# [Incompressible Box Transport and Finite Computation](manuscript.pdf)

**Author:** OpenAI  
**Date:** October 6, 2026

## Citation

```bibtex
@misc{OAI:Incompressible-Box-Transport-and-Finite-Computation-October-6-2026,
  author = {{OpenAI}},
  title = {{Incompressible Box Transport and Finite Computation}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Incompressible-Box-Transport-and-Finite-Computation-October-6-2026/manuscript.pdf}{OAI:Incompressible-Box-Transport-and-Finite-Computation-October-6-2026}},
  year = {2026}
}
```

## Version note

This version supplies effective torus-projection and common-clock decay estimates, including the projected-force and pressure bounds; see the [previous version](../Incompressible-Box-Transport-and-Finite-Computation-September-27-2026/manuscript.pdf).