{
  "abstract": "It is known that, for ordinary Hölder multifunctions with 0 < α < 1, Hölder regularity alone does not guarantee the existence of a Hölder selection, and in general even a continuous selection may fail to exist. We ask how this situation changes when the parameter is measured through a Stieltjes clock. For 0 < α < 1, we characterize the clocks for which every compact-valued g-Hölder multifunction admits a g-Hölder selection. The determining condition is uniform disconnectedness of the clock image Im(g). For left-continuous and nondecreasing clocks, this condition is equivalent to uniform jump dominance: every positive clock increment contains a jump carrying a fixed positive fraction of that increment. Under this condition, a selection can be chosen through any prescribed point of the graph, with explicit control of its Hölder regularity. Conversely, when the condition fails, there exists a compact-valued g-Hölder multifunction with no g-Hölder selection. The results show that the selection property is governed not simply by the presence of jumps, but by how their sizes are distributed across scales.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20706",
  "author_total": 4,
  "authors": [
    {
      "name": "Serkan İlter"
    },
    {
      "name": "Hülya Duru"
    },
    {
      "name": "Arkady Kitover"
    },
    {
      "name": "Mehmet Orhon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4x64nw69q927j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20706",
  "fulltext_url": null,
  "id": "4x64nw69q927j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20706",
  "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.GN"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7213611351",
  "pdf_url": "https://arxiv.org/pdf/2609.20706",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4x64nw69q927j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20706",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20706"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Hölder Selections under Stieltjes Clocks: Uniform Disconnectedness and Jump Dominance",
  "title_text": "Hölder Selections under Stieltjes Clocks: Uniform Disconnectedness and Jump Dominance",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/4x64nw69q927j",
  "venue": "arXiv",
  "versions": []
}