{
  "abstract": "We determine the intrinsic Fisher geometry of the two-parameter circular wrapped normal family. Although its finite parameters form a cylinder, its metric completion is a disk: adjoining the uniform law extends the Fisher metric to a positive-definite real-analytic metric. The Gaussian curvature vanishes at the added point, is positive nearby, and tends to $-1/2$ as the underlying standard deviation tends to zero. We prove that the curvature has exactly one nonuniform zero radius and exactly one critical radius, the latter a nondegenerate positive maximum. Opposite points sufficiently close to uniformity are joined by a unique minimizing geodesic through the uniform law, so their intrinsic distance is not attained inside the nonuniform family. In contrast, identifying the means of real normal distributions modulo a period retains a complete hyperbolic cylinder with an infinitely distant cusp. Wrapping strictly decreases Fisher information in every nonzero tangent direction, while the information deficit and its fixed-order derivatives are exponentially small as the standard deviation tends to zero. The curvature theorem is proved by convergent series and explicit analytic remainder estimates; numerical figures serve only as illustrations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37985",
  "author_total": 5,
  "authors": [
    {
      "name": "Hyun Chul Jang"
    },
    {
      "name": "Juna Lee"
    },
    {
      "name": "Nathan Negera"
    },
    {
      "name": "Kalea Plotnick"
    },
    {
      "name": "Antony Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cfar0ew6petf8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37985",
  "fulltext_url": null,
  "id": "cfar0ew6petf8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37985",
  "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"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.37985",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cfar0ew6petf8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.37985",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37985"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Fisher Geometry of Circular Wrapped Normals: Completion and Curvature",
  "title_text": "Fisher Geometry of Circular Wrapped Normals: Completion and Curvature",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:00Z",
  "url": "https://research.draconitic.com/paper/cfar0ew6petf8",
  "venue": "arXiv",
  "versions": []
}