{
  "abstract": "We give algebraic proofs of two conjectural relations between quantum $A$-periods and thermodynamic Bethe ansatz (TBA)-like equations for quantum mirror curves. The quadratic relation follows from constant terms of shifted product expansions. For higher-degree relations, a cyclic quantum-torus trace and a finite matrix determinant identify the period with the free energy of nonoverlapping rods. Their density equation yields the TBA-like equation, with normalization fixed by the rod length. Both proofs hold as formal power series in the complex structure parameter, with exact dependence on $q=e^{i\\hbar}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09922",
  "author_total": 1,
  "authors": [
    {
      "name": "Min-xin Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7y10dby5skg8c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09922",
  "fulltext_url": null,
  "id": "7y10dby5skg8c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09922",
  "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",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7220959838",
  "pdf_url": "https://arxiv.org/pdf/2610.09922",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7y10dby5skg8c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:37Z",
      "native_id": "2610.09922",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09922"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Algebraic Proofs of Quantum Period--TBA Relations",
  "title_text": "Algebraic Proofs of Quantum Period--TBA Relations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:37Z",
  "url": "https://research.draconitic.com/paper/7y10dby5skg8c",
  "venue": "arXiv",
  "versions": []
}