{
  "abstract": "The Generalized Fermat Equation (Beal’s Conjecture) asserts that the Diophantine relation A^x + B^y = C^z with integer exponents x, y, z \\ge 3 admits no positive integer solutions satisfying \\gcd(A, B, C) = 1. In classical Diophantine geometry, resolution of this conjecture has been obstructed by three structural barriers: (i) the Higher-Rank Modularity Wall (g \\ge 2), where deformation rings fail to be complete intersections; (ii) the Ineffective Height Barrier of Faltings' Theorem and the Darmon–Granville orbifold framework; and (iii) the Frictionless Continuum Fiction of first-order axiomatic set theory (\\mathsf{ZFC}), which treats modular curves as ungrounded continua lacking thermodynamic and metric backpressure on cusp degenerations (\\underline{\\operatorname{Cost}} \\equiv 0, \\rho_{\\text{info}} \\equiv \\infty). Consequently, the existence of coprime solutions resides on the Conjectural Horizon of \\mathsf{ZFC} with an operational truth-value of Null.\n\nTo resolve the conjecture without category errors, we reconstruct the modular geometry of the attached Frey curve E_{A,B,C} within the enriched process category \\mathbf{CostCat} over the Lawvere metric quantale \\mathcal{V}_{\\text{cost}} = ([0, \\infty], \\ge, +, 0)",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "August Tudor"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/852955svjf8em.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23546758",
  "fulltext_url": null,
  "id": "852955svjf8em",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23546758",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/852955svjf8em.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T12:20:54Z",
      "native_id": "23546758",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23546758"
    }
  ],
  "subjects": [],
  "title": "An Adèlic Height Obstruction to Coprime Solutions of the Generalized Fermat Equation: Process-Enriched Modularity, Cusp Dilations, and the Frictionless Barrier",
  "title_text": "An Adèlic Height Obstruction to Coprime Solutions of the Generalized Fermat Equation: Process-Enriched Modularity, Cusp Dilations, and the Frictionless Barrier",
  "type": "preprint",
  "updated_at": "2026-11-04T12:20:54Z",
  "url": "https://research.draconitic.com/paper/852955svjf8em",
  "venue": "Zenodo",
  "versions": []
}