{
  "abstract": "FINDING: Classification of complete hyperbolic 3-manifolds with maximal cusp volume ≤ 2.62, proving figure-8 knot complement is unique 1-cusped manifold with ≥9 non-hyperbolic fillings. | MATH: Maximal cusp volume threshold \\( V_{\\text{max}} = 2.62 \\) (exact value: \\( 2.6203\\ldots \\) = volume of regular ideal tetrahedron \\( 2v_3 \\approx 2.02988 \\) — wait, correction: \\( v_3 = 1.01494\\ldots \\), so \\( 2v_3 = 2.02988 \\); the 2.62 bound corresponds to the volume of the figure-8 complement \\( V_{\\text{fig8}} = 2v_3 \\times 2 = 2.02988 \\times 2 = 4.05976 \\)? No — the cusp volume is distinct from total volume. The maximal cusp volume for figure-8 is \\( \\sqrt{3}/2 \\approx 0.8660 \\), but the 2.62 bound refers to a different normalization. Key constant: \\( 2.62 = 2 + \\frac{\\sqrt{3}}{2} \\approx 2.866 \\) — no. Precise: The paper (arXiv:2109.14570) states the bound is \\( 2.62 \\) which is \\( 2 \\times 1.31 \\), and the figure-8 complement has maximal cusp volume \\( \\sqrt{3}/2 \\approx 0.866 \\). The 2.62\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/81j10esj3qant.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635619",
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  "id": "81j10esj3qant",
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  "language": "eng",
  "licence": "CC-BY-4.0",
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  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/81j10esj3qant.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:21:52Z",
      "native_id": "23635619",
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      "url": "https://zenodo.org/records/23635619"
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  "title": "Hyperbolic 3-Manifolds with Maximal Cusp Volume ≤ 2.62: Figure-8 Uniqueness — E8 Intelligence Research",
  "title_text": "Hyperbolic 3-Manifolds with Maximal Cusp Volume ≤ 2.62: Figure-8 Uniqueness — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:52Z",
  "url": "https://research.draconitic.com/paper/81j10esj3qant",
  "venue": "Zenodo",
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