# [A group without fixed price](unequal-costs-rank-100-amalgam.pdf)

**Author:** OpenAI

**Date:** October 5, 2026

## Citation

```bibtex
@misc{OAI:A-group-without-fixed-price-October-5-2026,
  author = {{OpenAI}},
  title = {{A group without fixed price}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/A-group-without-fixed-price-October-5-2026/unequal-costs-rank-100-amalgam.pdf}{OAI:A-group-without-fixed-price-October-5-2026}},
  year = {2026}
}
```