{
  "abstract": "Let $Q_{p,q}(t)\\in\\mathbb{Z}[t]$ be Sharipov's even monic degree-$10$ second cuboid polynomial, with coprime positive integers $p\\ne q$. We prove that $Q_{p,q}(t)$ is irreducible over $\\mathbb{Q}$, and hence over $\\mathbb{Z}$. More generally, the normalized associated quintic $P_s(x)$ and its composition $P_s(t^2)$ are irreducible over $\\mathbb{Q}$ for every $s\\in\\mathbb{Q}\\setminus\\{0,\\pm1\\}$. The proof reduces linear and quadratic factors to rational points and horizontal conjugate pairs on one fixed genus-$2$ curve. A certified rank upper bound for its Jacobian, together with an exact divisor calculation, gives a rank-one annihilating differential at the prime $3$. For the quadratic-factor case, the symmetric coordinates of a horizontal pair lie on an explicit double cover of an elliptic quartic. All rational affine points on this model are $3$-adically integral and reduce to six smooth residue classes. The pulled-back differential is a unit in each class, proving that six displayed points form the complete list. Their coordinates exclude every admissible parameter. A negative real root of the irreducible quintic then supplies the additional degree argument required for irreducibility of the degree-$10$ polynomial. The rank computation and all exact arithmetic certificates are specified explicitly for reproduction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25319",
  "author_total": 1,
  "authors": [
    {
      "name": "Valery Asiryan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/482ys7yz2er6d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25319",
  "fulltext_url": null,
  "id": "482ys7yz2er6d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25319",
  "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.GM"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7223001411",
  "pdf_url": "https://arxiv.org/pdf/2610.25319",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/482ys7yz2er6d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25319",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25319"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Algebraic Geometry and Number Theory",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Irreducibility of the Cuboid Polynomial $Q_{p,q}(t)$ via the Rank-One Chabauty-Coleman Method",
  "title_text": "Irreducibility of the Cuboid Polynomial Q_p,q(t) via the Rank-One Chabauty-Coleman Method",
  "type": "preprint",
  "updated_at": "2026-11-05T15:21:00Z",
  "url": "https://research.draconitic.com/paper/482ys7yz2er6d",
  "venue": "arXiv",
  "versions": []
}