{
  "abstract": "We identify a normalization defect in a determinantal construction of fourth-order Hahn difference equations and compare its scalar equation with Foupouagnigni's 1998 elimination and its published 2001 counterpart. On an explicit positive orthogonal family, all five prescribed coefficients vanish: the formula gives \\(0=0\\) and imposes no condition. Along an explicit regular perturbation, division by \\(\\varepsilon^2\\) before specialization recovers a nonzero equation on that family, the same scalar equation as the correctly executed old shift-and-eliminate procedure. On the common nondegenerate domain specified below, both constructions give the same scalar operator up to a nonzero rational factor. The first-order degree bounds follow directly from valid identities of 1998; preserving cancellations gives a bound that can be arbitrarily sharper on explicit admissible inputs, together with exact top coefficients and cancellation criteria. Explicit coefficient formulas do not by themselves yield a new scalar equation on this domain. Our comparison does not exclude corrective or expository contributions; additional computational gain or exceptional coverage must be demonstrated.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20192",
  "author_total": 2,
  "authors": [
    {
      "name": "K. Castillo"
    },
    {
      "name": "G. Gordillo-Núñez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2gb1wg3mj1wss.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20192",
  "fulltext_url": null,
  "id": "2gb1wg3mj1wss",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20192",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2604|Mathematical functions and polynomials"
    ]
  ],
  "openalex": "W7222015450",
  "pdf_url": "https://arxiv.org/pdf/2610.20192",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2gb1wg3mj1wss.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20192",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20192"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Old structures, a vanishing formula",
  "title_text": "Old structures, a vanishing formula",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/2gb1wg3mj1wss",
  "venue": "arXiv",
  "versions": []
}