{
  "abstract": "We obtain the $L^3$ reverse square function estimate for the light cone in four dimensions from the critical local-smoothing and round-cone propagation statements in the September 2026 OpenAI manuscript. We state these inputs, together with the plate maximal theorem of Di Plinio and Parissis, in a preliminaries section. The proof passes from geometric concentration of packet coefficients to regularity of the analyzed wave, and then from free waves to arbitrary functions supported near the cone. As a consequence, we obtain the corresponding $L^3$ estimate for the sphere and elliptic paraboloids in three dimensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12681",
  "author_total": 1,
  "authors": [
    {
      "name": "Faruk Temur"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/60k1shn52fehb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12681",
  "fulltext_url": null,
  "id": "60k1shn52fehb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12681",
  "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"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7221576730",
  "pdf_url": "https://arxiv.org/pdf/2610.12681",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/60k1shn52fehb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.12681",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12681"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The square function estimate for the cone in four dimensions",
  "title_text": "The square function estimate for the cone in four dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/60k1shn52fehb",
  "venue": "arXiv",
  "versions": []
}