{
  "abstract": "Let $G_n=\\sum_{k=0}^n4^k\\binom{2n-2k}{n-k}^{2}\\binom{2k}{k}$. Zhi-Hong Sun conjectured that, for primes $p\\equiv3\\pmod4$, positive odd integers $m$, and $r\\ge2$, the two-step congruence $G_{(mp^r-1)/2}\\equiv p^2G_{(mp^{r-2}-1)/2}\\pmod {p^{2r-1}}$ holds. We prove the stronger valuation statement $G_{(p^2M-1)/2}-p^2G_{(M-1)/2}\\in p^{2v_p(M)+3}\\mathbb Z_p$ for every positive odd $M$. The proof converts the sum to a terminating ${}_3F_2$, constructs a cancelled digit-transfer operator, and identifies a two-dimensional analytic quotient of its cubic difference operator. The quotient operator has characteristic polynomial $X^2-p^2$; its second trace is evaluated through the Gross--Koblitz formula and Greene's finite-field Dixon identity. A logarithmic-loss Green inverse converts this spectral identity into an actual integral analytic primitive. The exceptional prime $3$ requires a finite exact PARI/GP certificate, while the infinite tail is bounded symbolically. Thus the computation is finite, reproducible, and separated from the uniform part of the proof.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23355",
  "author_total": 1,
  "authors": [
    {
      "name": "Huimin Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3fvj6nb8wr49g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23355",
  "fulltext_url": null,
  "id": "3fvj6nb8wr49g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23355",
  "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.NT"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7214025501",
  "pdf_url": "https://arxiv.org/pdf/2609.23355",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3fvj6nb8wr49g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23355",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23355"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A two-step supercongruence for an Apéry-like sequence",
  "title_text": "A two-step supercongruence for an Apéry-like sequence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/3fvj6nb8wr49g",
  "venue": "arXiv",
  "versions": []
}