{
  "abstract": "The Donoho--Stark uncertainty principle asserts $N^d\\le|E|\\,|Σ|$, and the additive energy uncertainty principle of Aldahleh--Iosevich--Iosevich--Jaimangal--Mayeli--Pack refines it to $1\\le|E|\\cdot\\|1_Σ\\|_{U^2}^{4/3}$. It has been conjectured that the natural higher-order analogue \\[ 1\\le |E|\\cdot\\|1_Σ\\|_{U^k}^{2^k/(k+1)} \\] holds for every $k\\ge 2$, the coset case giving equality. We show that this fails for every $k\\ge 6$. The counterexample is the two-point signal $f=δ_0-δ_1$ on $\\mathbb{Z}_3$, for which the left-hand quantity equals $2/3(2(k+1))^{1/(k+1)}$; this is $<1$ precisely when $k\\ge 6$, and tends to $2/3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06531",
  "author_total": 1,
  "authors": [
    {
      "name": "Iana Vranesko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/19esb64gynqda.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06531",
  "fulltext_url": null,
  "id": "19esb64gynqda",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06531",
  "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|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7212076138",
  "pdf_url": "https://arxiv.org/pdf/2609.06531",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/19esb64gynqda.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06531",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06531"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A counterexample to the Gowers $U^k$ uncertainty conjecture for $k\\ge 6$",
  "title_text": "A counterexample to the Gowers U^k uncertainty conjecture for k≥ 6",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/19esb64gynqda",
  "venue": "arXiv",
  "versions": []
}