Problem detail · source-aware
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Sabok asked whether the compact convex set $S'(X)$ attached to a separable metric space of diameter at most one is always a simplex, and whether $S'(\mathbb{U}_1)$ is the Poulsen simplex. Both answers are negative, with obstructions already visible for finite $X$ and for the Urysohn space.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
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.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
arXiv preprint; not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.