Algebraic and complex geometry·OpenAI Math·Result 060
The Global Spherical Shell conjecture
One of the 372 results in OpenAI's public mathematics catalogue, filed under algebraic and complex geometry: 1 preprint, the latest dated 24 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and embeds the animation.
In one line: OpenAI reports a proof of the Global Spherical Shell conjecture (algebraic and complex geometry) in a preprint dated 24 September 2026. It has not been peer reviewed. The channel's animation, Every OpenAI Math Result, Part 1 of 4: Goldfeld's Conjecture and 82 More, is on YouTube.
Chapter 46 of 83 in Every OpenAI Math Result, Part 1 of 4: Goldfeld's Conjecture and 82 More · starts at 15:37 · watch from there on YouTube →
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
Global Spherical Shells on Minimal Surfaces of Class VII
OpenAI's abstract 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.
Quick answers
- Is it proven?
- Not independently yet. OpenAI posted a preprint on 24 September 2026; it has not been peer reviewed, so treat the result as OpenAI's claim until other mathematicians have checked it.
- What exactly does OpenAI claim?
- 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.
- Where is the proof?
- In the paper, Global Spherical Shells on Minimal Surfaces of Class VII (PDF).
- Is there a video?
- Yes, on YouTube (28:48, chapter 46).
Also in
- Chapter 6 of 10 in Kobayashi's Ampleness Conjecture, Kuznetsov Conjecture, Virasoro Conjecture and 7 More · starts at 1:44 · watch from there on YouTube →
The video
Every OpenAI Math Result, Part 1 of 4: Goldfeld's Conjecture and 82 More · Compilation · 28:48 · chapter 46 from 15:37 · description, sources and chapters →
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