{
  "abstract": "We supply the details of the subcritical dry Ten Martini statement announced in [6, Remark 1.3]: for every irrational frequency, every subcritical Type I energy with resonant rotation number is an endpoint of an open spectral gap. The proof combines the all-frequency Puig argument developed there with quantitative almost reducibility. A different proof was recently given by Li [7].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37438",
  "author_total": 1,
  "authors": [
    {
      "name": "Lingrui Ge"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/56w5sshnc1ktg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37438",
  "fulltext_url": null,
  "id": "56w5sshnc1ktg",
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  "landing_url": "https://arxiv.org/abs/2609.37438",
  "language": null,
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  "licence_label": "arXiv licence",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.DS"
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      "arxiv",
      "math.MP"
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      "2610|Spectral Theory in Mathematical Physics"
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  "openalex": "W7214988912",
  "pdf_url": "https://arxiv.org/pdf/2609.37438",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/56w5sshnc1ktg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.37438",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37438"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "The Dry Ten Martini Problem for subcritical Type I operators",
  "title_text": "The Dry Ten Martini Problem for subcritical Type I operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/56w5sshnc1ktg",
  "venue": "arXiv",
  "versions": []
}