HRT Conjecture
Statement
Heil, Ramanathan and Topiwala conjectured in 1996 that any finite set of time-frequency shifts of a nonzero square-integrable function is linearly independent. This refutes it: there is a Schwartz function admitting 12 linearly dependent time-frequency shifts.
Record
Comments
No person has examined this. Nothing here has been checked at all. say whether it holds →
construction · #1
Markus Faulhuber, Philipp Petersen, Jordy Timo van Velthoven and Felix Voigtlaender, using GPT-5.6 ProThat credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
ChatGPT (GPT-5.6 Pro) developed the counterexample and its proof strategy in dialogue with the authors. They initiated the search, told it to enlarge the phase-space configuration when it stalled, steered it from abstract methods toward elementary ones, and had it turn an existential construction into a fixed finite one. The authors then replaced several of the model's arguments with elementary proofs and closed gaps they call occasionally substantial: the whole of Section 6.2 and Appendix A was originally two sentences.
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