Group representation of general pseudo-cubes

Determine whether every pseudo-cube arises, up to coordinatewise relabeling, from a group class obtained by the action of the group of permutations preserving each coordinate panel.

Background

The paper proves that every two-fibered pseudo-cube decomposes into monodromy orbits that are coordinatewise images of coset complexes. In a general pseudo-cube, coordinate panels may contain more than two labels, so the involutive neighbor maps must be replaced by larger panel-preserving permutation groups.

It remains unresolved whether this generalized monodromy construction captures all pseudo-cubes up to coordinatewise relabeling.