{"paper":{"title":"Hausdorff dimension of some subsets of the Lagrange and Markov spectra near $3$","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Gustavo Moreira, Christian Camilo Silva Villamil","submitted_at":"2025-04-28T23:03:01Z","abstract_excerpt":"We study the sets $\\mathcal{L}$ and $\\mathcal{M}\\setminus\\mathcal{L}$ near $3$, where $\\mathcal{L}$ and $\\mathcal{M}$ are the classical Lagrange and Markov spectra. More specifically, we construct a strictly decreasing sequence $\\{a_r\\}_{r\\in \\mathbb{N}}$ converging to $3$, such that for any $r$ one can find a subset $\\mathcal{B}_r\\subset (a_{r+1},a_r)\\cap \\mathcal{L}^{'}$ with the property that the Hausdorff dimension of $((a_{r+1},a_r)\\cap \\mathcal{L})\\setminus \\mathcal{B}_r$ is less than the Hausdorff dimension of $\\mathcal{B}_r$ and for $t\\in \\mathcal{B}_r$ the sets of irrational numbers w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.20300","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.20300/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"}