{"id":"413.11.2.a","row":1040,"stored":{"file":"master_catalog.json","row":1040,"construction":null,"columns_sha256":null},"parameters":{"n":413,"k":11,"d":2,"N":18,"r":7,"level":3},"gate":{"string":"0+1+2+3+4+5+6+7+8+9+10","human":"T0\u00b7T1\u00b7T2\u00b7T3\u00b7T4\u00b7T5\u00b7T6\u00b7T7\u00b7T8\u00b7T9\u00b7T10","monomials":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]],"sk_key":[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]],"sk_fingerprint":"0b481873bf423e87","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,11,12,13,14],[0,11,12,13,15],[0,11,12,13,16],[0,11,12,13,17],[0,11,12,14,15],[0,11,12,14,16],[0,11,12,14,17],[0,11,12,15,16],[0,11,12,15,17],[0,11,12,16,17],[0,11,13,14,15],[0,11,13,14,16],[0,11,13,14,17],[0,11,13,15,16],[0,11,13,15,17],[0,11,13,16,17],[0,11,14,15,16],[0,11,14,15,17],[0,11,14,16,17],[0,11,15,16,17],[0,12,13,14,15],[0,12,13,14,16],[0,12,13,14,17],[0,12,13,15,16],[0,12,13,15,17],[0,12,13,16,17],[0,12,14,15,16],[0,12,14,15,17],[0,12,14,16,17],[0,12,15,16,17],[0,13,14,15,16],[0,13,14,15,17],[0,13,14,16,17],[0,13,15,16,17],[0,14,15,16,17],[1,11,12,13,14],[1,11,12,13,15],[1,11,12,13,16],[1,11,12,13,17],[1,11,12,14,15],[1,11,12,14,16],[1,11,12,14,17],[1,11,12,15,16],[1,11,12,15,17],[1,11,12,16,17],[1,11,13,14,15],[1,11,13,14,16],[1,11,13,14,17],[1,11,13,15,16],[1,11,13,15,17],[1,11,13,16,17],[1,11,14,15,16],[1,11,14,15,17],[1,11,14,16,17],[1,11,15,16,17],[1,12,13,14,15],[1,12,13,14,16],[1,12,13,14,17],[1,12,13,15,16],[1,12,13,15,17],[1,12,13,16,17],[1,12,14,15,16],[1,12,14,15,17],[1,12,14,16,17],[1,12,15,16,17],[1,13,14,15,16],[1,13,14,15,17],[1,13,14,16,17],[1,13,15,16,17],[1,14,15,16,17],[2,11,12,13,14],[2,11,12,13,15],[2,11,12,13,16],[2,11,12,13,17],[2,11,12,14,15],[2,11,12,14,16],[2,11,12,14,17],[2,11,12,15,16],[2,11,12,15,17],[2,11,12,16,17],[2,11,13,14,15],[2,11,13,14,16],[2,11,13,14,17],[2,11,13,15,16],[2,11,13,15,17],[2,11,13,16,17],[2,11,14,15,16],[2,11,14,15,17],[2,11,14,16,17],[2,11,15,16,17],[2,12,13,14,15],[2,12,13,14,16],[2,12,13,14,17],[2,12,13,15,16],[2,12,13,15,17],[2,12,13,16,17],[2,12,14,15,16],[2,12,14,15,17],[2,12,14,16,17],[2,12,15,16,17],[2,13,14,15,16],[2,13,14,15,17],[2,13,14,16,17],[2,13,15,16,17],[2,14,15,16,17],[3,11,12,13,14],[3,11,12,13,15],[3,11,12,13,16],[3,11,12,13,17],[3,11,12,14,15],[3,11,12,14,16],[3,11,12,14,17],[3,11,12,15,16],[3,11,12,15,17],[3,11,12,16,17],[3,11,13,14,15],[3,11,13,14,16],[3,11,13,14,17],[3,11,13,15,16],[3,11,13,15,17],[3,11,13,16,17],[3,11,14,15,16],[3,11,14,15,17],[3,11,14,16,17],[3,11,15,16,17],[3,12,13,14,15],[3,12,13,14,16],[3,12,13,14,17],[3,12,13,15,16],[3,12,13,15,17],[3,12,13,16,17],[3,12,14,15,16],[3,12,14,15,17],[3,12,14,16,17],[3,12,15,16,17],[3,13,14,15,16],[3,13,14,15,17],[3,13,14,16,17],[3,13,15,16,17],[3,14,15,16