Main local tangent-space dimension conjecture for trianguline varieties

Let $x\in X_{\rm tri}^\square(\overline{r})$ be a crystalline strictly dominant point whose Frobenius eigenvalues $(\varphi_1,\dots,\varphi_n)$ are pairwise distinct. Let $w_x$ be the Weyl group element associated to $x$, and set $d_x:=d_{w_x}$. Tangent-space dimension conjecture.

$$\dim_{k(x)}T_{\widetilde X_{\rm tri}^\square(\overline{r}),x}=\lg(w_x)-d_x+\dim X_{\rm tri}^\square(\overline{r})=\lg(w_x)-d_x+n^2+[K:\mathbb{Q}_p]\frac{n(n+1)}{2}.$$

This is the paper's main local conjecture about the geometry of the trianguline variety. It predicts the precise tangent-space dimension at crystalline strictly dominant points with distinct Frobenius eigenvalues; the supplied text gives no resolution status.