{
  "abstract": "Our main result is a $3\\sqrt{2π}$ bound for the Komlós signing problem: every finite family of real vectors of Euclidean norm at most one admits a signed sum of $\\ell_\\infty$-norm less than this constant, independently of the dimension and the family size. For any $κ\\ge0$, if a bounded open convex set supports a probability density with directional total variation at most $κ$ in every unit direction, then its open-set Banaszczyk transform supports another such density with the same $κ$, provided the translation vector $v$ satisfies $κ\\|v\\|_2\\le1/3$. As a consequence, every finite set system in which each element belongs to at most $t$ sets, where $t\\ge1$ is an integer, admits a two-coloring whose imbalance in each set is less than $3\\sqrt{2πt}$. This gives the square-root dependence predicted by the Beck-Fiala conjecture. The proof was discovered by the Odin Automatic AI Research Agent.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Biostatistics , Harvard T.H. Chan School of Public Health"
  ],
  "article_type": null,
  "arxiv": "2609.11189",
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Shengtao Guo",
      "orcid": "0000-0002-3404-1738"
    },
    {
      "affs": [
        0
      ],
      "name": "Ethan X. Fang",
      "orcid": "0000-0003-3762-9155"
    },
    {
      "affs": [
        0
      ],
      "name": "Junwei Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6y03s5pm63t99.bib",
  "cited_by": 14,
  "doi": "10.48550/arxiv.2609.11189",
  "fulltext_url": null,
  "id": "6y03s5pm63t99",
  "issns": [
    "2331-8422"
  ],
  "landing_url": "https://arxiv.org/abs/2609.11189",
  "language": "en",
  "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.CO"
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      "arxiv",
      "math.FA"
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      "openalex",
      "2607|Limits and Structures in Graph Theory"
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  "openalex": "W7212286109",
  "pdf_url": "https://arxiv.org/pdf/2609.11189",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": "Cornell University",
  "ris": "https://research.draconitic.com/paper/6y03s5pm63t99.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11189",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11189"
    },
    {
      "first_seen": "2026-11-07T13:20:41Z",
      "native_id": "W7212286109",
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      "url": "https://arxiv.org/abs/2609.11189"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Vector Balancing via Directional Total Variation",
  "title_text": "Vector Balancing via Directional Total Variation",
  "type": "preprint",
  "updated_at": "2026-11-08T13:20:36Z",
  "url": "https://research.draconitic.com/paper/6y03s5pm63t99",
  "venue": "arXiv",
  "versions": []
}