# [Midpoint lenses in segment spaces](manuscript.pdf)

OpenAI  
September 27, 2026

## Citation

```bibtex
@misc{OAI:Midpoint-lenses-in-segment-spaces-September-27-2026,
  author = {{OpenAI}},
  title = {{Midpoint lenses in segment spaces}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Midpoint-lenses-in-segment-spaces-September-27-2026/manuscript.pdf}{OAI:Midpoint-lenses-in-segment-spaces-September-27-2026}},
  year = {2026}
}
```