# [A directional zero-one law for finite-range-dependent random environments](directional-zero-one-finite-range.pdf)

**Author:** OpenAI

**Date:** October 5, 2026

## Citation

```bibtex
@misc{OAI:A-directional-zero-one-law-for-finite-range-dependent-random-environments-October-5-2026,
  author = {{OpenAI}},
  title = {{A directional zero--one law for finite-range-dependent random environments}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/A-directional-zero-one-law-for-finite-range-dependent-random-environments-October-5-2026/directional-zero-one-finite-range.pdf}{OAI:A-directional-zero-one-law-for-finite-range-dependent-random-environments-October-5-2026}},
  year = {2026}
}
```