{
  "abstract": "We prove two supercongruence conjectures of Li--Long--Tu concerning truncated very-well-poised ${}_7F_6(1)$ series and Fourier coefficients of modular forms. The proofs are based on a common deformation method. By deforming the original truncated hypergeometric series to suitable terminating series, we are able to apply classical hypergeometric transformations together with Mishev's $W(D_5)$ symmetry. This reduces both problems to congruences for lower-rank hypergeometric sums that can be treated using the $p$-adic methods of Long--Tu--Yui--Zudilin. Although the two cases require different local arithmetic calculations, their global proof structure is the same. The resulting argument gives a unified explanation of these two supercongruences and suggests that the same deformation-and-symmetry method may apply more broadly.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15176",
  "author_total": 1,
  "authors": [
    {
      "name": "Dianbin Bao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/26yesr8anzyzb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15176",
  "fulltext_url": null,
  "id": "26yesr8anzyzb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15176",
  "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.NT"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7221799358",
  "pdf_url": "https://arxiv.org/pdf/2610.15176",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/26yesr8anzyzb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15176",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15176"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Deformation and Symmetry in Two Hypergeometric Supercongruences",
  "title_text": "Deformation and Symmetry in Two Hypergeometric Supercongruences",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/26yesr8anzyzb",
  "venue": "arXiv",
  "versions": []
}