{
  "abstract": "We establish a resolvent factorization of the hyperbolic projection associated with the finite-range dual operators, by a kernel with exponential off-diagonal decay. As an application, we prove that, for every irrational frequency and every analytic potential, each subcritical Type I energy satisfying the gap-labelling condition is an endpoint of an open spectral gap. This confirms the conjecture of Ge--Jitomirskaya--You [GJY,You] in the subcritical regime.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23467",
  "author_total": 1,
  "authors": [
    {
      "name": "Xianzhe Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b7dtbb1qsm8nd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23467",
  "fulltext_url": null,
  "id": "b7dtbb1qsm8nd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23467",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
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      "arxiv",
      "math.DS"
    ],
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      "arxiv",
      "math.MP"
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      "arxiv",
      "math.SP"
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      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
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  "openalex": "W7214006276",
  "pdf_url": "https://arxiv.org/pdf/2609.23467",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b7dtbb1qsm8nd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.23467",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23467"
    }
  ],
  "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": "Dry Ten Martini Problem in the Subcritical Type I Regime",
  "title_text": "Dry Ten Martini Problem in the Subcritical Type I Regime",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/b7dtbb1qsm8nd",
  "venue": "arXiv",
  "versions": []
}