{
  "abstract": "FINDING: The search results are a mix of YouTube problem-solving videos (windmill problem, \"hardest easy geometry,\" USAMO problems) and one arXiv paper on Hilbert geometry asymptotics — no single unified discovery, but the Hilbert geometry paper offers the only novel mathematical content. | MATH: Hilbert geometry volume growth entropy equals that of Lobachevsky space; asymptotic ratio of metric ball volume to metric sphere area converges to the same constant as in hyperbolic space (related to curvature −1). No explicit constants given in the abstract, but the entropy equality implies the exponential growth rate is the same as in constant negative curvature — i.e., the volume of a ball of radius R grows like e^{(n−1)R} (up to polynomial factors), with the same leading coefficient as hyperbolic space. | CONNECTION: Hilbert geometry is a Finsler geometry whose unit ball is a convex body — when that body is an ellipsoid, it reduces to Klein's model of hyperbolic space. The entropy equality\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Andrew Stewart Caldin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4nsmqykdzhvm0.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635373",
  "fulltext_url": null,
  "id": "4nsmqykdzhvm0",
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  "landing_url": "https://zenodo.org/records/23635373",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
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  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4nsmqykdzhvm0.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:21:54Z",
      "native_id": "23635373",
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      "url": "https://zenodo.org/records/23635373"
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  "subjects": [],
  "title": "Hilbert Geometry Volume Asymptotics Match Hyperbolic Space Entropy — E8 Intelligence Research",
  "title_text": "Hilbert Geometry Volume Asymptotics Match Hyperbolic Space Entropy — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:54Z",
  "url": "https://research.draconitic.com/paper/4nsmqykdzhvm0",
  "venue": "Zenodo",
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}