{
  "abstract": "Let $P_t=\\exp(t\\D^2/2)$ be the heat semigroup. For every integer $k\\geq2$ and parameter $ρ\\in\\C$, we construct an entire function $Γ_{ρ,k}$ whose heat evolution has the prescribed moving zero $x=ρt^k$ and constant spatial flux there: \\[ (P_tΓ_{ρ,k})(ρt^k)=0, \\qquad \\partial_x(P_tΓ_{ρ,k})(ρt^k)=1. \\] The initial function is explicit, \\[ Γ_{ρ,k}(x) =x\\sum_{q\\geq0}\\frac{(-2^kρx^{2k-1})^q}{q!} \\frac{(kq)!}{((2k-1)q+1)!}, \\] and is a generalized hypergeometric function whose entire-function order is strictly below two. Most importantly, it is annihilated by an explicit polynomial-coefficient differential operator of order $2k-1$. Thus every monomial moving boundary admits a finite-order stationary realization after a natural boundary-flux selection, even though the naive order-$k$ family $\\D^k+a x^{k-1}$ already fails to produce the exact boundary at $k=4$. No minimality claim is made: the result gives a universal finite-order hierarchy, while the least possible differential order remains open and depends on the choice made inside the inverse kernel.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27326",
  "author_total": 1,
  "authors": [
    {
      "name": "Gerardo Hernandez-del-Valle"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0d1xqy58qgkx0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27326",
  "fulltext_url": null,
  "id": "0d1xqy58qgkx0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27326",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Meromorphic and Entire Functions"
    ]
  ],
  "openalex": "W7223147423",
  "pdf_url": "https://arxiv.org/pdf/2610.27326",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0d1xqy58qgkx0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27326",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27326"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Monomial Moving Zeros for the Heat Semigroup: An Explicit Finite-Order Differential Hierarchy",
  "title_text": "Monomial Moving Zeros for the Heat Semigroup: An Explicit Finite-Order Differential Hierarchy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/0d1xqy58qgkx0",
  "venue": "arXiv",
  "versions": []
}