# [Counterexamples to weak chromatic splitting: sphere kernels and descent exponents](paper.pdf)

**Author:** OpenAI

**Date:** September 27, 2026

## Citation

```bibtex
@misc{OAI:Counterexamples-to-weak-chromatic-splitting-sphere-kernels-and-descent-exponents-September-27-2026,
  author = {{OpenAI}},
  title = {{Counterexamples to weak chromatic splitting: sphere kernels and descent exponents}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Counterexamples-to-weak-chromatic-splitting-sphere-kernels-and-descent-exponents-September-27-2026/paper.pdf}{OAI:Counterexamples-to-weak-chromatic-splitting-sphere-kernels-and-descent-exponents-September-27-2026}},
  year = {2026}
}
```