{
  "abstract": "Ice I admits cubic, hexagonal, and mixed layer stackings, but rigorous comparisons of its proton configurational entropy have focused on the two ideal endmembers. We identify every cyclic uniform-registry ice-I stacking with a word in a nonnegative layer-transfer operator and its transpose. Applying the Schatten-Hölder inequality to every even-length word proves that alternating hexagonal stacking maximizes the ice-rule configuration count at each common finite cross-section. Consequently, hexagonal ice maximizes the thermodynamic configuration constant among all periodic uniform-registry ice-I polytypes. We also construct rigorous lower and upper bounds without finite-size extrapolation. Restricting Nagle's positive even-subgraph expansion to disjoint blocks gives the lower bound; Finner's hypergraph Hölder inequality and rational Collatz-Wielandt certificates for two-replica prism operators give the upper bounds. The resulting configuration constant $w$, whose logarithm is the entropy per molecule in units of Boltzmann's constant, satisfies $1.503360 \\le w \\le 1.540196$, with the sharper cubic-ice ceiling $w \\le 1.527699$. The same bracket controls lower and upper configuration growth rates of fixed aperiodic stackings along the specified prism-tileable exhaustions. These results establish hexagonal stacking as a possibly nonunique maximizer; equality of the cubic and hexagonal entropy constants remains unresolved.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.07613",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhengyue Chen"
    },
    {
      "name": "Sheng Ran"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/es6jp8ajdmhpk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.07613",
  "fulltext_url": null,
  "id": "es6jp8ajdmhpk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.07613",
  "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"
    ],
    [
      "openalex",
      "2610|advanced mathematical theories"
    ]
  ],
  "openalex": "W7202187756",
  "pdf_url": "https://arxiv.org/pdf/2608.07613",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/es6jp8ajdmhpk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2608.07613",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.07613"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Hexagonal Stacking Maximizes Proton Configurational Entropy among Ice-I Polytypes",
  "title_text": "Hexagonal Stacking Maximizes Proton Configurational Entropy among Ice-I Polytypes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/es6jp8ajdmhpk",
  "venue": "arXiv",
  "versions": []
}