VibeMathedMath problems solved by AI

The Existence Problem for Regular Gabor Frames

Does every lattice of density above one admit a Gabor frame with a nice window? No. For every dimension d>1d > 1 there are explicit criteria on lattices Λ⊂R2d\Lambda \subset \mathbb{R}^{2d} with D(Λ)>1D(\Lambda) > 1 such that no function with continuous Zak transform generates a Gabor frame along Λ\Lambda, which answers the existence problem negatively for Schwartz-class windows.

Result
Disproved
Status
Resolved
AI contribution
AI co-developed
Method
Argument
Field
Harmonic analysis
Posed by
time-frequency analysis literature
Year posed
—
Years open
—
Solved
2026-06-24
Model
GPT-5.4, Claude Opus 4.7
Vendor
OpenAI / Anthropic
Collaborators
Jaume de Dios Pont, Lukas Liehr, Mitchell A. Taylor
Verification
Unreviewed
Publication
Preprint
Significance
20 / 100
Disclosed cost
—
Wikipedia
No dedicated article

What the AI did

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.

Verification

A Lean formalization accompanies the paper; we have not compiled it. arXiv preprint, not peer-reviewed.

Sources

arXiv:2606.26052 - On the existence problem of regular Gabor frames

Discussion