{
  "abstract": "We study the de Bruijn--Newman family $H_τ(z)$, with heat-deformation parameter $τ$ and $H_0(z)=\\tfrac18,ξ(\\tfrac12+\\tfrac{iz}{2})$. The moving zeros considered here are therefore zeros of $H_τ$, not directly of $ζ(s)$. Retaining the collective interaction term in the zero dynamics, we prove that for a simple nonreal zero $z=x+iy$ of maximal imaginary height, [ \\frac{d}{dτ}y^2\\le -2-4y^2\\mathcal G_τ(z), ] where $\\mathcal G_τ\\ge0$ is a projected interaction sum. A second exact inequality bounds $\\mathcal G_τ$ below by an off-zero logarithmic derivative $-\\operatorname{Im}(H_τ'/H_τ)(x+iη)$, providing a direct interface with the effective Polymath approximation $H_τ=B_τF_τ$. At the frontier $X=6000000185827$, $τ_0=129/800$, and $y_0^2=87677/2500000$, a directed Cauchy certificate gives $\\mathcal G_τ>3/2$ for $τ_0\\leτ\\le0.178$, $x\\ge X$, and $|y|\\le y_0$. Combining this contraction with certified upper and lower zero-free barriers, a two-envelope argument reduces the maximal nonreal height to $0.08$ by time $0.1747532546428610755\\ldots$; the classical de Bruijn contraction then completes the landing. Relative to the publicly replayable but not yet peer-reviewed $0.1787854$ base certificate, this yields the audit-relative bound [ Λ\\le0.1779532546428610755\\ldots . ] The collective contraction, logarithmic-derivative bridge, and new high-$x$ certificates are independent contributions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37164",
  "author_total": 1,
  "authors": [
    {
      "name": "Michel Planat"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4se37q2agfhf5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37164",
  "fulltext_url": null,
  "id": "4se37q2agfhf5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37164",
  "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.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7214984124",
  "pdf_url": "https://arxiv.org/pdf/2609.37164",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4se37q2agfhf5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2609.37164",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37164"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Collective Contraction in the de Bruijn--Newman Heat Flow: Off-Zero Logarithmic Derivatives and Certified Barrier Refinements",
  "title_text": "Collective Contraction in the de Bruijn--Newman Heat Flow: Off-Zero Logarithmic Derivatives and Certified Barrier Refinements",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/4se37q2agfhf5",
  "venue": "arXiv",
  "versions": []
}