{
  "abstract": "We construct a symmetric numerical semigroup $Γ$ of multiplicity $56$, embedding dimension $26$, and Frobenius number $181$ such that, over every field $k$, the one-dimensional Gorenstein local domain $R=k[t^Γ]_{\\mathfrak{m}}$ has a nonprincipal ideal $I=(t^{56},t^{70})R$ for which $I\\otimes_R\\operatorname{Hom}_R(I,R)$ is torsion-free. This gives a counterexample to the Huneke-Wiegand conjecture in its general Gorenstein formulation. The proof reduces to an explicit finite sumset identity, interpreted through the Huneke-Iyengar-Wiegand colon criterion and Leamer's tensor-torsion formula. We also identify the tensor product with the trace ideal of $I$, compute $\\operatorname{End}_R(I)=R[t^{101},t^{107}]$ and its conductor, and show that the counterexample persists under completion. A separate graded tensor-graph calculation and exact, standard-library Python verifiers accompany the paper. We explain how the example differs from the field-extension construction of Christensen, Gerko, and Iyengar.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07615",
  "author_total": 1,
  "authors": [
    {
      "name": "Son Pham"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7101bsqrp1yk7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07615",
  "fulltext_url": null,
  "id": "7101bsqrp1yk7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07615",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7211986765",
  "pdf_url": "https://arxiv.org/pdf/2609.07615",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7101bsqrp1yk7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07615",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07615"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Counterexample to the Huneke-Wiegand Conjecture",
  "title_text": "A Counterexample to the Huneke-Wiegand Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/7101bsqrp1yk7",
  "venue": "arXiv",
  "versions": []
}