{
  "abstract": "A regular observed statistical model may converge to a limit in which a previously identifiable signed parameter becomes identifiable only modulo a reflection. We study the local information geometry of this transition. For a twice differentiable Hellinger embedding with an exact limiting reflection, the observed displacement is forced into the two-jet form \\(\\varepsilonλJ_-+λ^2J_+/2\\), up to higher-order terms. The mixed jet restores the sign away from the symmetric face, whereas the even jet is the first tangent inherited by the quotient. After nuisance elimination, a positive Gram determinant yields a nondegenerate cross-cap two-jet. The associated local asymptotic theory has three regimes governed by \\(τ_n=\\sqrt n\\,\\varepsilon_n^2\\): regular signed LAN, a critical curved Gaussian subexperiment, and a quotient regime with the \\(n^{-1/4}\\) signed scale. We prove that the same parabolic critical experiment persists for predictive likelihoods along a single stationary dependent trajectory. The limiting quotient has a regular Fisher metric in the invariant coordinate, while its pullback degenerates in the signed coordinate. For a solvable CIR--OU benchmark motivated by coherent sea-clutter observations, we derive the quotient Fisher metric and curvature explicitly and show that the curvature is strictly negative. We also determine the restricted holonomy of the full Amari family: \\(\\operatorname{Hol}_0(\\nabla^{(a)})=SO(2)\\) for \\(a=0\\), whereas \\(\\operatorname{Hol}_0(\\nabla^{(a)})=GL^+(2,\\mathbb R)\\) for \\(a\\neq0\\). The results separate the intrinsic geometry of the limiting quotient from the transverse geometry of its weak unfolding.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29260",
  "author_total": 2,
  "authors": [
    {
      "name": "Arnaud Coatanhay"
    },
    {
      "name": "Angélique Drémeau"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/27yy5kjrvgdd1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29260",
  "fulltext_url": null,
  "id": "27yy5kjrvgdd1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29260",
  "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",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7214287221",
  "pdf_url": "https://arxiv.org/pdf/2609.29260",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/27yy5kjrvgdd1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.29260",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29260"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Information geometry of emergent symmetry quotients and their weak unfoldings",
  "title_text": "Information geometry of emergent symmetry quotients and their weak unfoldings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:03Z",
  "url": "https://research.draconitic.com/paper/27yy5kjrvgdd1",
  "venue": "arXiv",
  "versions": []
}