Conjecture 3 of the Dynamical Sampling Survey
Aldroubi, Cabrelli, Krishtal and Molter conjectured that for a bounded normal operator and any vector , the normalized orbit is never a frame. It can be: an explicit construction produces a normalized orbit that is a frame.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Frame theory
- Posed by
- Akram Aldroubi, Carlos Cabrelli, Ilya Krishtal, Ursula Molter
- Year posed
- 2026
- Years open
- 0y
- Solved
- 2026-06-18
- Model
- ChatGPT
- Vendor
- OpenAI
- Collaborators
- Ilya A. Krishtal, Gotz E. Pfander
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The paper states the constructions were achieved using ChatGPT, whose assistance was also used in preparing the manuscript. One of the authors is among those who posed the conjecture.
Verification
arXiv preprint; not yet peer-reviewed.
Source
arXiv:2606.20848 - The normalized orbit of a bounded normal operator can be a frame