{
  "abstract": "For $n\\geq2$, two expectation equations identify the mean together with the $n$th central moment. How many coordinates must a report have if a one-observation loss uniquely elicits it and the report determines that moment? We prove that $n$ coordinates are necessary and sufficient among all identifiable intermediaries. The result holds on every open convex set of positive distributions on any $n+1$ distinct real outcomes. It requires no regularity of the loss, report map, identification function, or link. Thus $\\operatorname{elic}_{\\mathcal I}(μ_n)=n$ while $\\operatorname{iden}(μ_n)\\leq2$, giving an unbounded gap between identifiable elicitation and indirect identification. This resolves the central-moment conjecture of Frongillo and Kash on the stated domains. The proof constructs a $C^1$ manifold of supporting coefficients from the affine fibers of a convex negative Bayes risk. Translations along that manifold force an $n$-dimensional tangent space. Standardized moments of order at least three have the same exact complexity. The bound also extends to convex distribution classes with a full-dimensional raw-moment image.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24009",
  "author_total": 1,
  "authors": [
    {
      "name": "Jingyi Jia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1a3x98reycs62.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24009",
  "fulltext_url": null,
  "id": "1a3x98reycs62",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24009",
  "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.PR"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1803|Game Theory and Applications"
    ]
  ],
  "openalex": "W7223052359",
  "pdf_url": "https://arxiv.org/pdf/2610.24009",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1a3x98reycs62.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24009",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24009"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "An Unbounded Gap Between Identification and Identifiable Elicitation: Central Moments",
  "title_text": "An Unbounded Gap Between Identification and Identifiable Elicitation: Central Moments",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:54Z",
  "url": "https://research.draconitic.com/paper/1a3x98reycs62",
  "venue": "arXiv",
  "versions": []
}