{"paper":{"title":"Expansions of the real field by discrete subgroups of Gl$_n(\\mathbb{C})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Erik Walsberg, Philipp Hieronymi, Samantha Xu","submitted_at":"2018-09-07T01:42:36Z","abstract_excerpt":"Let $\\Gamma$ be an infinite discrete subgroup of Gl$_n(\\mathbb{C})$. Then either $(\\mathbb{R}, <, +, \\cdot, \\Gamma)$ is interdefinable with $(\\mathbb{R}, <, +, \\cdot, \\lambda^\\mathbb{Z})$ for some $\\lambda \\in \\mathbb{R}$, or $(\\mathbb{R}, < , +, \\cdot, \\Gamma)$ defines the set of integers. When $\\Gamma$ is not virtually abelian, the second case holds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02273","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}