The building-realization conjecture for exceptional Chevalley groups over finite fields

Let $\mathcal G$ be a Chevalley group of adjoint type $\tau$, rank $r$, and dimension $n=r+2m$, with Lie algebra $\mathfrak g$. Let $\mathbb P[\Psi]$ be the associated $\mathbb F_1$-model and let $\Delta({}^{+}\mathbb P[\mathfrak g]_{\mathbb F_q})$ denote the simplicial complex of the base change to $\mathbb F_q$. The building-realization conjecture. There is an $(r-1)$-simplex $\delta_q$ in ${}^{+}\mathbb P[\mathfrak g]_{\mathbb F_q}$ such that the orbit $G(\mathbb F_q).\delta_q$ in $\Delta({}^{+}\mathbb P[\mathfrak g]_{\mathbb F_q})$ is the spherical building of type $\tau$ over $\mathbb F_q$. The action of $G(\mathbb F_q)$ on $G(\mathbb F_q).\delta_q$ coincides with the usual action on the building.

This is presented as an expectation following the corresponding theorem for the Weyl-group orbit over the $\mathbb F_1$-model. The source gives no resolution or additional evidence, so the conjecture remains open.