{
  "abstract": "This paper develops the dynamical part of the Onsager-Cheeger scale-graph framework introduced in Scale Graphs I. The first paper established the finite-graph algebra: nonnegative edgewise Onsager production, Prigogine square completion, and an exact minimum-production Lyapunov identity under decimation. Here the algebra is coupled to dissipative scale dynamics on a global attractor. Under shellwise parabolic damping, controlled forcing tails, finite-window Onsager scale graphs, and a Cheeger alternative, we prove a conditional two-channel tail-control theorem. In coercive windows, the Prigogine defect budget controls chemical-potential oscillation through weighted Poincare and discrete BMO estimates; in bottleneck windows, Onsager positivity suppresses flux across a small Cheeger cut. Both channels feed a square-root-influx versus linear-damping tail inequality. The comparison estimate is stated in its sharp safe form. From dE/dt ≤ b√E + F − γE one obtains a comparison in √E. Consequently the robust energy estimate inherits an e^(−γt/2) factor at the square-root level; this is the estimate used throughout the paper. The numerical part is a theorem-level audit of the mechanisms in the proof. The accompanying Figshare dataset contains the frozen reproduction dossier v6.2; its master command regenerates every paper-facing numerical table from the shipped object. The paper-facing numerical outputs are: a regenerated Branch-B bottleneck certificate; an E1 terminal-band balance audit; an E2 stationary K⁴-plateau dichotomy, which is the main numerical diagnostic; a source-canonical Branch-A weighted-gap regrade; and an E3a direct-BMO diagnostic on regenerated canonical mu-fields. The claim levels are explicit in the manuscript and in the dataset certificate. This gives a reproducible numerical audit of the scale-graph mechanisms while keeping the mathematical theorem conditional on the stated hypotheses. Numerical dataset (frozen dossier v6.2): https://doi.org/10.6084/m9.figshare.33001511Paper I of the series: https://doi.org/10.6084/m9.figshare.32942279",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Andrea Caffagni"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cgjsha9ds17ys.bib",
  "cited_by": 6,
  "doi": "10.6084/m9.figshare.33002558",
  "fulltext_url": null,
  "id": "cgjsha9ds17ys",
  "issns": [],
  "landing_url": "https://doi.org/10.6084/m9.figshare.33002558",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7168661342",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-16",
  "publisher": "Figshare (United Kingdom)",
  "ris": "https://research.draconitic.com/paper/cgjsha9ds17ys.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:17Z",
      "native_id": "W7168661342",
      "source": "openalex",
      "url": "https://doi.org/10.6084/m9.figshare.33002558"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Mathematical Dynamics and Fractals",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Scale Graphs II: Cheeger Dichotomy, (t,s)-Transport, and Tail Drainage",
  "title_text": "Scale Graphs II: Cheeger Dichotomy, (t,s)-Transport, and Tail Drainage",
  "type": "preprint",
  "updated_at": "2026-11-06T13:20:22Z",
  "url": "https://research.draconitic.com/paper/cgjsha9ds17ys",
  "venue": "Figshare",
  "versions": []
}