{"paper":{"title":"Normality of the Thue--Morse sequence along Piatetski-Shapiro sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Lukas Spiegelhofer","submitted_at":"2017-07-17T11:49:24Z","abstract_excerpt":"We prove that for $1<c<4/3$ the subsequence of the Thue--Morse sequence $\\mathbf t$ indexed by $\\lfloor n^c\\rfloor$ defines a normal sequence, that is, each finite sequence $(\\varepsilon_0,\\ldots,\\varepsilon_{T-1})\\in \\{0,1\\}^T$ occurs as a contiguous subsequence of the sequence $n\\mapsto \\mathbf t\\left(\\lfloor n^c\\rfloor\\right)$ with asymptotic frequency $2^{-T}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05112","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"}