{
  "abstract": "Every quadratic Hessian slice of a Lorentzian polynomial yields bounded monomial ratios among the normalized coefficients of the polynomial. We determine exactly for which pairs $(n,d)$ these quadratic-slice ratios generate the full bounded-ratio cone for every $M$-convex support $S\\subseteqΔ_n^d$. For $d\\geq 2$, this quadratic local-to-global principle holds universally if and only if \\[ n\\leq 3,\\qquad d=2,\\qquad\\text{or}\\qquad (n,d)=(4,3). \\] In every remaining case, the principle fails already for Lorentzian polynomials with full support: for cubics in $n\\geq 5$ variables and for polynomials of degree $d\\geq 4$ in $n\\geq 4$ variables. We identify the two minimal obstructions, at $(n,d)=(4,4)$ and $(n,d)=(5,3)$, and propagate them throughout the failure region by degree and variable aggregation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07098",
  "author_total": 5,
  "authors": [
    {
      "name": "Dijia Chen"
    },
    {
      "name": "Bowen Gan"
    },
    {
      "name": "Ivy Liu"
    },
    {
      "name": "Zemeng Wang"
    },
    {
      "name": "Chengzhi Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aj3q37h18nrcm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07098",
  "fulltext_url": null,
  "id": "aj3q37h18nrcm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07098",
  "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.CO"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7212020652",
  "pdf_url": "https://arxiv.org/pdf/2609.07098",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aj3q37h18nrcm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.07098",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07098"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Bounded Ratios of Lorentzian Polynomials II: The Complete Quadratic Local-to-Global Classification",
  "title_text": "Bounded Ratios of Lorentzian Polynomials II: The Complete Quadratic Local-to-Global Classification",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/aj3q37h18nrcm",
  "venue": "arXiv",
  "versions": []
}