{"paper":{"title":"Mean dimension and a sharp embedding theorem: extensions of aperiodic subshifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Masaki Tsukamoto, Yonatan Gutman","submitted_at":"2012-07-17T07:45:45Z","abstract_excerpt":"We show that if $(X,T)$ is an extension of an aperiodic subshift (a subsystem of $({1,2,...,l}^{\\mathbb{Z}},\\mathrm{shift})$ for some $l\\in\\mathbb{N}$) and has mean dimension $mdim(X,T)<\\frac{D}{2}$ $(D\\in \\mathbb{N}$), then it embeds equivariantly in (([0,1]^{D})^{\\mathbb{Z}},\\mathrm{shift})$. The result is sharp. If $(X,T)$ is an extension of an aperiodic zero-dimensional system then it embeds equivariantly in $(([0,1]^{D+1})^{\\mathbb{Z}},\\mathrm{shift})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3906","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"}