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Does every lattice of density above one admit a Gabor frame with a nice window? No. For every dimension $d > 1$ there are explicit criteria on lattices $\Lambda \subset \mathbb{R}^{2d}$ with $D(\Lambda) > 1$ such that no function with continuous Zak transform generates a Gabor frame along $\Lambda$, which answers the existence problem negatively for Schwartz-class windows.
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The disclosure separates the two roles: GPT-5.4 was used mainly for mathematical exploration, including exploring whether homology-theoretic methods could give a common-zero criterion for two quasiperiodic functions, while Claude Opus 4.7 assisted with the Lean formalization. The authors verified everything independently. The same group's Cantor Fourier frame paper is also in this catalog.
Provider: OpenAI / Anthropic · Prompt public: unknown · Independence: unknown
A Lean formalization accompanies the paper; we have not compiled it. arXiv preprint, not peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.