{
  "abstract": "We generalise Yin's motivic integration with section to the Hensel-minimal framework, with and without volume forms, building on Stout and Vermeulen's work on a Hrushovski-Kazhdan style motivic integral for $1$-h-minimal valued fields. In particular, we get a bijective motivic integral \\emph{à la} Hrushovski-Kazhdan between certain Grothendieck groups of definable sets on the valued field and the coarse Grothendieck groups on $\\mathrm{RV}$ in the Denef-Pas language, with angular component. In the second half of the article, we build a Cluckers-Loeser-like framework and show that our constructions indeed give back Cluckers-Loeser motivic integral. Thus Cluckers-Loeser motivic integration derives from an isomorphism of Hrushovski-Kazhdan motivic integration, but in the Denef-Pas language with a section of $\\mathrm{RV}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08417",
  "author_total": 1,
  "authors": [
    {
      "name": "Xavier Pigé"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2gw4hb37tyay7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08417",
  "fulltext_url": null,
  "id": "2gw4hb37tyay7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08417",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7212036662",
  "pdf_url": "https://arxiv.org/pdf/2609.08417",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2gw4hb37tyay7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08417",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08417"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Kontsevich-Zagier conjecture for Hensel-minimal fields with sections",
  "title_text": "Kontsevich-Zagier conjecture for Hensel-minimal fields with sections",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/2gw4hb37tyay7",
  "venue": "arXiv",
  "versions": []
}