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The acknowledgement credits the model with providing the initial framework of the proof of Lemma 2, which the author then verified, refined and wrote up.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Problem detail · source-aware
Worst-Case Complexity of Shellsort with Tokuda's Gap Sequence
VibeMathed reports this item as partial. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise 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.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
What AI did
Verification boundary
Single-author arXiv preprint; not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
Timeline
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arXiv:2607.08997 - Improved lower bounds of the time complexity of shellsort
a lower bound for Tokuda's sequence; the general Shellsort complexity question stays open
Known method families
argument (source-reported)
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
- VibeMath has not independently verified the mathematical claim.
- AI-attempt independence and training-data exposure are unknown unless explicitly documented.
- VibeMath has not independently audited the mathematical statement, proof, or novelty claim.