Bak's inhomogeneous dyadic approximation conjecture in Cantor's set

Throughout, let $K$ be the middle-third Cantor set, let $\mu$ be its natural probability measure, and for $\psi:\mathbb R\to[0,\infty)$ and $y\in\mathbb R$ define

$$W_2(\psi,y)=\{x\in\mathbb R:\|2^n x-y\|<\psi(n)\text{ for infinitely many }n\in\mathbb N\}.$$

Here $\|x\|$ denotes the Euclidean distance from $x$ to the nearest integer. Bak's conjecture. If $y\in\mathbb R$, then

$$\mu(W_2(\psi,y))=\begin{cases}0,&\text{if }\displaystyle\sum_{n=1}^\infty\psi(n)<\infty,\\\\1,&\text{if }\displaystyle\sum_{n=1}^\infty\psi(n)=\infty. \end{cases}$$

This conjecture generalizes Velani's inhomogeneous-free conjecture by dropping monotonicity and allowing an arbitrary shift $y$; it connects dyadic approximation in the Cantor set with distribution modulo $1$ and shrinking-target problems. The supplied excerpt does not state whether the conjecture has been resolved.