{
  "abstract": "Given an $m$-dimensional weight $\\mathbf{r}$ and an $n$-dimensional weight $\\mathbf{s}$, we prove that the set of $(\\mathbf{r};\\mathbf{s})$-badly approximable $m\\times n$ matrices is hyperplane absolute winning on $\\mathbb{R}^{m\\times n}$. This fully answers a question \\cite[Question 8.2 (iii)]{Kl} of D. Kleinbock in 1998.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22016",
  "author_total": 1,
  "authors": [
    {
      "name": "Chengyang Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/25e5e30ck3d57.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22016",
  "fulltext_url": null,
  "id": "25e5e30ck3d57",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22016",
  "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": "W7213892520",
  "pdf_url": "https://arxiv.org/pdf/2609.22016",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/25e5e30ck3d57.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.22016",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22016"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "$\\mathbf{Bad}(\\mathbf{r};\\mathbf{s})$ is Hyperplane Absolute Winning",
  "title_text": "Bad(r;s) is Hyperplane Absolute Winning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/25e5e30ck3d57",
  "venue": "arXiv",
  "versions": []
}