The reductive-group triangulation uniqueness conjecture

Let $\mathsf G$ be a split connected reductive group with maximal torus $\mathsf T$ contained in a Borel subgroup $\mathsf B$, and let $D$ be a $\mathsf G$-$(\varphi,\Gamma_K)$-module over $\mathcal{R}_{K,A}$. Let $\delta\colon \mathsf T^{\vee}(K)\to A^{\times}$ be a continuous character. For every negative root $\lambda\in\Phi^-(\mathsf G,\mathsf B)$, assume that $\delta\circ\lambda^{\vee}\in\mathcal{T}_{\mathrm{reg}}(A)$.

Reductive-group triangulation uniqueness conjecture. Then $D$ has at most one triangulation of parameter $\delta$.

This is proposed as the natural generalization of the established $\operatorname{GL}_n$ uniqueness result. The supplied text gives no resolution of the general reductive-group statement.