{
  "abstract": "We prove three results as part of the program of diameter-free estimates initiated in [CDW26]. The first two are reverse square function estimates for the light cone in $\\mathbb{R}^3$. We first establish an abstract $L^4$ inequality of independent interest, under an ordered superorthogonality hypothesis: for every four distinct indices, only the two nonalternating pairings are required to vanish. The loss is $C(1+\\log N)^2$, where $N$ is the number of functions. An alternating-determinant argument verifies this hypothesis for separated cone sectors. This gives a diameter-free estimate for arbitrary disjoint angular intervals, at the thickness determined by their smallest width, with no upper restriction on the radial parameter. For the canonical equal-width partition on a fixed radial annulus, we obtain the loss $C(1+\\log N)^{1/4}$, which is sharp up to constants. This refines the estimate by Guth-Wang-Zhang, via a different approach. The improvement uses additional orthogonality between diagonal and off-diagonal differences, together with bounded overlap of dyadic difference shells. Our third result is the diameter-free $\\ell^2L^6$ decoupling for arbitrary partitions of the parabola, with an $N^\\varepsilon$ loss independent of the interval widths. The argument is an adaptation of the method from \\cite{Cushman-Demeter-Wu} and implies their three-fold additive-energy estimate for the parabola. The three proofs use variants of interlacing and special orthogonality in place of wave packet analysis, multilinearity and parabolic/Lorentz rescaling. Together, these results provide further evidence for the scope of the paradigm introduced in [CDW26].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13105",
  "author_total": 3,
  "authors": [
    {
      "name": "Adam Cushman"
    },
    {
      "name": "Ciprian Demeter"
    },
    {
      "name": "Shukun Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5c84vf0msf0v1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13105",
  "fulltext_url": null,
  "id": "5c84vf0msf0v1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13105",
  "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.CA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7213067130",
  "pdf_url": "https://arxiv.org/pdf/2609.13105",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5c84vf0msf0v1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.13105",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13105"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Diameter-free reverse inequalities and superorthogonality",
  "title_text": "Diameter-free reverse inequalities and superorthogonality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/5c84vf0msf0v1",
  "venue": "arXiv",
  "versions": []
}