{
  "abstract": "How nonlinear gluon saturation erases the memory of initial conditions is a central question in high-energy QCD. We develop the Fisher-Rao information geometry of saturation fronts in the Balitsky-Kovchegov (BK) equation and its Fisher-KPP diffusive limit. Using the normalized coordinate-space front density $p = \\partial N/\\partial\\ln r^2$, we isolate the transverse metric $g^\\perp_{θθ}$ that quantifies shape distinguishability once longitudinal propagation along the flow is factored out. Nonlinear saturation arrests diffusive broadening and freezes the Fisher speed. Transverse deformations exhibit a universal $t^{-4}$ relaxation in the Fisher-KPP asymptotic analysis, with full BK evolution providing numerical evidence for the corresponding $τ^{-4}$ behavior. We trace this steep power law to a relaxation mechanism: deforming the initial profile is equivalent, to leading order, to a spatial translation combined with an effective time delay of the universal relaxation flow. Extracting the translation and the delay from neighboring runs alone predicts the ratio of $g^\\perp_{θθ}$ to its shift-control value within $1\\%$ for Fisher-KPP and for BK up to $τ= 15$. For Fisher-KPP, the asymptotic front expansion yields the $t^{-4}$ law conditionally on stated analytic hypotheses, with a universal amplitude $C_*$ that agrees with numerical extrapolations to sub-percent accuracy. For BK, the asymptotic translation information exceeds its diffusive approximation by a factor of 3.5, which we attribute to the non-diffusive Levin-Tuchin saturation region. These results provide an information-geometric characterization of the approach to geometric scaling, consistent with the persistent sensitivity of pre-asymptotic HERA fits to initial shape parameters, and motivate systematic studies of parameter sensitivity in EIC kinematics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02459",
  "author_total": 1,
  "authors": [
    {
      "name": "Edoardo Spezzano"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/efmtkva5hh3pd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02459",
  "fulltext_url": null,
  "id": "efmtkva5hh3pd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02459",
  "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",
      "hep-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02459",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/efmtkva5hh3pd.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.02459",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02459"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "Fisher-Rao Geometry of Gluon Saturation Fronts",
  "title_text": "Fisher-Rao Geometry of Gluon Saturation Fronts",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:58Z",
  "url": "https://research.draconitic.com/paper/efmtkva5hh3pd",
  "venue": "arXiv",
  "versions": []
}