{
  "abstract": "We show that full negative regression dependence implies neither negative right-tail dependence nor negative left-tail dependence. A strictly positive distribution on a 2*2*3 rectangular state space provides an exact counterexample for the right-tail case, and its coordinatewise reflection yields a counterexample for the left-tail case. We further prove that this state-space size is minimal. The counterexample is established via a finite upper-set criterion using exact integer arithmetic. We also resolve the open question of whether full negative regression dependence implies negative association. A strictly positive distribution on {0,1,2}^4 satisfies full negative regression dependence yet violates negative association; this counterexample is verified by 17532 exact integer inequalities. The main results of this paper were first uncovered by the multi-agent mathematical system Eureka and later verified by the authors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23313",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuting Su"
    },
    {
      "name": "Taizhong Hu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/79k1dnz7t0wta.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23313",
  "fulltext_url": null,
  "id": "79k1dnz7t0wta",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23313",
  "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.PR"
    ],
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      "openalex",
      "2613|Probability and Statistical Research"
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  "openalex": "W7214004460",
  "pdf_url": "https://arxiv.org/pdf/2609.23313",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/79k1dnz7t0wta.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23313",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23313"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Full negative regression dependence: counterexamples for tail dependence and negative association",
  "title_text": "Full negative regression dependence: counterexamples for tail dependence and negative association",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/79k1dnz7t0wta",
  "venue": "arXiv",
  "versions": []
}