# [Stable self-similar blowup for a supercritical defocusing Schrödinger equation on the torus](paper.pdf)

**Author:** OpenAI

**Date:** September 24, 2026

## Citation

```bibtex
@misc{OAI:Stable-Self-Similar-Blowup-for-a-Supercritical-Defocusing-Schrodinger-Equation-on-the-Torus-September-24-2026,
  author = {{OpenAI}},
  title = {{Stable self-similar blowup for a supercritical defocusing Schr{\"o}dinger equation on the torus}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Stable-Self-Similar-Blowup-for-a-Supercritical-Defocusing-Schrodinger-Equation-on-the-Torus-September-24-2026/paper.pdf}{OAI:Stable-Self-Similar-Blowup-for-a-Supercritical-Defocusing-Schrodinger-Equation-on-the-Torus-September-24-2026}},
  year = {2026}
}
```

## Verification

The exact-arithmetic verification requires Python 3.8 or newer with only its
standard library, and GNU `sha256sum`. Follow the
[verification guide](verification/certificates/README.md) for the verifier run,
the strict comparison with historical results, and the current file-integrity
check. Success requires all three steps to pass. These checks recompute the
finite integer and rational comparisons; they do not verify the analytic
arguments connecting those comparisons to the blowup theorem.
