Direct-observation conjecture for conditional mixing

Let $(X_v,Y_v)_{v\in\mathbb{Z}^2}$ be a hidden Markov field with $E=F=\{-1,1\}$. Suppose

$$Y_v=X_v\xi_v,$$

where $(\xi_v)_{v\in\mathbb{Z}^2}$ are independent and identically distributed, independent of $X$, and satisfy $\mathbf{P}[\xi_v=-1]=p$. Direct-observation conditional-mixing conjecture. If the underlying random field $X$ is mixing, then the model is conditionally mixing. This is the spatial analogue of the filter-stability conjecture and expresses the expectation that conditioning preserves mixing when the observation mechanism has no symmetry. The claim is presented as open; conditional mixing can fail in models with observation symmetries.