{
  "abstract": "We prove that the set of bounded ratios $\\BR(X)$ on a semialgebraic set $X\\subset\\R^n_{>0}$ is the convex cone of linear forms that are nonnegative on the tropicalization $\\trop(X)$. In particular, it is a rational polyhedral convex cone. For $X$ the set of Lorentzian polynomials with fixed M-convex support, it is the dual to the set of M-convex functions. We record an explicit counterexample to a conjecture of Huang--Huh--Soskin--Wang on the bounded ratios on Lorentzian polynomials. The bounded ratio in the counterexample corresponds to the non-hypermetric clique-web facet $\\mathrm{CW}^1_7(1,1,1,1,1,-1,-1)$ of the cut cone on seven vertices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03934",
  "author_total": 2,
  "authors": [
    {
      "name": "Lorenzo Baldi"
    },
    {
      "name": "Mario Kummer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/67sn3t7v6cdry.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03934",
  "fulltext_url": null,
  "id": "67sn3t7v6cdry",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03934",
  "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.AG"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7208782119",
  "pdf_url": "https://arxiv.org/pdf/2609.03934",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/67sn3t7v6cdry.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03934",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03934"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A note on bounded ratios",
  "title_text": "A note on bounded ratios",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/67sn3t7v6cdry",
  "venue": "arXiv",
  "versions": []
}