,17],[4,11,12,13,14],[4,11,12,13,15],[4,11,12,13,16],[4,11,12,13,17],[4,11,12,14,15],[4,11,12,14,16],[4,11,12,14,17],[4,11,12,15,16],[4,11,12,15,17],[4,11,12,16,17],[4,11,13,14,15],[4,11,13,14,16],[4,11,13,14,17],[4,11,13,15,16],[4,11,13,15,17],[4,11,13,16,17],[4,11,14,15,16],[4,11,14,15,17],[4,11,14,16,17],[4,11,15,16,17],[4,12,13,14,15],[4,12,13,14,16],[4,12,13,14,17],[4,12,13,15,16],[4,12,13,15,17],[4,12,13,16,17],[4,12,14,15,16],[4,12,14,15,17],[4,12,14,16,17],[4,12,15,16,17],[4,13,14,15,16],[4,13,14,15,17],[4,13,14,16,17],[4,13,15,16,17],[4,14,15,16,17],[5,11,12,13,14],[5,11,12,13,15],[5,11,12,13,16],[5,11,12,13,17],[5,11,12,14,15],[5,11,12,14,16],[5,11,12,14,17],[5,11,12,15,16],[5,11,12,15,17],[5,11,12,16,17],[5,11,13,14,15],[5,11,13,14,16],[5,11,13,14,17],[5,11,13,15,16],[5,11,13,15,17],[5,11,13,16,17],[5,11,14,15,16],[5,11,14,15,17],[5,11,14,16,17],[5,11,15,16,17],[5,12,13,14,15],[5,12,13,14,16],[5,12,13,14,17],[5,12,13,15,16],[5,12,13,15,17],[5,12,13,16,17],[5,12,14,15,16],[5,12,14,15,17],[5,12,14,16,17],[5,12,15,16,17],[5,13,14,15,16],[5,13,14,15,17],[5,13,14,16,17],[5,13,15,16,17],[5,14,15,16,17],[6,11,12,13,14],[6,11,12,13,15],[6,11,12,13,16],[6,11,12,13,17],[6,11,12,14,15],[6,11,12,14,16],[6,11,12,14,17],[6,11,12,15,16],[6,11,12,15,17],[6,11,12,16,17],[6,11,13,14,15],[6,11,13,14,16],[6,11,13,14,17],[6,11,13,15,16],[6,11,13,15,17],[6,11,13,16,17],[6,11,14,15,16],[6,11,14,15,17],[6,11,14,16,17],[6,11,15,16,17],[6,12,13,14,15],[6,12,13,14,16],[6,12,13,14,17],[6,12,13,15,16],[6,12,13,15,17],[6,12,13,16,17],[6,12,14,15,16],[6,12,14,15,17],[6,12,14,16,17],[6,12,15,16,17],[6,13,14,15,16],[6,13,14,15,17],[6,13,14,16,17],[6,13,15,16,17],[6,14,15,16,17],[7,11,12,13,14],[7,11,12,13,15],[7,11,12,13,16],[7,11,12,13,17],[7,11,12,14,15],[7,11,12,14,16],[7,11,12,14,17],[7,11,12,15,16],[7,11,12,15,17],[7,11,12,16,17],[7,11,13,14,15],[7,11,13,14,16],[7,11,13,14,17],[7,11,13,15,16],[7,11,13,15,17],[7,11,13,16,17],[7,11,14,15,16],[7,11,14,15,17],[7,11,14,16,17],[7,11,15,16,17],[7,12,13,14,15],[7,12,13,14,16],[7,12,13,14,17],[7,12,13,15,16],[7,12,13,15,17],[7,12,13,16,17],[7,12,14,15,16],[7,12,14,15,17],[7,12,14,16,17],[7,12,15,16,17],[7,13,14,15,16],[7,13,14,15,17],[7,13,14,16,17],[7,13,15,16,17],[7,14,15,16,17],[8,11,12,13,14],[8,11,12,13,15],[8,11,12,13,16],[8,11,12,13,17],[8,11,12,14,15],[8,11,12,14,16],[8,11,12,14,17],[8,11,12,15,16],[8,11,12,15,17],[8,11,12,16,17],[8,11,13,14,15],[8,11,13,14,16],[8,11,13,14,17],[8,11,13,15,16],[8,11,13,15,17],[8,11,13,16,17],[8,11,14,15,16],[8,11,14,15,17],[8,11,14,16,17],[8,11,15,16,17],[8,12,13,14,15],[8,12,13,14,16],[8,12,13,14,17],[8,12,13,15,16],[8,12,13,15,17],[8,12,13,16,17],[8,12,14,15,16],[8,12,14,15,17],[8,12,14,16,17],[8,12,15,16,17],[8,13,14,15,16],[8,13,14,15,17],[8,13,14,16,17],[8,