{
  "abstract": "Guo, Fang, and Lu recently proved the Komlós conjecture: for vectors $v_1,\\ldots,v_n\\in\\mathbb R^d$ of Euclidean norm at most one, there are signs $\\varepsilon_j\\in\\{-1,1\\}$ with $\\|\\sum_j\\varepsilon_jv_j\\|_\\infty\\le3\\sqrt{2π}$. We give a short proof of the bound $3π$ that keeps the geometric lifting framework of (Guo, Fang, and Lu 2026a) while replacing the analytic core by a quadratic Dirichlet energy. Moreover, using a more fine-grained analysis of the stability of the product-cosine function of (Smirnov and Vershynin 2026) under translations, we further sharpen the bound to below $6.9013$. On the algorithmic side, based on the polynomial-time construction of (Guo, Fang, and Lu 2026b) we give a deterministic algorithm that finds a coloring of discrepancy at most $37.54$ using at most $\\widetilde O(mn+n^4)$ arithmetic operations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27172",
  "author_total": 2,
  "authors": [
    {
      "name": "Emrullah Akbas"
    },
    {
      "name": "Suvrit Sra"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cgtx25snc8yjh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27172",
  "fulltext_url": null,
  "id": "cgtx25snc8yjh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27172",
  "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.CO"
    ],
    [
      "openalex",
      "2612|Mathematical Approximation and Integration"
    ]
  ],
  "openalex": "W7214231447",
  "pdf_url": "https://arxiv.org/pdf/2609.27172",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cgtx25snc8yjh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.27172",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27172"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Tighter bounds on Komlós discrepancy: existence and algorithmic results",
  "title_text": "Tighter bounds on Komlós discrepancy: existence and algorithmic results",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/cgtx25snc8yjh",
  "venue": "arXiv",
  "versions": []
}