Upper-bound validity of moment hierarchies without symmetry

Determine whether the moment hierarchy and block moment hierarchy provide upper bounds on the measurable independence number for uniform measurable hypergraphs in the absence of a group action or homogeneity assumption.

Background

The dissertation establishes upper-bound results for the moment and block moment hierarchies under the assumption that the underlying measurable hypergraph is homogeneous under a compact group. The group action is used to average feasible solutions and construct the required continuous or invariant objects.

The authors explicitly leave unresolved whether an analogous upper-bound property holds for general measurable hypergraphs without such symmetry. Resolving this would extend the applicability of the moment-based hierarchies beyond homogeneous settings.