# [Purely cosmetic surgery on knots in the three-sphere](paper.pdf)

OpenAI  
September 23, 2026

## Citation

```bibtex
@misc{OAI:Purely-Cosmetic-Surgery-on-Knots-in-the-Three-Sphere-September-23-2026,
  author = {{OpenAI}},
  title = {{Purely cosmetic surgery on knots in the three-sphere}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Purely-Cosmetic-Surgery-on-Knots-in-the-Three-Sphere-September-23-2026/paper.pdf}{OAI:Purely-Cosmetic-Surgery-on-Knots-in-the-Three-Sphere-September-23-2026}},
  year = {2026}
}
```