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Sabok's S-Prime Simplex Questions

Geometry & topology · posed by Marcin Sabok · disproved

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Statement

Sabok asked whether the compact convex set S′(X)S'(X) attached to a separable metric space of diameter at most one is always a simplex, and whether S′(U1)S'(\mathbb{U}_1) is the Poulsen simplex. Both answers are negative, with obstructions already visible for finite XX and for the Urysohn space.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    Yutong Zhang and Yaoran Yang, using GPT-based models

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai assisted
    — a person led the work and used a model along the way.

    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.

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