# [A uniformly discrete counterexample to bounded approximation in Lipschitz-free spaces](main.pdf)

**Author:** OpenAI  
**Date:** September 26, 2026

## Citation

To cite this manuscript:

```bibtex
@misc{OAI:Failure-of-Bounded-Approximation-in-a-Lipschitz-Free-Space-over-a-Uniformly-Discrete-Metric-Space-September-26-2026,
  author = {{OpenAI}},
  title = {{A uniformly discrete counterexample to bounded approximation in Lipschitz-free spaces}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Failure-of-Bounded-Approximation-in-a-Lipschitz-Free-Space-over-a-Uniformly-Discrete-Metric-Space-September-26-2026/main.pdf}{OAI:Failure-of-Bounded-Approximation-in-a-Lipschitz-Free-Space-over-a-Uniformly-Discrete-Metric-Space-September-26-2026}},
  year = {2026}
}
```