{
  "abstract": "We prove the Colomo-Pronko conjecture for alternating sign matrices with a prescribed square of zeros at a corner, for all matrix sizes and freezing parameters. A known multiple-integral formula for the frozen-corner count yields determinant representations built from fixed polynomial kernels. We relate these kernels to the conjectured determinant through an inverse identity for the commutator of a signed Pascal matrix with reversal. In odd dimension, the comparison uses the one-dimensional nullspace and projection along it to eliminate the central coordinate. Combined with the asymptotic analysis of Colomo and Pronko, our result removes the conjectural assumption from their GUE Tracy-Widom fluctuation theorem for the intersection of the frozen boundary with the main diagonal in uniformly random alternating sign matrices. The finite-dimensional algebraic core of the proof has been formalized in Lean 4.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14351",
  "author_total": 1,
  "authors": [
    {
      "name": "Yinjie Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f0qnk6cwm27m5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14351",
  "fulltext_url": null,
  "id": "f0qnk6cwm27m5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14351",
  "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.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7213293550",
  "pdf_url": "https://arxiv.org/pdf/2609.14351",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f0qnk6cwm27m5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14351",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14351"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The Colomo-Pronko conjecture for frozen-corner alternating sign matrices",
  "title_text": "The Colomo-Pronko conjecture for frozen-corner alternating sign matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/f0qnk6cwm27m5",
  "venue": "arXiv",
  "versions": []
}