{
  "abstract": "Motivated by applications in Diophantine approximation, we develop a new fibering mechanism for non-degenerate manifolds in $\\mathbb{R}^n$, showing that they admit local decompositions into families of non-degenerate curves with uniform quantitative non-degeneracy properties. The manifolds are required to be $C^N$ with the essentially optimal bound $N\\geq \\max\\lbrace n,l+1\\rbrace$, where the manifold is $l$ non-degenerate. Furthermore, we show that this uniform quantitative local control can be globalised into a qualitative statement, so that almost every point of a non-degenerate manifold lies on a non-degenerate curve contained in the manifold. Our approach is perturbative and shows that the fibering structure arising in the analytic setting is stable under sufficiently small $C^N$ perturbations. The method provides a framework for extending fibering based results in Diophantine approximation from curves to manifolds. Such applications are considered in the paper.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10799",
  "author_total": 1,
  "authors": [
    {
      "name": "ZiAn Cody Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/44sfbvky4hnrt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10799",
  "fulltext_url": null,
  "id": "44sfbvky4hnrt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10799",
  "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.NT"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7221193999",
  "pdf_url": "https://arxiv.org/pdf/2610.10799",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/44sfbvky4hnrt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.10799",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10799"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Non-degeneracy and Fibering with Applications to Diophantine Approximation",
  "title_text": "Non-degeneracy and Fibering with Applications to Diophantine Approximation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/44sfbvky4hnrt",
  "venue": "arXiv",
  "versions": []
}