# [Counterexamples to the duality conjecture for metric entropy](main.pdf)

**Author:** OpenAI

**Date:** September 24, 2026

## Citation

```bibtex
@misc{OAI:Counterexamples-to-the-duality-conjecture-for-metric-entropy-September-24-2026,
  author = {{OpenAI}},
  title = {{Counterexamples to the duality conjecture for metric entropy}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Counterexamples-to-the-duality-conjecture-for-metric-entropy-September-24-2026/main.pdf}{OAI:Counterexamples-to-the-duality-conjecture-for-metric-entropy-September-24-2026}},
  year = {2026}
}
```