Integral invariance of orbifold Morse homology for stable Morse functions

Determine whether the homology theories constructed from stable Morse functions on orbifolds are invariant over the integers, as conjectured by Bao and Liu.

Background

The paper seeks examples of contact manifolds whose cylindrical contact homology computations reflect the failure of integral invariance in orbifold Morse homology. It notes that Bao and Liu introduced a special subclass of Morse functions, called stable Morse functions, in their treatment of orbifold Morse homology. The cited work conjectures that the associated homology theories are invariant, leaving the integral-invariance question unresolved in the passage quoted here.