Han and Jiang's Question on klt Type in Flat Families
Han and Jiang asked whether being of klt type is an open condition in flat families of varieties. It is not.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Birational geometry
- Posed by
- Jingjun Han, Chen Jiang
- Year posed
- 2025
- Years open
- 1y
- Solved
- 2026-05-21
- Model
- ChatGPT Pro 5.5 and Rethlas
- Vendor
- OpenAI; Frenzy Math
- Collaborators
- Jihao Liu
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 20 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The division of labour is stated precisely, which is rare: ChatGPT Pro 5.5 suggested the general idea for the counterexample, and the Rethlas system found the explicit example and proved it. The author describes the construction as substantially using generative AI.
Verification
No independent check. The refutation is an explicit counterexample, so it reduces to checking that the stated family has the claimed properties. arXiv preprint, not peer-reviewed.