{"paper":{"title":"On the Steinhaus tiling problem in three dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Daniel Goldstein, R. Daniel Mauldin","submitted_at":"2013-04-30T16:06:58Z","abstract_excerpt":"H. Steinhaus asked in the 1950's whether there exists a set in the plane R^2 meeting every isometric copy of Z^2 in precisely one point. Such a \"Steinhaus set\" was constructed by Jackson and Mauldin. What about three-space R^3? Is there a subset of R^3 meeting every isometric copy of Z^3 in exactly one point? We offer heuristic evidence that the answer is \"no\"."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.8047","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"}