The truncation invariance conjecture for matroid zeta-function coefficients

Let $M$ be a matroid of rank $r>0$, and let $\tr(M)$ denote its truncation. Write $Z^{\top}_M(s)$ for the topological zeta function of $M$.

Truncation invariance conjecture. For every integer $k$ with $0\leqslant k<\operatorname{rk}(M)$,

$$\left(\frac{d^k}{ds^k}Z^{\top}_M(s)\right)\bigg|_{s=0}=\left(\frac{d^k}{ds^k}Z^{\top}_{\tr(M)}(s)\right)\bigg|_{s=0}.$$

This conjecture generalizes the known result for matroids whose truncation is uniform. A proof would show that the low-order Taylor coefficients of the topological zeta function are controlled by the corresponding truncation and, consequently, by low-rank information in the lattice of flats.