{
  "abstract": "We completely solve Colombo's 1928 determinant problem. For distinct real $x_1,\\ldots,x_N$, $N\\geq 2$, and an integer $D\\geq 1$, we prove that $\\det[(x_j-x_i)^D]\\neq 0$ if and only if $D\\geq N-1$ and either $N$ is even or $D$ is even. The even-exponent case follows from Dyn--Goodman--Micchelli (1986); the remaining odd case is proved by a strict Pfaffian sign theorem. The new odd-exponent theorem and its complete proof chain have also been formalized in Lean 4.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00101",
  "author_total": 1,
  "authors": [
    {
      "name": "Qianli Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7m8cfh638eq5c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00101",
  "fulltext_url": null,
  "id": "7m8cfh638eq5c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00101",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.00101",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7m8cfh638eq5c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00101",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00101"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Colombo's Determinant Problem",
  "title_text": "Colombo's Determinant Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/7m8cfh638eq5c",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.5281/zenodo.22028832",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}