{"paper":{"title":"$HD(M\\setminus L)>0.353$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Gustavo Moreira, Carlos Matheus","submitted_at":"2017-03-13T09:35:38Z","abstract_excerpt":"The complement $M\\setminus L$ of the Lagrange spectrum $L$ in the Markov spectrum $M$ was studied by many authors (including Freiman, Berstein, Cusick and Flahive). After their works, we disposed of a countable collection of points in $M\\setminus L$.\n  In this article, we describe the structure of $M\\setminus L$ near a non-isolated point $\\alpha_{\\infty}$ found by Freiman in 1973, and we use this description to exhibit a concrete Cantor set $X$ whose Hausdorff dimension coincides with the Hausdorff dimension of $M\\setminus L$ near $\\alpha_{\\infty}$.\n  A consequence of our results is the lower "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04302","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":""},"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"}