{
  "abstract": "Let $f_n:\\{0,1\\}^n\\to\\{0,1\\}$ be Boolean functions, and let $C_n$ count their changes in a unit time interval under stationary dynamics in which each coordinate is independently resampled at rate one from the Bernoulli$(p_n)$ distribution. We prove that, if $f_n$ is transitive and $n\\min\\{p_n,1-p_n\\}^{r}\\to\\infty$ for every $r>0$, then tightness of $(C_n)$ implies $\\mathrm{Var}(f_n)\\to0$. This settles Forsström's conjecture in the $p_n\\le 1/2$ regime and extends it symmetrically to arbitrary biases. The proof uses a mixed jump sum whose second moment is bounded by the generator of a low degree Fourier projection.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09725",
  "author_total": 1,
  "authors": [
    {
      "name": "Xinyu Long"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cxa70563jw7ae.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09725",
  "fulltext_url": null,
  "id": "cxa70563jw7ae",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09725",
  "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.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7220976264",
  "pdf_url": "https://arxiv.org/pdf/2610.09725",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cxa70563jw7ae.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09725",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09725"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Tameness of transitive Boolean functions",
  "title_text": "Tameness of transitive Boolean functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/cxa70563jw7ae",
  "venue": "arXiv",
  "versions": []
}