{
  "abstract": "FINDING: The search results are a mix of competition-problem videos (windmill problem, \"hardest easy geometry,\" USAMO problems) and one arXiv paper on Hilbert geometry asymptotics. The only substantive mathematical content is the Hilbert geometry paper; the rest are pedagogical artifacts without extractable equations.\n\nMATH: From the Hilbert geometry paper (arXiv:0711.0446v1): - Volume growth entropy of metric balls in Hilbert geometry equals that of Lobachevsky space (hyperbolic space). - Asymptotic ratio: \\( \\frac{\\text{Vol}(B_R)}{\\text{Area}(S_R)} \\sim \\frac{R}{n-1} \\) (for dimension \\(n\\)), matching hyperbolic space behavior. - No explicit constants like 0.382, 0.618, 0.786, 1.618, 2.618 appear in the abstract.\n\nCONNECTION: Hilbert geometry is a projective generalization of hyperbolic geometry. Its metric balls share the same exponential growth rate as Lobachevsky space — implying a deep projective invariance of the entropy. No direct link to golden-ratio or base-60 struc\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/6t26zd3p3927w.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23409563",
  "fulltext_url": null,
  "id": "6t26zd3p3927w",
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  "landing_url": "https://zenodo.org/records/23409563",
  "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/",
  "metadata_licence": null,
  "native_subjects": [],
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  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6t26zd3p3927w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "23409563",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23409563"
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  ],
  "subjects": [],
  "title": "Volume Growth Entropy in Hilbert Geometry Matches Hyperbolic Space — E8 Intelligence Research",
  "title_text": "Volume Growth Entropy in Hilbert Geometry Matches Hyperbolic Space — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:29Z",
  "url": "https://research.draconitic.com/paper/6t26zd3p3927w",
  "venue": "Zenodo",
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}