# [Product-projection localization and the QAC⁰ parity lower bound](paper.pdf)

OpenAI  
September 24, 2026

## Citation

```bibtex
@misc{OAI:Product-projection-localization-and-the-QAC0-parity-lower-bound-September-24-2026,
  author = {{OpenAI}},
  title = {{Product-projection localization and the $\mathrm{QAC}^0$ parity lower bound}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Product-projection-localization-and-the-QAC0-parity-lower-bound-September-24-2026/paper.pdf}{OAI:Product-projection-localization-and-the-QAC0-parity-lower-bound-September-24-2026}},
  year = {2026}
}
```