{
  "abstract": "We study how two geometries of mass on a finite graph interact: the information geometry of the generalized entropy $F_q$ used for regularized transport, and the arithmetic of divisors governed by the Riemann--Roch theorem of Baker and Norine and by the Jacobian. Because the correction term of $F_q$ is affine, $F_q$-regularization at strength $γ$ is Tsallis regularization at temperature $γ/q$. Over the reals, chip-firing connects all configurations of equal degree, so the Jacobian enters transport only through integrality. We introduce the transport defect, the worst-case cost of steering $d$ chips towards a target by chip-firing, and prove $1/d\\leδ_{\\TV}(D)\\le(d-r(D))/d=(g-1-r(K-D))/d\\le\\min(1,g/d)$ whenever $g\\ge1$; vertex multiplicities give a lower bound and an equality criterion. A regularized topological gap $Γ_{q,γ}(D,E)$ tends to the chip-move defect as $γ\\to0$, lies in an explicit window, has a high-temperature slope given by Tsallis coupling entropies, and admits a positive regime if and only if $g\\ge1$. Dual potentials certify exactly the convex relaxation of a linear system; the remainder is an integrality gap. Zeros in optimal plans occur only for $q>1$, by a mechanism different from the sign change of $Γ$. Exact computations on $1784$ divisor classes find the rank bound $(d-r(D))/d$ attained in $1769$ of them, an observed frequency. Experiments on honeycomb and Erdős--Rényi networks with $10^2$ to $10^5$ nodes test the statements on regularized plans, not $Γ$; over $10^3\\le n\\le10^5$ their transport costs are consistent with growth like $n^{1/2}$ and $\\log n$, respectively.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.09968",
  "author_total": 1,
  "authors": [
    {
      "name": "Shintaro Yoshizawa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fxfyyvhmms7pf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.09968",
  "fulltext_url": null,
  "id": "fxfyyvhmms7pf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.09968",
  "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",
      "cond-mat.soft"
    ],
    [
      "arxiv",
      "cs.DM"
    ],
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.09968",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fxfyyvhmms7pf.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:23Z",
      "native_id": "2611.09968",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.09968"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.soft",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Topology and Information in Regularized Transport on Graphs",
  "title_text": "Topology and Information in Regularized Transport on Graphs",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:33Z",
  "url": "https://research.draconitic.com/paper/fxfyyvhmms7pf",
  "venue": "arXiv",
  "versions": []
}