{
  "abstract": "Let $X$ be a random vector in $\\mathbb{F}_2^m$, and let $X'$ be an independent copy. We prove that, for every $\\varepsilon>0$, there is a subspace $G$ with $\\dim G\\le 2^{320(1+\\varepsilon)/\\varepsilon}H(X)$ such that $H(q_GX)\\le(1+\\varepsilon)(H(q_GX+q_GX')-H(q_GX))$. In particular, the quotient entropy is at most $(1+\\varepsilon)(H(X+X')-H(X))$. The coefficient is independent of the ambient dimension, and its exponential order in $1/\\varepsilon$ is necessary. The structural result is a logarithmic rigidity estimate for finite weighted families of laws with averaged subspace entropy sparsity. A common variational quotient controls both a family and its convolution family without decreasing the original family's normalized mean entropy defect. Posterior families preserve averaged sparsity, and a fresh-index argument combines a local-to-global estimate with the entropic Marton theorem to increase the defect ratio at a fixed multiplicative sparsity cost. We also obtain two-input almost-additivity and concentration of moderate-doubling sets on subspace cosets at the same exponential scale. The constants are not optimized.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38525",
  "author_total": 1,
  "authors": [
    {
      "name": "Josiah Park"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1f00pc70145g8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38525",
  "fulltext_url": null,
  "id": "1f00pc70145g8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38525",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38525",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1f00pc70145g8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38525",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38525"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Dimension-free exponential entropy quotients over $\\mathbb{F}_2$",
  "title_text": "Dimension-free exponential entropy quotients over 𝔽_2",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/1f00pc70145g8",
  "venue": "arXiv",
  "versions": []
}