{"paper":{"title":"Assouad dimension of the Takagi function","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Lai Jiang","submitted_at":"2025-02-03T08:16:47Z","abstract_excerpt":"For any integer $b\\geq2$ and real series $\\{c_n\\}$ such that $\\sum_{n=0}^\\infty|c_n|<\\infty$, the generalized Takagi function $f_{{\\mathbf c},b}(x)$ is defined by $$\n  f_{{\\mathbf c},b}(x):=\\sum_{n=0}^\\infty c_n\\phi(b^n x), \\quad x\\in [0,1], $$ where $\\phi(x)=dist(x,\\mathbb{Z})$ is the distance from $x$ to the nearest integer. The collection of functions with the form are called the Takagi class. In this paper, we show that in the case that $\\varlimsup_{n \\to \\infty} b^n |c_n|<\\infty$, the Assouad dimension of the graph ${\\mathcal G} f_{{\\mathbf c},b}=\\{(x,f_{{\\mathbf c},b}(x)):x\\in[0,1]\\}$ fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.01140","kind":"arxiv","version":2},"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/2502.01140/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"}