For every Diophantine pair, the paper constructs a nonzero function with exponential tails and a finite linear dependence among its time-frequency shifts.
An intrinsically subcritical four-point counterexample
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abstract
Building on the vector-Zak and cohomological framework developed by Faulhuber, Petersen, van Velthoven, and Voigtlaender in their twelve-point counterexample, we give a computer-assisted four-point counterexample with a nonzero complex-valued Schwartz window. Every symplectic triangle determinant of the explicit configuration has absolute value below one, placing it in the intrinsically subcritical regime.
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2026 1verdicts
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HRT counterexamples with exponential tails
For every Diophantine pair, the paper constructs a nonzero function with exponential tails and a finite linear dependence among its time-frequency shifts.