Wolff's conjecture on the dimension of Furstenberg sets

Let $0 \leq s \leq 1$. A Furstenberg $s$-set is a compact set $K \subset \mathbb{R}^{2}$ such that there is a set of unit vectors $S_K \subset S^1$ with positive length and, for every $e \in S_K$, a line $L_e$ parallel to $e$ satisfying $\dim_{\mathrm{H}}(K \cap L_e) \geq s$. Wolff's conjecture. The Hausdorff dimension of every compact Furstenberg $s$-set is at least

$$\frac{1+3s}{2}.$$

Wolff's bound gives the lower bound $\max\\{1/2+s,2s\\}$; the conjecture asks for a stronger bound and remains open in the form stated here.