# [Deforming hypersymplectic four-manifolds to hyperkähler triples](paper.pdf)

**Author:** OpenAI

**Date:** October 7, 2026

## Citation

```bibtex
@misc{OAI:Deforming-hypersymplectic-four-manifolds-to-hyperkahler-triples-October-7-2026,
  author = {{OpenAI}},
  title = {{Deforming hypersymplectic four-manifolds to hyperk\"ahler triples}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Deforming-hypersymplectic-four-manifolds-to-hyperkahler-triples-October-7-2026/paper.pdf}{OAI:Deforming-hypersymplectic-four-manifolds-to-hyperkahler-triples-October-7-2026}},
  year = {2026}
}
```

## Version note

This version clarifies the prescribed cohomology-class criterion used in the deformation argument, removes an unnecessary cone-comparison citation, and updates the companion-paper citation; see the [previous version](../Deforming-hypersymplectic-four-manifolds-to-hyperkahler-triples-September-23-2026/paper.pdf).