{
  "abstract": "We use geometry to solve a problem in arithmetic relevant for physics. Namely, for any $m$ we find all integer solutions to the equations $\\sum_{i=1}^m x_i^k = \\sum_{i=1}^m y_i^k$, where $k \\in \\{1,2,3\\}$; this seems to be new for $m \\geq 5$. In physics, these are the anomaly cancellation conditions for models with $m$ fermions which can be naturally light and carry small electric charges (a.k.a. millicharged or minicharged particles). The small charges arise by kinetic mixing of the Standard Model $U(1)$ gauge symmetry with an unbroken non-chiral (a.k.a. vector-like) $U(1)$ and the masses are suppressed by a spontaneously-broken chiral $U(1)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26092",
  "author_total": 1,
  "authors": [
    {
      "name": "Ben Gripaios"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7s1weygypagsy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26092",
  "fulltext_url": null,
  "id": "7s1weygypagsy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26092",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "3106|Particle physics theoretical and experimental studies"
    ]
  ],
  "openalex": "W7223069296",
  "pdf_url": "https://arxiv.org/pdf/2610.26092",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7s1weygypagsy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.26092",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26092"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Millicharged particles and the degree-3 Prouhet-Tarry-Escott problem",
  "title_text": "Millicharged particles and the degree-3 Prouhet-Tarry-Escott problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/7s1weygypagsy",
  "venue": "arXiv",
  "versions": []
}