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  "problem_id": "vibemathed:online-discrepancy-linear-time",
  "title": "Optimal Online Discrepancy in Linear Time",
  "canonical_statement": "Given online vectors $v_t \\in \\mathbb{R}^d$ with $\\|v_t\\|_2 \\le 1$, can signs $\\varepsilon_t \\in \\{-1, 1\\}$ be chosen in $O(dT)$ total time so that every prefix has $\\ell_\\infty$ discrepancy $O(\\sqrt{\\log T})$ with high probability? The previous optimal algorithm ran in time exponential in $T$ and $d$.",
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      "status": "resolved",
      "occurred_at": "2026-07-06T00:00:00.000Z",
      "title": "arXiv:2607.04388 - Optimal online discrepancy minimization in linear time",
      "summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
      "ai_contribution": "ai_discovered",
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      "provider": "OpenAI",
      "attempted_at": "2026-07-06T00:00:00.000Z",
      "human_collaborators": [
        "Ishaq Aden-Ali"
      ],
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      "prompt_public": null,
      "outcome": "The algorithm and main proof were discovered in a GPT-5.5 Pro Extended conversation prompted by the author; every prefix sum is written as a sum of three coupled Gaussian vectors.",
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}