Uniform filling conjecture for finite quotients of Bruhat–Tits buildings

Let $\mathcal{B}$ be the Bruhat–Tits building associated with $\mathrm{PGL}_{d}(F)$, where $F$ is a local field and $d\geq3$. For a finite quotient $X$ of $\mathcal{B}$, let $\nu_i(X)$ denote its filling in dimension $i$. Uniform filling conjecture. There exists a constant $\nu=\nu(d,F)$ such that

$$\nu_i(X)\leq\nu$$

for every finite quotient $X$ of $\mathcal{B}$. This would provide a filling-based form of higher-dimensional expansion that remains meaningful even when cohomology does not vanish. The source gives no resolution, so the conjecture is open.