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arXiv · 2608.13539

HRT counterexamples with exponential tails

John Jasper·Dustin G. Mixon
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Abstract

We build on the recent breakthrough of Faulhuber, Petersen, van Velthoven, and Voigtlaender that disproved the HRT conjecture with a Schwartz function and a $12$-point configuration. We give a human-readable treatment of their mechanism and find HRT counterexample functions with exponential (or faster) decay. By a result of Bownik and Speegle, this is the fastest possible decay for an HRT counterexample, up to a logarithmic factor in the exponent.

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John Jasper, Dustin G. Mixon. 2026-08-13. HRT counterexamples with exponential tails. https://arxiv.org/abs/2608.13539

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