{
  "abstract": "We study the energy minimization problem for eight points on the unit sphere. For the logarithmic and Coulomb energies, we show that the unique global minimizer up to congruence is a square antiprism with height characterized by a unique stationarity equation. The proof is computer-assisted and fully verified in Lean. After this, we consider generalizations of the result to other important energies. For the Riesz $s$-energies, we provide a Lean-verified, non-computer-assisted proof that the square antiprism with height depending on $s$ is the unique global minimizer for all sufficiently large $s$, and a computer-assisted proof that this in fact holds for all $s\\geq 0$. We also give examples of energies arising from completely monotonic potentials for which the square antiprism is not a global minimizer, answering in the negative a universality question of Cohn and Woo.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22077",
  "author_total": 3,
  "authors": [
    {
      "name": "Liudmyla Kryvonos"
    },
    {
      "name": "Lukas Liehr"
    },
    {
      "name": "Mitchell A. Taylor"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4a87xx7007ck9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22077",
  "fulltext_url": null,
  "id": "4a87xx7007ck9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22077",
  "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.MG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.22077",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4a87xx7007ck9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.22077",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22077"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Energy minimization for eight points on the sphere",
  "title_text": "Energy minimization for eight points on the sphere",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/4a87xx7007ck9",
  "venue": "arXiv",
  "versions": []
}