{"paper":{"title":"Coincidence and noncoincidence of dimensions in compact subsets of $[0,1]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Andrew Mitchell, Lars Olsen","submitted_at":"2018-12-22T15:16:48Z","abstract_excerpt":"We show that given any six numbers $r,s,t,u,v,w \\in (0,1]$ satisfying $r \\leq s \\leq \\min(t,u) \\leq \\max(t,u) \\leq v \\leq w$, it is possible to construct a compact subset of $[0,1]$ with Hausdorff dimension equal to $r$, lower modified box dimension equal to $s$, packing dimension equal to $t$, lower box dimension equal to $u$, upper box dimension equal to $v$ and Assouad dimension equal to $w$. Moreover, the set constructed is an $r$-Hausdorff set and a $t$-packing set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09542","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"}