AI-Assisted Proof Overturns a 25-Year-Old Conjecture in Signal Processing
A partial digestion of the HRT counterexample
In a surprising turn, researchers have disproved the Heil-Ramanathan-Topiwala (HRT) conjecture, a longstanding open problem in time-frequency analysis. The counterexample, constructed with AI assistance, involves a Schwartz function and 12 distinct time-frequency shifts that satisfy a nontrivial linear relation. The proof combines a vector-valued Zak transform, a contraction mapping argument, and careful numerical verification, pushing the boundary of what was thought possible.
It was thus a nice surprise to see that it has just been resolved by Faulhuber, Petersen, van Velthoven, and Voigtlaender, even in the Schwartz case.