{
  "abstract": "Let $F$ be a rank-two symmetrizable Nahm sum, with any symmetrizer $\\operatorname{diag}(d_1,d_2)$, a positive-definite rational matrix and rational shifts, and let $K$ be the field generated by its Nahm point; write $m=d_2/d_1$. We prove that if $q^cF$ is modular, then $[K:\\mathbb{Q}]\\le 24$. Modularity forces the higher coefficients of the logarithmic radial asymptotic expansion to vanish; we study the resulting polynomial equations through their Newton polygons and a pole-order analysis along the determinant conic, and for $m=1$ show that their common components occur only on one explicit family, whose Nahm point is rational. For equal row sums, Bloch-group torsion gives $[K:\\mathbb{Q}]\\le 2$. For complementary Nahm coordinates, the bound is $2$ when $m\\ne 1$ and $4$ when $m=1$, using the first two asymptotic corrections in the latter case. Several steps of the proofs rely on exact computation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02743",
  "author_total": 1,
  "authors": [
    {
      "name": "Cetin Hakimoglu-Brown"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/81wy53ctr93yy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02743",
  "fulltext_url": null,
  "id": "81wy53ctr93yy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02743",
  "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": "W7220421901",
  "pdf_url": "https://arxiv.org/pdf/2610.02743",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/81wy53ctr93yy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02743",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02743"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A uniform degree bound for modular rank-two Nahm sums",
  "title_text": "A uniform degree bound for modular rank-two Nahm sums",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/81wy53ctr93yy",
  "venue": "arXiv",
  "versions": []
}