{
  "abstract": "Local-basis Shannon entropies of critical wave functions contain universal subleading information, but the Shannon point of the critical transverse-field Ising chain is singular in the conventional Rényi approach. We treat it directly at $n=1$ by representing the complete computational-basis Born distribution as the odd-degree boundary of independent long-range Bernoulli edges. The Shannon chain rule separates the entropy into explicit independent-edge and conditional cycle-space terms. For the periodic chain this isolates the analytic edge anomaly and organizes the remaining constant by linked vertex support. Conditional on the stated finite-part matching and forest assumptions, every nonvanishing linked coefficient is represented by an explicit finite-dimensional integral, giving an all-orders analytic hierarchy; the four-vertex term is evaluated in closed form, and the first few linked sectors already nearly saturate the established periodic constant, which is also reconstructed independently from the exact finite-size distribution. For an interval, the exterior reduces exactly to one ghost vertex and the explicit squared logarithms cancel, leaving the analytic edge contribution $γ_E=\\log2/4-1/16$. The conditional cycle term has an exact all-support decomposition into physical-line and ghost-linked sectors; conditional on closure of the boundary forest subtraction, these sectors define an all-orders hierarchy of renormalized line and monomer--dimer boundary periods for the remaining logarithmic coefficient. The first complete augmented linked coefficient is evaluated in closed form, with an exact cancellation between its line and ghost boundary-layer anomalies; an independent reconstruction from exact finite-size probabilities recovers the established coefficient $γ_1=0.060020(3)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08591",
  "author_total": 1,
  "authors": [
    {
      "name": "M. A. Rajabpour"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ac1b7evxb9c33.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08591",
  "fulltext_url": null,
  "id": "ac1b7evxb9c33",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08591",
  "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.stat-mech"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7220893667",
  "pdf_url": "https://arxiv.org/pdf/2610.08591",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ac1b7evxb9c33.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2610.08591",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08591"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Analytical results for the Shannon entropy of the critical transverse-field Ising chain",
  "title_text": "Analytical results for the Shannon entropy of the critical transverse-field Ising chain",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/ac1b7evxb9c33",
  "venue": "arXiv",
  "versions": []
}