# [A cubic lower bound for border determinantal complexity of the permanent](A-cubic-lower-bound-for-border-determinantal-complexity-of-the-permanent-September-24-2026.pdf)

**Author:** OpenAI

**Date:** September 24, 2026

## Citation

```bibtex
@misc{OAI:A-cubic-lower-bound-for-border-determinantal-complexity-of-the-permanent-September-24-2026,
  author = {{OpenAI}},
  title = {{A cubic lower bound for border determinantal complexity of the permanent}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/A-cubic-lower-bound-for-border-determinantal-complexity-of-the-permanent-September-24-2026/A-cubic-lower-bound-for-border-determinantal-complexity-of-the-permanent-September-24-2026.pdf}{OAI:A-cubic-lower-bound-for-border-determinantal-complexity-of-the-permanent-September-24-2026}},
  year = {2026}
}
```