{
  "abstract": "We investigate the geometric structure of leading-order (LO) nonsinglet DGLAP evolution on the Fisher--Rao manifold of normalized valence distributions, asking whether the QCD-selected trajectory is geodesic and how its departure from geodesic motion is organized. Through the isometric embedding $Φ=2\\sqrt{p}$, the evolution is represented as a curve on a Hilbert sphere of radius two, with its velocity and acceleration determined directly by the DGLAP operator. For a GRV98-based total-valence trajectory over $2\\leq Q^2\\leq 2000~{\\rm GeV}^2$, we find a nonzero but weakly scale-dependent geodesic curvature. An arc-length-weighted principal-component analysis shows that two affine directions capture more than $99.999\\%$ of the trajectory variance. The corresponding affine plane intersects the Fisher sphere in a small circle, whose predicted geodesic curvature closely agrees with that reconstructed from the DGLAP-generated acceleration. An $x$-resolved analysis further reveals that Fisher motion is governed by relative PDF reshaping rather than probability weight alone, with different momentum-fraction regions contributing to motion along the trajectory and its transverse bending. The Mellin representation provides a complementary perspective on the effective dimensional reduction through the collective evolution of the spectral hierarchy. These results establish a quantitative information-geometric characterization of the reference LO DGLAP trajectory and reveal an organized, near-small-circle structure over the finite evolution interval.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27886",
  "author_total": 2,
  "authors": [
    {
      "name": "Wei Kou"
    },
    {
      "name": "Xurong Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e93vsz3d2ptd4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27886",
  "fulltext_url": null,
  "id": "e93vsz3d2ptd4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27886",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-ph"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Quantum Chromodynamics and Particle Interactions"
    ]
  ],
  "openalex": "W7223092458",
  "pdf_url": "https://arxiv.org/pdf/2610.27886",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e93vsz3d2ptd4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.27886",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27886"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "Information Geometry of DGLAP Evolution: From Geodesic Tests to Emergent Small-Circle Geometry",
  "title_text": "Information Geometry of DGLAP Evolution: From Geodesic Tests to Emergent Small-Circle Geometry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:04Z",
  "url": "https://research.draconitic.com/paper/e93vsz3d2ptd4",
  "venue": "arXiv",
  "versions": []
}