The Hypergeometrical Universe Theory challenges General Relativity and Special Relativity. The reason for that is that they seem to be a perfect replacement to the Geodesics Paradigm Einstein proposed.
Do you have a preferred test that you think HU might fail?
HU tools are:
a) Natural Laws
b) Lightspeed Expanding Hyperspherical Topology
c) Homology between the topology and the Minkowski Metric