{
  "abstract": "We prove a closed-string remodeling statement for the affine binary dihedral Calabi--Yau orbifold threefold $\\mathcal X=[\\mathbb C^2/Γ]\\times\\mathbb C$, where $Γ$ is a binary dihedral subgroup of $SU(2)$. This target lies outside the toric setting of the Bouchard--Klemm--Mariño--Pasquetti remodeling conjecture: the toric mirror curve is replaced by the type-$D_l$ relativistic Toda curve of Brini--Ma--Strachan, and the Chekhov--Eynard--Orantin topological recursion is replaced by the $\\mathbb Z_2$-equivariant topological recursion of Giacchetto--Kramer--Lewański, run in the sign sector of the Toda-curve involution with the Prym kernel as its two-point input. We identify the equivariant orbifold quantum cohomology Frobenius manifold of $\\mathcal X$ with the invariant Jacobian Frobenius structure of the Toda curve, and we prove that the B-model $R$-matrix, defined by regularized stationary phase, equals the A-side normalized canonical Givental--Teleman $R$-matrix on a chosen simply connected domain; this equality is anchored at the orbifold point through a semistable degeneration of the Toda curve. Comparing the resulting Givental--Teleman and Dunin-Barkowski--Orantin--Shadrin--Spitz graph sums then identifies, after a parity-twisted leaf substitution, the sign-sector recursion with the descendant Gromov--Witten generating functions of $\\mathcal X$ in the stable range ($2g-2+n>0$ with $n>0$), and identifies the recursion free energies with the equivariant Gromov--Witten free energies of $\\mathcal X$ for $g\\geq2$. We also match the genus-one potential defined by the reduced calibrated tau function with the Gromov--Witten potential up to an additive constant.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.07355",
  "author_total": 3,
  "authors": [
    {
      "name": "Bohan Fang"
    },
    {
      "name": "Zhuoming Lan"
    },
    {
      "name": "Jingxiang Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0qpc1stkwmmk2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.07355",
  "fulltext_url": null,
  "id": "0qpc1stkwmmk2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.07355",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7167825349",
  "pdf_url": "https://arxiv.org/pdf/2607.07355",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0qpc1stkwmmk2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2607.07355",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.07355"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Involution-equivariant topological recursion and mirror symmetry for the affine binary dihedral Calabi--Yau threefold",
  "title_text": "Involution-equivariant topological recursion and mirror symmetry for the affine binary dihedral Calabi--Yau threefold",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/0qpc1stkwmmk2",
  "venue": "arXiv",
  "versions": []
}