{
  "abstract": "FINDING: The perfect cuboid problem reduces to rational points on elliptic curves, whose rank-zero Diophantine obstructions remain unresolved; related research explores curve maps over finite fields and rank≥5 elliptic curve families via Heron triples. | MATH: Perfect cuboid ⇔ rational solutions to \\(a^2+b^2=c^2,\\ a^2+d^2=e^2,\\ b^2+d^2=f^2,\\ c^2+d^2=g^2\\) (8 variables, 4 quadratic constraints). Elliptic curve \\(E: y^2=x^3+Ax+B\\) — rank \\(r\\) determines rational point structure; rank zero ⇒ finite rational points (Mordell–Weil). Diophantine stability (Mazur): \\(E(\\mathbb{Q})\\) unchanged under base change. Heron triple family: \\(A^2,B^2,C^2\\) with area \\(\\Delta\\) yields elliptic curve \\(y^2=x(x-A^2)(x+B^2)\\) — rank≥5 constructed via parameterization. | CONNECTION: No direct golden-ratio or base-60 link in these abstracts. However, elliptic curves over finite fields carry lattice structure (Tate module, \\(\\mathbb{Z}_\\ell\\)-rank 2) — crystallographic analogy: root lattice \\(E_8\\) and ellip\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/6jn2n6h606b52.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635527",
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  "id": "6jn2n6h606b52",
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  "landing_url": "https://zenodo.org/records/23635527",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "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/6jn2n6h606b52.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:21:54Z",
      "native_id": "23635527",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23635527"
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  "subjects": [],
  "title": "Elliptic Curves and the Perfect Cuboid: Rank-Zero Obstructions and Heron Triple Families — E8 Intelligence Research",
  "title_text": "Elliptic Curves and the Perfect Cuboid: Rank-Zero Obstructions and Heron Triple Families — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:54Z",
  "url": "https://research.draconitic.com/paper/6jn2n6h606b52",
  "venue": "Zenodo",
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}