{
  "abstract": "We give a two-term Weyl asymptotic for the Steklov spectrum of a solid regular tetrahedron. Its linear coefficient is the total edge length times an explicit, absolutely convergent dihedral invariant. A trace-class difference of massive Neumann-to-Dirichlet operators computes the full invariant, including the continuous spectrum. The main analytic step is a fixed-time cumulative trace comparison between the compact tetrahedron and its exact half-space or dihedral models. Localized Hilbert-Schmidt defects have vanishing high-energy tails; retaining the time factor in Duhamel's formula makes this sufficient for an $o(L)$ cumulative error. A separate trace-class face comparison fixes the model's infinite exterior primitive and permits one observation time independent of the inner collar width. Compact-band Mourre estimates and a harmonic comparison establish immediate reflection/transmission support for incident face waves. Triangular unfolding gives null periodic and dead-end sets for the maximal branching relation. Actual edge-window bounds, adapted conical annuli and an ordered-limit Fourier-Tauberian argument then prove the sharp remainder. The proof treats guided and continuum channels together in the edge trace and requires neither a guided metric graph nor a lower-departure estimate uniform at zero tangential momentum.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02733",
  "author_total": 1,
  "authors": [
    {
      "name": "Josiah Park"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bv9kbmq9yta60.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02733",
  "fulltext_url": null,
  "id": "bv9kbmq9yta60",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02733",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.SP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02733",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bv9kbmq9yta60.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02733",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02733"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Edge spectral invariants and second-order Steklov asymptotics for the regular tetrahedron",
  "title_text": "Edge spectral invariants and second-order Steklov asymptotics for the regular tetrahedron",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/bv9kbmq9yta60",
  "venue": "arXiv",
  "versions": []
}