{"paper":{"title":"Keller's cube-tiling conjecture is false in high dimensions","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Jeffrey C. Lagarias, Peter W. Shor","submitted_at":"1992-10-01T00:00:00Z","abstract_excerpt":"O. H. Keller conjectured in 1930 that in any tiling of $\\Bbb R^n$ by unit $n$-cubes there exist two of them having a complete facet in common. O. Perron proved this conjecture for $n\\le 6$. We show that for all $n\\ge 10$ there exists a tiling of $\\Bbb R^n$ by unit $n$-cubes such that no two $n$-cubes have a complete facet in common."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9210222","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"}