{
  "abstract": "The Gál--Koksma lemma is a standard tool for converting quadratic-mean estimates on consecutive blocks into almost-everywhere bounds for partial sums, without assumptions of independence, mixing, or orthogonality. A natural open problem is to determine exactly which universal growth normalizations are forced by this hypothesis alone. The corresponding universal normalization problem under the abstract consecutive-block second-moment hypothesis is resolved by characterizing exactly which non-decreasing normalizations are valid uniformly over the entire admissible class. The resulting necessary-and-sufficient summability criterion is sharp even for bounded exactly centred systems with constant majorants and exact linear block variance, and determines the critical logarithmic and iterated-logarithmic thresholds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18198",
  "author_total": 1,
  "authors": [
    {
      "name": "Ying Wai Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9n72ej1zyd18f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18198",
  "fulltext_url": null,
  "id": "9n72ej1zyd18f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18198",
  "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.NT"
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    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7213530067",
  "pdf_url": "https://arxiv.org/pdf/2609.18198",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9n72ej1zyd18f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18198",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18198"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Exact universal normalizations for the Gál--Koksma lemma",
  "title_text": "Exact universal normalizations for the Gál--Koksma lemma",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/9n72ej1zyd18f",
  "venue": "arXiv",
  "versions": []
}