# [Smooth counterexamples to Yau's nodal upper bound in dimensions three and four](paper.pdf)

**Author:** OpenAI

**Date:** September 23, 2026

## Citation

```bibtex
@misc{OAI:Smooth-counterexamples-to-Yaus-nodal-upper-bound-in-dimensions-three-and-four-September-23-2026,
  author = {{OpenAI}},
  title = {{Smooth counterexamples to Yau's nodal upper bound in dimensions three and four}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Smooth-counterexamples-to-Yaus-nodal-upper-bound-in-dimensions-three-and-four-September-23-2026/paper.pdf}{OAI:Smooth-counterexamples-to-Yaus-nodal-upper-bound-in-dimensions-three-and-four-September-23-2026}},
  year = {2026}
}
```