{
  "abstract": "FINDING: Frey's curve construction shows a FLT counterexample (a^p + b^p = c^p) would yield a semistable elliptic curve with discriminant a perfect p-th power, violating the Taniyama-Shimura (modularity) theorem — the core of Wiles' proof. | MATH: Frey curve: y² = x(x - a^p)(x + b^p); discriminant Δ = (abc)^(2p) / 2^8 (up to sign and 2-adic factors); conductor N is squarefree (semistable) with specific primes; Ribet's level-lowering: if modular of level N, then modular of level 2 — impossible for p ≥ 3 due to weight-2 cusp form dimension zero at level 2. Key constants: p ≥ 3 prime; the curve has multiplicative reduction at primes dividing abc; j-invariant = 2^8 (a^(2p) + b^(2p) + ... )^3 / (abc)^(2p) — denominator is a perfect p-th power. | CONNECTION: The discriminant's exponent 2p and the conductor's squarefree nature force a rigid arithmetic structure; the modular form's weight 2 and level 2 relate to the elliptic point of order 2 in the modular curve X₀(2) — a lattice symmetry (the\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/65g3zhhqy3mze.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23464938",
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  "id": "65g3zhhqy3mze",
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  "landing_url": "https://zenodo.org/records/23464938",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/65g3zhhqy3mze.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:50Z",
      "native_id": "23464938",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23464938"
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  ],
  "subjects": [],
  "title": "Frey's Curve: Linking FLT Counterexamples to Modularity Violations — E8 Intelligence Research",
  "title_text": "Frey's Curve: Linking FLT Counterexamples to Modularity Violations — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-02T12:21:50Z",
  "url": "https://research.draconitic.com/paper/65g3zhhqy3mze",
  "venue": "Zenodo",
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}