{
  "abstract": "FINDING: The perfect cuboid problem is linked to irreducibility of a degree-8 \"cuboid polynomial\" via a rank-zero elliptic curve, while quartic models of elliptic curves govern rational Diophantine D(q)-quintuples. | MATH: Cuboid polynomial \\(P_{a,u}(t)\\) (even, monic, degree 8) from Sharipov's first-cuboid specialization; irreducibility in \\(\\mathbb{Z}[t]\\) proven for nonzero integers \\(a,u\\) with \\(u^2 \\neq a^2\\) by reducing to a rank-zero elliptic curve. Quartic model: \\(y^2 = x^4 + a x^3 + b x^2 + c x + d\\) (or \\(y^2 = a x^4 + b x^3 + c x^2 + d x + e\\)) — divisibility-by-2 maps on such quartics relate to Diophantine \\(D(q)\\)-quintuples (sets \\(\\{a_1,...,a_5\\}\\) where \\(a_i a_j + q\\) is square). | CONNECTION: Rank-zero elliptic curves have finite Mordell–Weil group — their torsion structure connects to root systems (e.g., \\(E_8\\) lattice via \\(j=0\\) curves, or \\(A_4\\) from quintuple symmetries). The degree-8 polynomial's even symmetry hints at \\(D_4\\) (hyperoctahedral) symmetry, a c\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/0jkjee5nsq74b.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23587298",
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  "id": "0jkjee5nsq74b",
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  "landing_url": "https://zenodo.org/records/23587298",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0jkjee5nsq74b.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:21:47Z",
      "native_id": "23587298",
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      "url": "https://zenodo.org/records/23587298"
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  "subjects": [],
  "title": "Perfect Cuboids and Elliptic Curves: A Degree-8 Polynomial Link — E8 Intelligence Research",
  "title_text": "Perfect Cuboids and Elliptic Curves: A Degree-8 Polynomial Link — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-06T12:21:47Z",
  "url": "https://research.draconitic.com/paper/0jkjee5nsq74b",
  "venue": "Zenodo",
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