{"paper":{"title":"Tiling with arbitrary tiles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Imre Leader, Ta Sheng Tan, Vytautas Gruslys","submitted_at":"2015-05-14T12:00:44Z","abstract_excerpt":"Let $T$ be a tile in $\\mathbb{Z}^n$, meaning a finite subset of $\\mathbb{Z}^n$. It may or may not tile $\\mathbb{Z}^n$, in the sense of $\\mathbb{Z}^n$ having a partition into copies of $T$. However, we prove that $T$ does tile $\\mathbb{Z}^d$ for some $d$. This resolves a conjecture of Chalcraft."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03697","kind":"arxiv","version":2},"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"}