Universal countable d-sphere graphs

Determine whether a strongly universal element exists for the class of countable d-sphere graphs for every integer d>1.

Background

The paper generalizes circle graphs to d-sphere graphs, defined as intersection graphs of the family of flat d-dimensional discs with boundary on the d-sphere. It asks whether the universality theorem proved for countable circle graphs extends to these higher-dimensional graph classes.

References

Is there a strongly universal element for the class of countable $d$-sphere graph s for every $d>1$?

— Circle graphs and the automorphism group of the circle  (2501.07698 - Georgakopoulos, 13 Jan 2025) in Problem following the definition of the d-sphere graph, Section 6 (Further problems)