7,8,10,12,13],[7,8,11,12,13],[7,9,10,11,12],[7,9,10,11,13],[7,9,10,12,13],[7,9,11,12,13],[7,10,11,12,13],[8],[8,9,10,11,12],[8,9,10,11,13],[8,9,10,12,13],[8,9,11,12,13],[8,10,11,12,13],[9],[9,10,11,12,13],[10],[11],[12],[13]]},"distance":{"d":2,"is_exact":true,"upper":2,"witness":[0,35],"A_d":735,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,3],[1,3],[2,3],[3,3],[4,3],[5,3],[6,3],[7,2],[8,2],[9,2],[10,2],[11,2],[12,2],[13,2]],"CZ":[]},"rotation_powers":[[0,7],[1,7],[4,7],[10,7],[20,7],[35,5],[65,3],[66,3],[67,3],[68,3],[69,3],[70,5],[100,3],[101,3],[102,3],[103,3],[104,3],[105,5],[135,3],[136,3],[137,3],[138,3],[139,3],[140,5],[170,3],[171,3],[172,3],[173,3],[174,3],[175,5],[205,3],[206,3],[207,3],[208,3],[209,3],[210,5],[240,3],[241,3],[242,3],[243,3],[244,3],[251,3],[254,3],[255,3],[258,3],[259,3],[260,3],[264,3],[265,3],[266,3],[268,3]]},"metrics":{"gamma":5.285402218862249,"gamma_t":null,"gamma_rho":5.285402218862249,"gamma_claim":5.285402218862249,"gamma_t_claim":null,"gamma_rho_claim":5.285402218862249,"v_ex":7,"rate":0.02564102564102564,"t_count":null,"poly_degree":null,"effective_width":7},"provenance":{"regimes":["borrowed-identity search: two-group"],"discovery":"pre-existing","strongest_claim":"found by the two-group borrowed-identity search of Singh, Gidney and Jones (arXiv:2606.28518; borrowed_identities/): an identity circuit symmetric within its output and check blocks, with its output-only gates removed; a verified witness, not a maximum","sources":[{"regime":"borrowed-identity search: two-group","file":"borrowed_identities/circuits/large_unified_l3.json","label":"lu-0740","N":14,"d":2,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at ae9fbf8, outputs/large_unified_factories_l3.csv line 740","provenance":"larger unified search l=3, two-group s_total=4,s_O=7"}]},"references":[{"key":"singh2026borrowed","short":"Singh et al. (2026)","full":"S. Singh, C. Gidney, and C. Jones, \"Borrowed Identities: Malleable Distillation Factories and a Unified Numerical Search,\" arXiv:2606.28518 (2026).","url":"https://arxiv.org/abs/2606.28518","date":"2026-06-26"}]}