{
  "abstract": "This paper addresses the structural breakdown of the Edgeworth expansion in the finite-blocklength (FBL) regime, where conventional asymptotic approximations yield unphysical negative probabilities in the deep-tail region. We propose a $q$-deformed framework that resolves this inconsistency by replacing additive polynomial perturbations with a geometric deformation of the information density space. Motivated by the linearization of nonlinear dynamics, we prove that dynamically scaling the $q$-logarithmic parameter exactly absorbs the third-order skewness while preserving global nonnegativity. We establish a universal asymptotic matching, demonstrating that the framework encapsulates higher-order asymptotic scales. Numerical results confirm that the proposed method matches the state-of-the-art precision of the Cornish-Fisher bound without the risk of negative probabilities. The framework offers a robust and computationally stable foundation for evaluating operational limits in ultra-reliable communications such as 6G and URLLC.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.23303",
  "author_total": 1,
  "authors": [
    {
      "name": "Hiroki Suyari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1kna48h1fb24h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.23303",
  "fulltext_url": null,
  "id": "1kna48h1fb24h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.23303",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
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      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "3109|Statistical Mechanics and Entropy"
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  "openalex": "W7204174071",
  "pdf_url": "https://arxiv.org/pdf/2608.23303",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1kna48h1fb24h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.23303",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.23303"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Breakdown of Edgeworth Expansion in Finite-Blocklength Regime and Exact Absorption via $q$-Deformation",
  "title_text": "Breakdown of Edgeworth Expansion in Finite-Blocklength Regime and Exact Absorption via q-Deformation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/1kna48h1fb24h",
  "venue": "arXiv",
  "versions": []
}