Mutation compatibility conjecture for g-vectors

Let $\text{T}_n$ be the $n$-regular tree indexing seeds, let $t_0$ and $t_1$ be adjacent vertices in direction $k$, and let $B_0$ and $B_1$ be exchange matrices with $B_1=\mu_k(B_0)$. For a cluster variable indexed by $i$ at $t$, write its $\boldsymbol{g}$-vectors relative to these initial seeds as $\boldsymbol{g}_{i;t}^{B_0;t_0}$ and $\boldsymbol{g}_{i;t}^{B_1;t_1}$. Mutation compatibility conjecture. For every $t$ and $i$,

$$\boldsymbol{g}_{i;t}^{B_1;t_1}=\eta_k^{B_0^T}(\boldsymbol{g}_{i;t}^{B_0;t_0}),$$

where $B_0^T$ is the transpose of $B_0$. This is presented as an equivalent reformulation of the weak version of the cited $\boldsymbol{g}$-vector mutation conjecture; it is known when the relevant exchange matrices are skew-symmetric.