The degree conjecture for topological zeta functions of algebras

Let $\cA$ be a non-associative $\fo$-algebra that is free of rank $d$ as an $\fo$-module, where $\fo$ is the ring of integers in a number field $k$. Degree conjecture.

$$\deg_{\ess}\bigl(\zeta_{\cA,\topo}(\ess)\bigr)=-d.$$

This is proposed without further assumptions on $\cA$, based on experimental evidence for $k=\QQ$; unlike topological zeta functions of polynomials, the degree here is conjectured to depend only on the module rank.