{
  "abstract": "Let $F_k(G)$ be the $k$-token graph of a finite graph with nonnegative edge weights, and let $A_k$ and $D_k$ be its weighted adjacency and degree matrices. For every $-1\\leq\\vartheta\\leq1$, we prove that $k\\mapstoλ_{\\max}(A_k+\\vartheta D_k)$ is discretely concave. Complement symmetry then makes this sequence nondecreasing up to the middle level. At $\\vartheta=1$ and $\\vartheta=0$, this gives the signless-Laplacian and adjacency spectral-radius monotonicity conjectures of Apte, Parekh, and Sud. The spectral result follows from a finite-time theorem: for every $t\\geq0$, the heat contents $\\binom{n}{k}^{-1}\\mathbf{1}^{*}e^{t(A_k+\\vartheta D_k)}\\mathbf{1}$ are log-concave in $k$. We encode all token levels in one Lorentzian polynomial. A four-variable operator symbol proves preservation by each edge heat gate, and the Lie-Trotter formula passes this preservation to the full semigroup. Large-time growth rates recover the top eigenvalues. The same construction also yields Lorentzian polynomials from top spectral projections. Finally, we show that the local symbol certifies exactly the parameter range $[-1,1]$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25037",
  "author_total": 1,
  "authors": [
    {
      "name": "Weiqi Jiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1rjr1j8v3t8p6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25037",
  "fulltext_url": null,
  "id": "1rjr1j8v3t8p6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25037",
  "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.CO"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7214072560",
  "pdf_url": "https://arxiv.org/pdf/2609.25037",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1rjr1j8v3t8p6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:39Z",
      "native_id": "2609.25037",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25037"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Discrete Concavity of Token-Graph Spectral Radii via Lorentzian Semigroups",
  "title_text": "Discrete Concavity of Token-Graph Spectral Radii via Lorentzian Semigroups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/1rjr1j8v3t8p6",
  "venue": "arXiv",
  "versions": []
}