# [Hard-sphere fluctuations on the regular Boltzmann lifespan](paper.pdf)

**Author:** OpenAI

**Date:** September 23, 2026

## Citation

```bibtex
@misc{OAI:Hard-sphere-fluctuations-on-the-regular-Boltzmann-lifespan-September-23-2026,
  author = {{OpenAI}},
  title = {{Hard-sphere fluctuations on the regular Boltzmann lifespan}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Hard-sphere-fluctuations-on-the-regular-Boltzmann-lifespan-September-23-2026/paper.pdf}{OAI:Hard-sphere-fluctuations-on-the-regular-Boltzmann-lifespan-September-23-2026}},
  year = {2026}
}
```