{
  "abstract": "We use tools and techniques from $p$-adic analysis and algebraic number theory to study the algebraicity of the hard square entropy constant and its high dimensional analogues. Specifically, we study arithmetic properties of $a_d(n)$, the number of independent sets in the $d$-dimensional discrete torus, and the associated entropy constants $κ_d=\\lim_{n\\to\\infty}a_d(n)^{1/n^d}$. It is not known whether $κ_d$ is algebraic or transcendental for $d>1$. Using the fact that the sequence $a_d(p^k)$ converges $p$-adically for every prime $p$ and other arithmetic facts, we present a collection of criteria for the algebraicity of $κ_d$ and bound the number of possible values of prime powers $p^k$ for which $a_d(p^k)=κ_d^{p^{kd}}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28332",
  "author_total": 1,
  "authors": [
    {
      "name": "Yotam Svoray"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3b3a26mb2s97x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28332",
  "fulltext_url": null,
  "id": "3b3a26mb2s97x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28332",
  "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.AG"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|advanced mathematical theories"
    ]
  ],
  "openalex": "W7204824553",
  "pdf_url": "https://arxiv.org/pdf/2608.28332",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3b3a26mb2s97x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2608.28332",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28332"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The Algebraicity Problem for Hard-Core Entropy Constants on the Discrete Hypertori",
  "title_text": "The Algebraicity Problem for Hard-Core Entropy Constants on the Discrete Hypertori",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/3b3a26mb2s97x",
  "venue": "arXiv",
  "versions": []
}