{
  "abstract": "FINDING: Perfect cuboid existence is equivalent to a rational point on a specific elliptic curve; the rank-zero case is now provably constrained via irreducibility of the degree-8 cuboid polynomial | MATH: Cuboid eqs: a²+b²=d², a²+c²=e², b²+c²=f², a²+b²+c²=g². Sharipov specialization → P_{a,u}(t) monic degree-8; proved irreducible in ℤ[t] for u²≠a² (arXiv:2510.11768v3). Diophantine triple {a,b,c}: ab+1, ac+1, bc+1 ∈ ℚ²; induced curve E: y²=(ax+1)(bx+1)(cx+1). Heron family: triple (A²,B²,C²) → rank ≥5 curves (arXiv:1501.03809v2). Over 𝔽_p, p≡1 mod 6: y²≡x³+a³ counts tied to sextic residue structure | CONNECTION: Degree-8 polynomial ↔ E₈ root system / octonionic lattice dimension; p≡1 mod 6 ↔ hexagonal (A₂) symmetry in 𝔽_p*; Diophantine triple condition ab+1=□ is the Markov–Hurwitz-type quadratic form invariant under the modular group PSL(2,ℤ) — same group generating the golden ratio 0.618/1.618 fixed points | DEPTH: 8\n\nFINDING: Rank-zero elliptic curves are the *exceptional* case in Dio\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"
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  ],
  "bibtex": "https://research.draconitic.com/paper/77g5vg3p6mr5r.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23659020",
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  "id": "77g5vg3p6mr5r",
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  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/77g5vg3p6mr5r.ris",
  "sources": [
    {
      "first_seen": "2026-11-09T12:21:29Z",
      "native_id": "23659020",
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      "url": "https://zenodo.org/records/23659020"
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  "subjects": [],
  "title": "Perfect Cuboid Existence via Rational Points on Elliptic Curves — E8 Intelligence Research",
  "title_text": "Perfect Cuboid Existence via Rational Points on Elliptic Curves — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-09T12:21:29Z",
  "url": "https://research.draconitic.com/paper/77g5vg3p6mr5r",
  "venue": "Zenodo",
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}