{"paper":{"title":"There is but one PDS in $\\mathbb{Z}^{3}$ inducing just square components","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carlos A. Araujo, Italo J. Dejter, Luis R. Fuentes","submitted_at":"2017-06-25T20:24:39Z","abstract_excerpt":"It is known that in the unit distance graph of the lattice $\\mathbb{Z}^3\\subset\\mathbb{R}^3$ there exists a dominating set $S$ with $4$-cycles as sole induced components and each vertex of $\\mathbb{Z}^3\\setminus S$ having a unique neighbor in $S$. We show $S$ is unique."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08165","kind":"arxiv","version":9},"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"}