{
  "abstract": "Let $(A_{ij}(x))_{1 \\leq i \\leq N, 1 \\leq j \\leq M}$ be a matrix of univariate semialgebraic functions. We study the solvability of the system of linear inequalities \\begin{equation*} \\sum_{j=1}^M A_{ij}(x)F_j(x)\\leq f_i(x) \\ \\ \\text{ for } i = 1, \\ldots, N, \\end{equation*} where we assume each forcing $f_i$ is a Nash function. We show that the $C^m$ solvability of the system can be characterized by finitely many linear ordinary differential inequalities in $f$ with semialgebraic coefficients depending only on $(A_{ij})$. When the system is solvable, the solution may be chosen semialgebraic, and the proof gives a constructive procedure in the semialgebraic sense. We also study the semimodule structure of admissible forcings, establishing finite generation and lack thereof in various settings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22772",
  "author_total": 2,
  "authors": [
    {
      "name": "Fushuai Jiang"
    },
    {
      "name": "Garving K. Luli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fbamah3fxfny3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22772",
  "fulltext_url": null,
  "id": "fbamah3fxfny3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22772",
  "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.AG"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "1703|Polynomial and algebraic computation"
    ]
  ],
  "openalex": "W7222953341",
  "pdf_url": "https://arxiv.org/pdf/2610.22772",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fbamah3fxfny3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.22772",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22772"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Semialgebraic ${C^m}$ solutions to a univariate system of linear inequalities with Nash forcing",
  "title_text": "Semialgebraic C^m solutions to a univariate system of linear inequalities with Nash forcing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/fbamah3fxfny3",
  "venue": "arXiv",
  "versions": []
}