{
  "abstract": "In the paper, we establish congruences for twisted Dirac indices and signatures on closed string manifolds by specializing the two-parameter modular forms of Liu and Wang to the tangent bundle. Fourier coefficient comparisons yield uniform congruences modulo $3$ in dimensions $4k$, $1\\leq k\\leq7$. Suitable parameter choices give explicit formulas involving only genuine twisting bundles in dimensions $8,12,16,20,24,$ and $28$, and recover the comparisons of Chen and Han in dimension $24$. The level-one Witten genus further strengthens selected Dirac congruences to moduli $729,27,27,$ and $9$ in dimensions $16,20,24,$ and $28$, respectively. The proofs use Fourier expansions in reduced $K$-theory and integer identities obtained by clearing powers of two from the denominators before reduction modulo $3$. We also construct non-string spin counterexamples in each of the six listed dimensions and identify the additional coefficient that obstructs extending the uniform argument to dimension $32$ without further information.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21959",
  "author_total": 2,
  "authors": [
    {
      "name": "Tong Wu"
    },
    {
      "name": "Yong Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1smt5kj95k70x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21959",
  "fulltext_url": null,
  "id": "1smt5kj95k70x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21959",
  "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.DG"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7222752594",
  "pdf_url": "https://arxiv.org/pdf/2610.21959",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1smt5kj95k70x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21959",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21959"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Mod 3 Congruence Families for twisted signatures of string manifolds in dimensions up to twenty-eight",
  "title_text": "Mod 3 Congruence Families for twisted signatures of string manifolds in dimensions up to twenty-eight",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/1smt5kj95k70x",
  "venue": "arXiv",
  "versions": []
}