{
  "abstract": "We study strictly positive multivariate binary distributions by separating one-body marginals from dependence. Local positive reweighting defines a dependence nucleus, completely characterized by the higher-order Walsh log-linear coefficients $J_S$, $|S|\\ge2$. Any such nucleus and any strictly positive one-body marginals determine a unique joint distribution. In finite-spin Gibbs systems, these coefficients are the many-body interaction couplings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12805",
  "author_total": 1,
  "authors": [
    {
      "name": "Yi-Yu Lin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ar34rdpms006w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12805",
  "fulltext_url": null,
  "id": "ar34rdpms006w",
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  "landing_url": "https://arxiv.org/abs/2610.12805",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "1702|Bayesian Modeling and Causal Inference"
    ]
  ],
  "openalex": "W7221526990",
  "pdf_url": "https://arxiv.org/pdf/2610.12805",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ar34rdpms006w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2610.12805",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12805"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "A Sklar-Type Decomposition for Positive Binary Distributions and a Gibbs Interpretation",
  "title_text": "A Sklar-Type Decomposition for Positive Binary Distributions and a Gibbs Interpretation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/ar34rdpms006w",
  "venue": "arXiv",
  "versions": []
}