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  "problem_id": "vibemathed:shellsort-tokuda-lower-bound",
  "title": "Worst-Case Complexity of Shellsort with Tokuda's Gap Sequence",
  "canonical_statement": "Shellsort's worst-case running time is unknown for the gap sequences actually used in practice. Encoding a permutation as the polynomial $\\sigma(1)z + \\cdots + \\sigma(n)z^n$ gives a framework for lower bounds, and yields $\\Omega(N^{1.26})$ for Tokuda's 1992 sequence, extending to any strictly decreasing sequence staying within a fixed distance of a rational geometric one.",
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      "occurred_at": "2026-07-10T00:00:00.000Z",
      "title": "arXiv:2607.08997 - Improved lower bounds of the time complexity of shellsort",
      "summary": "a lower bound for Tokuda's sequence; the general Shellsort complexity question stays open",
      "ai_contribution": "ai_assisted",
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      "attempted_at": "2026-07-10T00:00:00.000Z",
      "human_collaborators": [
        "Zhenghan Zang"
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