The completion conjecture for plus test ideals

Let $X$ be a normal integral scheme of finite type over a complete local ring $(R,\mathfrak{m})$ such that $R/\mathfrak{m}$ has positive characteristic. Let $B\geq 0$ be a $\mathbb{Q}$-divisor on $X$ such that $K_X+B$ is $\mathbb{Q}$-Cartier. Fix a point $x\in X$ with residual characteristic $p>0$, and let $S=\mathcal{O}_{X,x}$ be the stalk at $x$. The completion conjecture. One has

$$\tau_+(\mathcal{O}_{X},B)_x\cdot\widehat{S}=\tau_+(\widehat{S},\widehat{B})=\tau_{\widehat{R^+}}(\widehat{S},\widehat{B})$$

and

$$\tau_+(\mathcal{O}_{X},B)_x=\tau_+(\widehat{S},\widehat{B})\cap S.$$

This asks whether plus test ideals commute with completion and contract back from the completed local ring. The source presents it as an open question in mixed characteristic.