{
  "abstract": "Let $d\\ge2$ and let $\\mathbf w=(w_1,\\ldots,w_d)$ satisfy $w_1\\ge\\cdots\\ge w_d>0$ and $\\sum_i w_i=1$. Set $s_*=d-(1+w_1)^{-1}$. We prove that there exist constants $C_{d,\\mathbf w}>0$ and $\\varepsilon_0=\\varepsilon_0(d,\\mathbf w)>0$ such that for all $0<\\varepsilon<\\varepsilon_0$, $$ \\dim_H\\operatorname{DI}_{\\mathbf w}(\\varepsilon)\\le s_*+C_{d,\\mathbf w}\\sqrt\\varepsilon. $$ Together with the lower bound of Kim--Park, this gives the exact formula $$ \\dim_H\\operatorname{Sing}(\\mathbf w)=s_*. $$",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35009",
  "author_total": 2,
  "authors": [
    {
      "name": "Bohan Yang"
    },
    {
      "name": "Tianru Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8sgqamwgd5zky.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35009",
  "fulltext_url": null,
  "id": "8sgqamwgd5zky",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35009",
  "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.DS"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7214741521",
  "pdf_url": "https://arxiv.org/pdf/2609.35009",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8sgqamwgd5zky.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35009",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35009"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Hausdorff Dimension of Weighted Singular Vectors",
  "title_text": "Hausdorff Dimension of Weighted Singular Vectors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/8sgqamwgd5zky",
  "venue": "arXiv",
  "versions": []
}