{"paper":{"title":"Cubes of integral vectors in dimension four","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Emil W. Kiss, P\\'eter Kutas","submitted_at":"2011-08-15T22:54:20Z","abstract_excerpt":"A system of $m$ nonzero vectors in $\\mathbb{Z}^n$ is called an $m$-icube if they are pairwise orthogonal and have the same length. The paper describes $m$-icubes in $\\mathbb{Z}^4$ for $2\\le m\\le 4$ using Hurwitz integral quaternions, counts the number of them with given edge length, and proves that unlimited extension is possible in $\\mathbb{Z}^4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3113","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"}