Levesley–Salp–Velani conjecture for very well approximable points in the Cantor set

Let $K$ be the middle-third Cantor set, and let $\mathrm{VWA}$ denote the set of very well approximable real numbers. Then

Levesley–Salp–Velani conjecture.

$$\dim_H(\mathrm{VWA}\cap K)=\dim_H(K).$$

Levesley, Salp, and Velani established the lower bound $\dim_H(\mathrm{VWA}\cap K)\geq \dim_H(K)/2$ for missing digit sets. The conjecture predicts full Hausdorff dimension for the middle-third Cantor set; its status is not resolved in the supplied source.