{
  "abstract": "For every quartic Salem number $β$, we prove that the equal-weight Bernoulli convolution $ν_{β^{-1}}$ has Hausdorff dimension strictly less than one. The main step converts large Fourier coefficients at geometrically separated frequencies into a deficit in the Shannon entropy of a finite convolution. A positive trigonometric product gives the entropy estimate, while the algebraic norm controls the number of distinct atoms in each spatial cell. For the two quartic Salem numbers in $(1,2)$, reciprocal differences at suitable return times produce the required Fourier coefficients. A finite block cover then gives the dimension bound. This proof is independent of numerical computation. Separate exact calculations give $\\dimHν_{β_1^{-1}}<1-1.4\\cdot10^{-23}$ and $\\dimHν_{β_2^{-1}}<1-7.8\\cdot10^{-22}$, where $β_1<β_2$ are the two parameters in $(1,2)$. The accompanying verification programs use rational interval arithmetic and the Python standard library.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12072",
  "author_total": 4,
  "authors": [
    {
      "name": "Guozheng Cheng"
    },
    {
      "name": "Xiang Fang"
    },
    {
      "name": "Xueqing Ma"
    },
    {
      "name": "Hongli Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9x6dhkkr6a2b4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12072",
  "fulltext_url": null,
  "id": "9x6dhkkr6a2b4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12072",
  "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",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7221150816",
  "pdf_url": "https://arxiv.org/pdf/2610.12072",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9x6dhkkr6a2b4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.12072",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12072"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Strict Hausdorff-dimension drop for Quartic Salem Bernoulli convolutions",
  "title_text": "Strict Hausdorff-dimension drop for Quartic Salem Bernoulli convolutions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/9x6dhkkr6a2b4",
  "venue": "arXiv",
  "versions": []
}