{
  "abstract": "For an ordered ideal triangulation of a knot exterior in $S^3$, we give a cochain construction relating its face matrix $C$ to its preferred-longitude gluing matrices $A,B$. The obstruction to uniqueness is the first cohomology of the ideal compactification. Its vanishing yields nullity doubling and the FAMED matrix identity, including a constrained formulation for singular face matrices. A separate rank argument under a strict angle structure supplies a proposed proof of Wong's generalized FAMED conjecture. Over the integers, the construction gives a direct-sum decomposition of $\\ker_{\\mathbb{Z}}B$ and an exact sequence from the two face cokernels to the gluing cokernel, with quotient $\\mathbb{Z}/2\\mathbb{Z}$. In the unhalved longitude convention this implies $|\\det B|=2|\\det C|^2$. We also obtain cyclic face torsion, order-reversal invariance of Smith normal form, and affine face coordinates for fixed lifted gluing systems. The determinant-one assertion and the full Andersen--Kashaev volume conjecture remain open here.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04103",
  "author_total": 1,
  "authors": [
    {
      "name": "Sai Kambampati"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dratares1rz20.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04103",
  "fulltext_url": null,
  "id": "dratares1rz20",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04103",
  "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.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7220690364",
  "pdf_url": "https://arxiv.org/pdf/2610.04103",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dratares1rz20.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04103",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04103"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Integral face-edge duality for knot triangulations",
  "title_text": "Integral face-edge duality for knot triangulations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/dratares1rz20",
  "venue": "arXiv",
  "versions": []
}