Stump's interval-count conjecture for the m-Tamari and type A m-Cambrian lattices

The $m$-Tamari lattice and the linear type $A$ $m$-Cambrian lattice are lattices associated with the same parameter $m$. Stump's interval-count conjecture. The $m$-Tamari lattice and the linear type $A$ $m$-Cambrian lattice have the same number of intervals. This conjecture compares two different generalizations of the Tamari lattice and predicts equality of their interval enumerations; the source gives no resolution status.