From coarsely Helly to Helly

Determine whether every coarsely Helly group is a Helly group.

Background

Coarse Hellyness guarantees a coarsely dense Helly hull under additional hypotheses, but the notes do not establish that every coarsely Helly group admits a proper cocompact action on a Helly graph.

References

Is every coarsely Helly group a Helly group?

— Group actions on injective spaces and Helly graphs  (2307.00414 - Haettel, 2023) in Section 14, “Open questions,” item 10