{
  "abstract": "Iima and Yoshino asked for an ideal $I$ in $S=k[x_1,x_2,\\ldots]$, with $\\operatorname{deg} x_i=i$, and a monomial order such that $S/I\\cong k[x_i:i\\equiv\\pm1\\pmod5], \\operatorname{in}(I)=(x_i^2,x_ix_{i+1}:i\\geq1).$ We construct such an ideal and monomial order over every field $k$ of characteristic different from $5$ containing an element $c$ with $c^2+c=1$. The ideal has an explicit infinite homogeneous reduced Gröbner basis. A five-periodic syzygy derived from a pentagon identity proves that all basis relations belong to $I$ and supplies standard representations for the non-coprime critical pairs. Triangular elimination establishes the graded quotient isomorphism. Together, the quotient and initial ideal descriptions yield the partition form of the first Rogers-Ramanujan identity. In each weighted degree, a perfect matching in the support of the normal-form matrix gives a bijection between the two partition classes. We formalize the complex specialization in Lean 4 using Mathlib and our set-based theory of infinite Gröbner bases, including the reduced basis, the graded quotient isomorphism, and the partition-matching theorem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06477",
  "author_total": 4,
  "authors": [
    {
      "name": "Junyu Guo"
    },
    {
      "name": "Hao Shen"
    },
    {
      "name": "Junqi Liu"
    },
    {
      "name": "Lihong Zhi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0ha95tzr1hg05.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06477",
  "fulltext_url": null,
  "id": "0ha95tzr1hg05",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06477",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7212032790",
  "pdf_url": "https://arxiv.org/pdf/2609.06477",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0ha95tzr1hg05.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06477",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06477"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Solution to Iima--Yoshino Problem 2.3",
  "title_text": "A Solution to Iima--Yoshino Problem 2.3",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/0ha95tzr1hg05",
  "venue": "arXiv",
  "versions": []
}