{"paper":{"title":"$M\\setminus L$ near 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Carlos Gustavo Moreira, Carlos Matheus, Davi Lima, Sandoel Vieira","submitted_at":"2019-03-30T18:56:08Z","abstract_excerpt":"We construct four new elements $3.11>m_1>m_2>m_3>m_4$ of $M\\backslash L$ lying in distinct connected components of $\\mathbb{R}\\setminus L$, where $M$ is the Markov spectrum and $L$ is the Lagrange spectrum.\n  These elements are part of a decreasing sequence $(m_k)_{k\\in\\mathbb{N}}$ of elements in $M$ converging to $3$ and we give some evidence towards the possibility that $m_k\\in M\\setminus L$ for all $k\\geq 1$. In particular, this indicates that $3$ might belong to the closure of $M\\setminus L$, so that the answer to Bousch's question about the closedness of $M\\setminus L$ might be negative."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00269","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"}