The Global Spherical Shell conjecture

What OpenAI claims

Every connected minimal compact complex surface of class VII with b₂ > 0 contains a global spherical shell, proving the positive-b2 Global Spherical Shell conjecture. Such a shell is a holomorphically embedded neighborhood of the standard three-sphere in ℂ²∖{0} whose complement is connected.

Paper

1. Global Spherical Shells on Minimal Surfaces of Class VII

   24 September 2026 · Preprint, not peer reviewed · PDF

   We prove the Global Spherical Shell conjecture: every connected minimal compact complex surface of class VII with positive second Betti number contains a global spherical shell. This is a holomorphically embedded neighborhood of the standard three-sphere in ℂ²∖{0} whose complement is connected.

Status

Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.