HRT counterexamples with exponential tails

John Jasper, Dustin G. Mixon

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.

Disclosure

“Acknowledgments JJ was supported in part by NSF DMS 2220320. DGM was supported by NSF DMS 2220304. DGM thanks OpenAI for complimentary access to ChatGPT-5.6 Pro. The authors first used ChatGPT to help digest the proof of the breakthrough result in [4], and then to explore possible extensions of that result, to examine various proof strategies, and to give feedback on writing. All mathematical claims were checked by the authors,”
PDF page 12

Classification: Proof ideas or individual proof-step assistance
Multiplier: 8
Verified: 2026-08-23T05:14:20.493771Z

Structural counts

Pages 12 pdf

Theorems 2 source

Lemmas 5 source

Propositions 1 source

Corollaries 0 source

Definitions 0 source

Displayed equations 75 source

Bibliography entries 9 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file hrt_exp.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.