Bugeaud–Durand dimension conjecture for rationally approximable points in the Cantor set

Let $K$ be the middle-third Cantor set and let $W(v)$ denote the set of real numbers satisfying the relevant Diophantine approximation condition with exponent $v$. Then

Bugeaud–Durand conjecture.

$$\dim_H(K\cap W(v))=\max\left\{\dim_H(K)-1+\frac{2}{v+1},\frac{\dim_H(K)}{v+1}\right\}.$$

Bugeaud and Durand had established an almost-everywhere upper bound for translates of the middle-third Cantor set. The supplied source does not resolve whether this exact formula holds, so the conjecture remains open.