# [An exponential two-way deterministic state lower bound for one-way liveness](main.pdf)

**Author:** OpenAI  
**Date:** September 25, 2026

## Citation

```bibtex
@misc{OAI:An-exponential-two-way-deterministic-state-lower-bound-for-one-way-liveness-September-25-2026,
  author = {{OpenAI}},
  title = {{An exponential two-way deterministic state lower bound for one-way liveness}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/An-exponential-two-way-deterministic-state-lower-bound-for-one-way-liveness-September-25-2026/main.pdf}{OAI:An-exponential-two-way-deterministic-state-lower-bound-for-one-way-liveness-September-25-2026}},
  year = {2026}
}
```