{
  "abstract": "We study the sharp constant in the differential inequality \\[ I(t)I''(t)\\geq c\\,[I'(t)]^2 \\] for Fisher information along the probability-normalized heat flow on $\\mathbb R^2$. The unrestricted log-convexity value $c=1$ is false in two dimensions, whereas the known square-root convexity theorem gives the universal value $c=1/2$. We construct an exact, machine-verifiable sum-of-squares certificate proving the stronger universal bound \\[ c\\geq \\frac{231691}{250000}=0.926764. \\] Together with an independent exact Fourier/Gaussian-envelope construction, this gives \\[ 0.926764\\leq c_*<0.94176665012062, \\] where $c_*$ is the sharp constant for positive-time Gaussian convolutions of arbitrary probability measures on $\\mathbb R^2$. We formulate the proof in explicit two-dimensional index notation. The lower bound follows from an exact rational polynomial identity involving a strictly positive denominator, a weighted total derivative, and eleven positive rational Gram matrices. All $491$ recorded leading principal minors are strictly positive and the complete polynomial identity has zero residual. No symmetry, log-concavity, finite-variance, or finite-entropy assumption is imposed on the initial measure. The sharp value remains open.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20653",
  "author_total": 2,
  "authors": [
    {
      "name": "Fayez Abu-Ajamieh"
    },
    {
      "name": "Xiaoyan Huo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9ee4xrpe6rsbr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20653",
  "fulltext_url": null,
  "id": "9ee4xrpe6rsbr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20653",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7222690846",
  "pdf_url": "https://arxiv.org/pdf/2610.20653",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9ee4xrpe6rsbr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2610.20653",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20653"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "An exact computer-assisted lower bound for Fisher-information convexity along the two-dimensional heat flow",
  "title_text": "An exact computer-assisted lower bound for Fisher-information convexity along the two-dimensional heat flow",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/9ee4xrpe6rsbr",
  "venue": "arXiv",
  "versions": []
}