{
  "abstract": "We prove that four cosines with distinct positive integer frequencies have the same sign on at least $1/33$ of a period, with equality precisely for positive integer dilates of $\\{1,3,11,33\\}$. If both odd and even frequencies occur, the optimal proportion is $1/24$; equality holds precisely for odd positive integer dilates of $\\{1,3,4,12\\}$ and $\\{2,4,5,15\\}$. For arbitrary $n$, we establish the universal lower bound $4^{1-n}$ and construct frequency sets for which this proportion is at most $16n^\\theta4^{-n}$, where $θ=\\log_2(3/2)$. These bounds determine the optimal exponential decay rate $1/4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33190",
  "author_total": 4,
  "authors": [
    {
      "name": "Shengyang Zang"
    },
    {
      "name": "Yingyu Zhao"
    },
    {
      "name": "Yunhao Zhao"
    },
    {
      "name": "Chen Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/88krtq0f5grj5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33190",
  "fulltext_url": null,
  "id": "88krtq0f5grj5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33190",
  "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",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7223865085",
  "pdf_url": "https://arxiv.org/pdf/2610.33190",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/88krtq0f5grj5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33190",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33190"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Extremal cosine sign correlations",
  "title_text": "Extremal cosine sign correlations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/88krtq0f5grj5",
  "venue": "arXiv",
  "versions": []
}