{
  "abstract": "Recently, it was shown in arXiv:2607.27629 that under a very general condition, a generic family of curved Kakeya sets in $\\mathbb{R}^3$ not trivially contained in a hypersurface has Hausdorff dimension strictly greater than 2. In this paper we leverage large language models to give an explicit construction of a family of curves failing the worst compression phenomenon in arXiv:2607.27629, but whose union has Hausdorff dimension and upper box dimension $5/2$. The example shows that there are Kakeya compression phenomena besides the trivial example of concentrating near a hypersurface. This answers a question raised in section 1.9 of arXiv:2607.27629. The models used are ChatGPT 5.6 Sol and ChatGPT 6 Astra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05404",
  "author_total": 1,
  "authors": [
    {
      "name": "Jiahan Du"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/etam7mpbcwp6j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05404",
  "fulltext_url": null,
  "id": "etam7mpbcwp6j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05404",
  "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"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7220731796",
  "pdf_url": "https://arxiv.org/pdf/2610.05404",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/etam7mpbcwp6j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05404",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05404"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Fraction Dimensional Kakeya Compression",
  "title_text": "A Fraction Dimensional Kakeya Compression",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/etam7mpbcwp6j",
  "venue": "arXiv",
  "versions": []
}