{
  "abstract": "For each sufficiently large $N$, we construct smooth solutions of the magnetohydrostatic equations on embedded solid tori whose regular pressure levels are nested tori, whose magnetic field vanishes exactly on a round magnetic axis, and whose group of Euclidean symmetries, even when isometries reversing the sign of the field are admitted, is exactly the cyclic group $C_N$ of rotations through multiples of $2π/N$. For each such $N$, these equilibria form a smooth one-parameter family which is locally nontrivial in the moduli space of embedded configurations and have none of the plane-reflection, axial, or helical symmetries conjectured by Grad. A Lean 4 certification of the above results is also provided.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24739",
  "author_total": 3,
  "authors": [
    {
      "name": "Javier Gómez-Serrano"
    },
    {
      "name": "Lukas Liehr"
    },
    {
      "name": "Mitchell A. Taylor"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9rsctmv0sq1kr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24739",
  "fulltext_url": null,
  "id": "9rsctmv0sq1kr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24739",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2604|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7214015310",
  "pdf_url": "https://arxiv.org/pdf/2609.24739",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9rsctmv0sq1kr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.24739",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24739"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Counterexamples to Grad's conjecture",
  "title_text": "Counterexamples to Grad's conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/9rsctmv0sq1kr",
  "venue": "arXiv",
  "versions": []
}