# [Conditional good minimal models for compact Kähler fourfolds](paper.pdf)

Author: OpenAI  
Date: October 6, 2026

## Citation

```bibtex
@misc{OAI:Conditional-good-minimal-models-for-compact-Kahler-fourfolds-October-6-2026,
  author = {{OpenAI}},
  title = {{Conditional good minimal models for compact K\"ahler fourfolds}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Conditional-good-minimal-models-for-compact-Kahler-fourfolds-October-6-2026/paper.pdf}{OAI:Conditional-good-minimal-models-for-compact-Kahler-fourfolds-October-6-2026}},
  year = {2026}
}
```

## Version note

This version clarifies the independent ordinary-MMP input and states the remaining Iitaka-subadditivity and effective-abundance hypotheses explicitly; see the [previous version](../Conditional-good-minimal-models-for-compact-Kahler-fourfolds-October-5-2026/paper.pdf).