{"paper":{"title":"Purity results for some arithmetically defined measures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Peter J. Grabner","submitted_at":"2019-08-23T20:11:50Z","abstract_excerpt":"We study measures that are obtained as push-forwards of measures of maximal entropy on sofic shifts under digital maps\n  $(x_k)_{k\\in\\mathbb{N}}\\mapsto\\sum_{k\\in\\mathbb{N}}x_k\\beta^{-k}$, where $\\beta>1$ is a Pisot number. We characterise the continuity of such measures in terms of the underlying automaton and show a purity result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.09023","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.09023/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}