Palis' sumset conjecture for missing digits sets

Let $A,B\subset[0,1]$ be missing digits sets. Palis' conjecture. Suppose that

$$\dim_{\mathrm{H}}A+\dim_{\mathrm{H}}B>1.$$

Then, generically, $A+B$ contains a non-trivial interval. In the paper's missing-digits setting, the source explains that genericity means that $A+T_x(B)$ contains a non-trivial interval for Lebesgue almost every $x\in\mathbb{R}$, where $T_x(y)=xy$. The source notes that this is an informal version of Palis' conjecture and recalls stronger precise results in related dynamical settings.