The semisimple-quotient conjecture for submodule zeta functions

Let $k$ be a number field, let $V$ be a finite-dimensional vector space over $k$, and let $\mathcal A\subset \operatorname{End}_k(V)$ be an associative unital subalgebra. Let $\operatorname{rad}(\mathcal A)$ be its nilradical, and choose a Wedderburn-Malcev complement $\mathcal S\subset\mathcal A$ such that $\mathcal A=\operatorname{rad}(\mathcal A)\oplus\mathcal S$. Choose compatible $\mathfrak{o}$-forms $\mathsf V$, $\mathsf A$, and $\mathsf S$, and write $\mathsf X_v=\mathsf X\otimes_{\mathfrak{o}}\mathfrak{o}_v$.

Semisimple-quotient conjecture. For almost all $v\in\mathcal V_k$,

$$\left.\frac{\zeta_{\mathsf A_v\curvearrowright\mathsf V_v}(s)}{\zeta_{\mathsf S_v\curvearrowright\mathsf V_v}(s)}\right|_{s=0}=1.$$

This conjecture generalises the earlier simple-pole conjecture by asserting that the radical of the acting algebra does not alter the value at zero relative to its semisimple complement. The supplied text states the conjecture but gives no proof or resolution.