{
  "abstract": "We study the mosaic Almost Mathieu operator, a quasiperiodic model that naturally admits a singular strip-Jacobi representation. By establishing a duality framework and extending the correspondence between the integrated density of states and the fibered rotation number to this setting, we obtain an effective reduction to $SL(2,\\mathbb{R})$ cocycles. As a consequence, combining Aubry duality, reducibility theory, and the Moser--Pöschel argument, we prove that the spectrum is a Cantor set for all noncritical parameters.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.23422",
  "author_total": 3,
  "authors": [
    {
      "name": "Jiawei He"
    },
    {
      "name": "Yuan Shan"
    },
    {
      "name": "Yongjian Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e0fdsbv623t1q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.23422",
  "fulltext_url": null,
  "id": "e0fdsbv623t1q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.23422",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.23422",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e0fdsbv623t1q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:11Z",
      "native_id": "2606.23422",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.23422"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Cantor Spectrum via a Reducibility-Duality Bridge for the Mosaic Almost Mathieu Operator",
  "title_text": "Cantor Spectrum via a Reducibility-Duality Bridge for the Mosaic Almost Mathieu Operator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/e0fdsbv623t1q",
  "venue": "arXiv",
  "versions": []
}