Equality of adoption levels in one-sided and two-sided Cartesian Bass models

Let $f^{\rm D, \, 1-sided}(t;p,q)$ and $f^{\rm D}(t;p,q)$ denote the expected adoption levels in the discrete Bass models on homogeneous $D$-dimensional one-sided and two-sided Cartesian networks on $\mathbb{Z}^D$, respectively.

Equality conjecture. The expected adoption levels are identical:

$$f^{\rm D, \, 1-sided}(t;p,q)=f^{\rm D}(t;p,q).$$

This claims that the directional structure of the one-sided network does not change the expected adoption level relative to the two-sided Cartesian network. The supplied text does not state whether the claim has been proved or disproved.