The leading-term conjecture for the Möbius inversion of matroid topological zeta functions

Let $M$ be a matroid of rank $r$, let $Y_M(s)$ denote the Möbius inversion of its topological zeta function, and let $\mathcal{B}(M)$ denote the set of bases of $M$.

Leading-term conjecture. The Taylor expansion of $Y_M(s)$ at $s=0$ satisfies

$$Y_M(s)=(-1)^r\lvert\mathcal{B}(M)\rvert s^r+O(s^{r+1}).$$

The source proposes this as a stronger conjecture that implies the truncation invariance conjecture. If true, it would describe the first nonzero Taylor term of the Möbius-inverted topological zeta function in terms of the rank and number of bases of the matroid.