{
  "abstract": "FINDING: The Frey curve construction — a semistable elliptic curve with discriminant linked to a hypothetical Fermat counterexample — is the pivotal bridge forcing the contradiction between modularity and level lowering, completing the FLT proof. | MATH: Frey curve: \\( E_{a,b,c}: y^2 = x(x-a^p)(x+b^p) \\) for \\( a^p + b^p = c^p \\), \\( p \\ge 5 \\) prime. Discriminant \\( \\Delta = (abc)^{2p} \\cdot 16 \\) (up to sign), conductor \\( N = \\text{rad}(abc) \\) (squarefree — semistable). Ribet's level lowering: if \\( E \\) is modular of level \\( N \\), then a newform of level \\( 2 \\) exists (since \\( p \\mid \\Delta \\) with \\( p \\ge 5 \\) and \\( p \\nmid N \\)), but no elliptic curves over \\( \\mathbb{Q} \\) have conductor \\( 2 \\) (or any level \\( < 11 \\)). Modularity (Taniyama–Shimura–Weil, proved by Wiles–Taylor–Breuil–Conrad–Diamond–Taylor): every semistable elliptic curve over \\( \\mathbb{Q} \\) is modular. Contradiction: \\( E \\) cannot exist → FLT true. | CONNECTION: The Frey curve's \\( j \\)-invariant: \\(\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
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  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
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        0
      ],
      "name": "Andrew Stewart Caldin"
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  "bibtex": "https://research.draconitic.com/paper/4ht5jj97be8wm.bib",
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  "doi": "10.5281/zenodo.23447118",
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  "id": "4ht5jj97be8wm",
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  "landing_url": "https://zenodo.org/records/23447118",
  "language": "eng",
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  "published": "2026-10-18",
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  "ris": "https://research.draconitic.com/paper/4ht5jj97be8wm.ris",
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      "first_seen": "2026-11-01T12:21:47Z",
      "native_id": "23447118",
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  "title": "The Frey Curve: The Bridge Between Fermat's Last Theorem and Modularity — E8 Intelligence Research",
  "title_text": "The Frey Curve: The Bridge Between Fermat's Last Theorem and Modularity — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:47Z",
  "url": "https://research.draconitic.com/paper/4ht5jj97be8wm",
  "venue": "Zenodo",
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