Sabok's S-Prime Simplex Questions
Sabok asked whether the compact convex set attached to a separable metric space of diameter at most one is always a simplex, and whether is the Poulsen simplex. Both answers are negative, with obstructions already visible for finite and for the Urysohn space.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Construction
- Field
- Convex geometry
- Posed by
- Marcin Sabok
- Year posed
- 2013
- Years open
- 13y
- Solved
- 2026-06-18
- Model
- GPT-based models
- Vendor
- OpenAI
- Collaborators
- Yutong Zhang, Yaoran Yang
- Verification
- Lean-checked, statement unaudited
- Publication
- Preprint
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The acknowledgement says the authors used GPT-based large language models to generate and compare possible proof strategies. Same authors as the Baker anti-Bertini entry in this catalog.
Verification
arXiv preprint; not yet peer-reviewed. Lean formalization available, but not yet audited by a third party.