{
  "abstract": "We determine the optimal order of the scaling parameter in the metric cotype $2$ inequality for complete Alexandrov spaces of nonnegative curvature. It grows linearly with the dimension $n$ of the discrete torus. This answers Question 17 of Eskenazis, Mendel, and Naor. In their sign-vector normalization on $\\bigl(\\mathbb{Z}/(2m\\mathbb{Z})\\bigr)^n$, the square of the optimal metric cotype $2$ constant for this class lies between $\\max\\{1,n/m\\}$ and $e\\lceil n/m\\rceil$ for every dyadic $m\\geq 2$. The upper bound follows from a dyadic Bernoulli-thinning argument using only the Lang--Schroeder--Sturm inequality. Snowflake universality of the fixed Wasserstein space $\\mathcal{P}_2(\\mathbb{R}^3)$ gives the $n/m$ lower bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08754",
  "author_total": 3,
  "authors": [
    {
      "name": "Qingjin Cheng"
    },
    {
      "name": "Longfa Sun"
    },
    {
      "name": "Yipeng Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2xg9dsym3tvpp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08754",
  "fulltext_url": null,
  "id": "2xg9dsym3tvpp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08754",
  "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.FA"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7212026603",
  "pdf_url": "https://arxiv.org/pdf/2609.08754",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2xg9dsym3tvpp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.08754",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08754"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Optimal Scaling Parameter in Metric Cotype for Alexandrov Spaces of Nonnegative Curvature",
  "title_text": "The Optimal Scaling Parameter in Metric Cotype for Alexandrov Spaces of Nonnegative Curvature",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/2xg9dsym3tvpp",
  "venue": "arXiv",
  "versions": []
}