{
  "abstract": "Unlike ordinary time, a Stieltjes clock may advance continuously, remain constant over intervals, or jump. For an ordinary continuous clock, Hölder regularity with exponent $α>1$ forces constancy, whereas jumps of a Stieltjes clock may allow nonconstant behavior. We refer to Hölder regularity of exponent $α>1$ measured relative to g as super-g-Hölder regularity, and show that, in finite dimensions, such functions admit an atomic representation determined entirely by their jumps, with their g-Hölder seminorms given exactly by the corresponding normalized jump sizes. This atomic representation yields a linear isometric description of the associated function space, together with its Banach and separability properties, an exact total-variation formula with an optimal bound, and finite-jump approximation results. We then apply this structure to Stieltjes differential equations. Nonzero state jumps require positive clock jumps, leading to quantitative finite-jump bounds and, for affine dynamics, exact thresholds for the number of jumps and extremal terminal distances under a prescribed total Stieltjes mass. Finally, we study recovery of the Stieltjes clock from observed state jumps. For known single-valued dynamics, clock jumps can be recovered under a natural local identifiability condition, while for nonconvex differential inclusions the super-g-Hölder bound can reduce, and in some cases remove, nonuniqueness.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21050",
  "author_total": 3,
  "authors": [
    {
      "name": "Serkan İlter"
    },
    {
      "name": "Hülya Duru"
    },
    {
      "name": "Seyit Koca"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bx93dg04jd1d5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21050",
  "fulltext_url": null,
  "id": "bx93dg04jd1d5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21050",
  "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.CA"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Nonlinear Differential Equations Analysis"
    ]
  ],
  "openalex": "W7213930185",
  "pdf_url": "https://arxiv.org/pdf/2609.21050",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bx93dg04jd1d5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21050",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21050"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Super-g-Hölder Regularity in Stieltjes Dynamics: Atomic Structure, Exact Extremal Values, and Recovery of the Stieltjes Clock",
  "title_text": "Super-g-Hölder Regularity in Stieltjes Dynamics: Atomic Structure, Exact Extremal Values, and Recovery of the Stieltjes Clock",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/bx93dg04jd1d5",
  "venue": "arXiv",
  "versions": []
}