# [Nonuniqueness for the periodic hard-sphere Boltzmann equation](paper.pdf)

**Author:** OpenAI

**Date:** September 23, 2026

## Citation

```bibtex
@misc{OAI:Nonuniqueness-for-the-periodic-hard-sphere-Boltzmann-equation-September-23-2026,
  author = {{OpenAI}},
  title = {{Nonuniqueness for the periodic hard-sphere Boltzmann equation}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Nonuniqueness-for-the-periodic-hard-sphere-Boltzmann-equation-September-23-2026/paper.pdf}{OAI:Nonuniqueness-for-the-periodic-hard-sphere-Boltzmann-equation-September-23-2026}},
  year = {2026}
}
```