{
  "abstract": "We introduce spread-out measures, a notion of local non-concentration near pencils for measures on Grassmannians. We establish an optimal $δ$-discretized dual Furstenberg estimate for ``sticky spread-out'' shadings. A simple-to-state corollary is the following. Assume that $ν$ is an Ahlfors $s$-regular measure on $\\mathbb{G}(2,1)$ with $s > 0$. Let $E \\subset \\mathbb{R}^{2}$ be a Borel set with equal Hausdorff and packing dimension. Then, $\\dim_{\\mathrm{H}} Π_{V}(E) = \\min\\{\\dim_{\\mathrm{H}} E,1\\} \\quad \\text{for $ν$-a.e. } V \\in S^1$. The general $δ$-discretized estimate for ``sticky spread out'' configurations here is the starting point for a more general theorem in the companion paper of Cohen, Shmerkin, Wang and Zakharov, where the ``stickiness'' hypothesis is removed. For instance, the assumption of equal Hausdorff and packing dimension in the result stated above will be dispensed with in the companion paper.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13677",
  "author_total": 2,
  "authors": [
    {
      "name": "Tuomas Orponen"
    },
    {
      "name": "Pablo Shmerkin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9wsfc1dpjqcmc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13677",
  "fulltext_url": null,
  "id": "9wsfc1dpjqcmc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13677",
  "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.CA"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7221561869",
  "pdf_url": "https://arxiv.org/pdf/2610.13677",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9wsfc1dpjqcmc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13677",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13677"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Spread-out Furstenberg sets I: the sticky case",
  "title_text": "Spread-out Furstenberg sets I: the sticky case",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/9wsfc1dpjqcmc",
  "venue": "arXiv",
  "versions": []
}