Baker–Schmidt conjecture for the Hausdorff dimension of polynomial approximation sets

Let $n\geqslant 2$ be an integer, let $0<\mu<\frac{n+1}3$, and let $w>n-2\mu$. Define

\mathcal{P}_n(\mu,w)=\Big\\{x\in[-\tfrac12,\tfrac12]:\left\{\begin{array}{l} |P(x)| < H(P)^{-w-\mu}\\\\[1ex] |P'(x)| < H(P)^{1-\mu} \end{array} \right.\text{ holds for infinitely many }P\in\mathbb{Z}[x],\deg P\leqslant n\Big\\},

where $H(P)$ is the absolute height of $P$, and let $\dim$ denote Hausdorff dimension. Baker–Schmidt conjecture. The lower bound

$$\dim\mathcal{P}_n(\mu,w) \geqslant \frac{n+1-2\mu}{w+1}$$

is an equality. The case $\mu=0$ was proved by Bernik, while the stated generalisation remains open in the source.