{
  "abstract": "We study the new eigenvalues of a fixed point interaction on the cubic three-torus. Their mean-one consecutive spacings converge to a probability law independent of the interaction parameter. We characterize this law by the consecutive zeros of a random meromorphic function built from three-squares congruence densities. Its small-gap distribution has the form $s^5Ψ(\\log_2(s^{-2}))+o(s^5)$, where $Ψ$ is continuous, positive, and one-periodic. The proof combines periodic mean-square approximation, a weighted Hilbert-transform estimate, and Fourier estimates that retain the interactions between primes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10031",
  "author_total": 1,
  "authors": [
    {
      "name": "Christopher Lutsko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/da4q3x48n63rq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10031",
  "fulltext_url": null,
  "id": "da4q3x48n63rq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10031",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7220897569",
  "pdf_url": "https://arxiv.org/pdf/2610.10031",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/da4q3x48n63rq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:37Z",
      "native_id": "2610.10031",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10031"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Spacing statistics for a point scatterer on the cubic three-torus",
  "title_text": "Spacing statistics for a point scatterer on the cubic three-torus",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/da4q3x48n63rq",
  "venue": "arXiv",
  "versions": []
}