{
  "abstract": "Filtering by spatial convolution underlies coarse-graining and Large Eddy Simulation, the analysis of multiscale dynamics, and data processing across the sciences. Yet, as commonly practiced on the sphere, it violates a basic consistency requirement: commutation with differential operators, which is necessary for deriving coarse-grained dynamics and preserving the physics across lengthscales. We discuss the root of the problem, which is intrinsic to the curved geometry rather than being a result of metric terms, coordinate system, or numerical grid. A recently proposed generalized spherical convolution is, for a given scalar kernel, the unique linear operator commuting with the radial projection, divergence, and curl. Any consistent linear operator, be it spectral truncation, wavelet transform, diffusion, Green's-function inversion, or a machine-learned convolution, necessarily takes this form. From a simulation of an unstable jet, we demonstrate commutation to within numerical round-off, whereas common filtering that ignores curvature produces significant spurious divergence where none exists and gradient errors comparable to the gradients themselves.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26896",
  "author_total": 2,
  "authors": [
    {
      "name": "Chayut Teeraratkul"
    },
    {
      "name": "Hussein Aluie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0x72gkgj0cram.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26896",
  "fulltext_url": null,
  "id": "0x72gkgj0cram",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26896",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "physics.ao-ph"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "arxiv",
      "physics.plasm-ph"
    ],
    [
      "openalex",
      "2206|Fluid Dynamics and Turbulent Flows"
    ]
  ],
  "openalex": "W7223085194",
  "pdf_url": "https://arxiv.org/pdf/2610.26896",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0x72gkgj0cram.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.26896",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26896"
    }
  ],
  "subjects": [
    {
      "field": "earth",
      "origin": "arxiv:physics.ao-ph",
      "subfield": "atmospheric"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.plasm-ph",
      "subfield": "plasma"
    }
  ],
  "title": "Commutative Coarse-graining on the Sphere",
  "title_text": "Commutative Coarse-graining on the Sphere",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/0x72gkgj0cram",
  "venue": "arXiv",
  "versions": []
}