{
  "abstract": "We prove sharp arithmetic localization for one-dimensional quasiperiodic potentials with jump discontinuities, beyond uniform transversality. Our results include every non-constant $C^1$ monotone sampling function, even with arbitrarily large flat regions, and also certain non-monotone potentials. A key new mechanism is a symbolic unique-continuation principle: first-return words to the region where $f'>0$ have no common Dirichlet resonance, forcing eigenfunction mass to transfer away from flat or negatively sloped regions and recovering quantitative monotonicity of finite-volume eigenvalue branches.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17139",
  "author_total": 3,
  "authors": [
    {
      "name": "Svetlana Jitomirskaya"
    },
    {
      "name": "Netanel Levi"
    },
    {
      "name": "Tom Stoiber"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9vehxxsrvjyp1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17139",
  "fulltext_url": null,
  "id": "9vehxxsrvjyp1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17139",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.DS"
    ],
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      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.SP"
    ],
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      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7221746313",
  "pdf_url": "https://arxiv.org/pdf/2610.17139",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9vehxxsrvjyp1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.17139",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17139"
    }
  ],
  "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": "(Sharp arithmetic) localization beyond transversality",
  "title_text": "(Sharp arithmetic) localization beyond transversality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/9vehxxsrvjyp1",
  "venue": "arXiv",
  "versions": []
}