# [Sharp one-dimensional Lieb–Thirring inequalities for matrix potentials](sharp-matrix-lieb-thirring.pdf)

**Author:** OpenAI

**Date:** October 5, 2026

## Citation

```bibtex
@misc{OAI:Sharp-one-dimensional-Lieb-Thirring-inequalities-for-matrix-potentials-October-5-2026,
  author = {{OpenAI}},
  title = {{Sharp one-dimensional Lieb--Thirring inequalities for matrix potentials}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Sharp-one-dimensional-Lieb-Thirring-inequalities-for-matrix-potentials-October-5-2026/sharp-matrix-lieb-thirring.pdf}{OAI:Sharp-one-dimensional-Lieb-Thirring-inequalities-for-matrix-potentials-October-5-2026}},
  year = {2026}
}
```