{"paper":{"title":"The Archimedean Projection Property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jeff Dodd, Michael Harrison, Vincent Coll","submitted_at":"2015-04-12T07:45:07Z","abstract_excerpt":"Let $H$ be a hypersurface in $\\mathbb R^n$ and let $\\pi$ be an orthogonal projection in $\\mathbb R^n$ restricted to $H$. We say that $H$ satisfies the $Archimedean$ $projection$ $property$ corresponding to $\\pi$ if there exists a constant $C$ such that $Vol(\\pi^{-1}(U)) = C \\cdot Vol(U)$ for every measurable $U$ in the range of $\\pi$. It is well-known that the $(n-1)$-dimensional sphere, as a hypersurface in $\\mathbb R^n$, satisfies the Archimedean projection property corresponding to any codimension 2 orthogonal projection in $\\mathbb R^n$, the range of any such projection being an $(n-2)$-di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02941","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"}