13,15,16,17],[8,14,15,16,17],[9,11,12,13,14],[9,11,12,13,15],[9,11,12,13,16],[9,11,12,13,17],[9,11,12,14,15],[9,11,12,14,16],[9,11,12,14,17],[9,11,12,15,16],[9,11,12,15,17],[9,11,12,16,17],[9,11,13,14,15],[9,11,13,14,16],[9,11,13,14,17],[9,11,13,15,16],[9,11,13,15,17],[9,11,13,16,17],[9,11,14,15,16],[9,11,14,15,17],[9,11,14,16,17],[9,11,15,16,17],[9,12,13,14,15],[9,12,13,14,16],[9,12,13,14,17],[9,12,13,15,16],[9,12,13,15,17],[9,12,13,16,17],[9,12,14,15,16],[9,12,14,15,17],[9,12,14,16,17],[9,12,15,16,17],[9,13,14,15,16],[9,13,14,15,17],[9,13,14,16,17],[9,13,15,16,17],[9,14,15,16,17],[10,11,12,13,14],[10,11,12,13,15],[10,11,12,13,16],[10,11,12,13,17],[10,11,12,14,15],[10,11,12,14,16],[10,11,12,14,17],[10,11,12,15,16],[10,11,12,15,17],[10,11,12,16,17],[10,11,13,14,15],[10,11,13,14,16],[10,11,13,14,17],[10,11,13,15,16],[10,11,13,15,17],[10,11,13,16,17],[10,11,14,15,16],[10,11,14,15,17],[10,11,14,16,17],[10,11,15,16,17],[10,12,13,14,15],[10,12,13,14,16],[10,12,13,14,17],[10,12,13,15,16],[10,12,13,15,17],[10,12,13,16,17],[10,12,14,15,16],[10,12,14,15,17],[10,12,14,16,17],[10,12,15,16,17],[10,13,14,15,16],[10,13,14,15,17],[10,13,14,16,17],[10,13,15,16,17],[10,14,15,16,17],[11],[11,12,13,14,15],[11,12,13,14,16],[11,12,13,14,17],[11,12,13,15,16],[11,12,13,15,17],[11,12,13,16,17],[11,12,14,15,16],[11,12,14,15,17],[11,12,14,16,17],[11,12,15,16,17],[11,13,14,15,16],[11,13,14,15,17],[11,13,14,16,17],[11,13,15,16,17],[11,14,15,16,17],[12],[12,13,14,15,16],[12,13,14,15,17],[12,13,14,16,17],[12,13,15,16,17],[12,14,15,16,17],[13],[13,14,15,16,17],[14],[15],[16],[17]]},"distance":{"d":2,"is_exact":true,"upper":2,"witness":[0,35],"A_d":1925,"certified":null},"clifford":{"kind":"powers","correction":{"S":[[0,3],[1,3],[2,3],[3,3],[4,3],[5,3],[6,3],[7,3],[8,3],[9,3],[10,3],[11,2],[12,2],[13,2],[14,2],[15,2],[16,2],[17,2]],"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],[245,5],[275,3],[276,3],[277,3],[278,3],[279,3],[280,5],[310,3],[311,3],[312,3],[313,3],[314,3],[315,5],[345,3],[346,3],[347,3],[348,3],[349,3],[350,5],[380,3],[381,3],[382,3],[383,3],[384,3],[391,3],[394,3],[395,3],[398,3],[399,3],[400,3],[404,3],[405,3],[406,3],[408,3]]},"metrics":{"gamma":5.230566352782148,"gamma_t":null,"gamma_rho":5.230566352782148,"gamma_claim":5.230566352782148,"gamma_t_claim":null,"gamma_rho_claim":5.230566352782148,"v_ex":11,"rate":0.026634382566585957,"t_count":null,"poly_degree":null,"effective_width":11},"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-1186","N":18,"d":2,"d_is_exact":true,"origin":"https://github.com/shraggy/Magic_state_factory_search at ae9fbf8, outputs/large_unified_factories_l3.csv line 1186","provenance":"larger unified search l=3, two-group s_total=4,s_O=11"}]},"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"}]}