Exact overlap conjecture for self-similar sets on the real line

Let $\Phi=\{\varphi_i\}_{i\in\Lambda}$ be an iterated function system consisting of similarity maps on $\mathbb{R}$. Its attractor $X$ satisfies

$$X=\bigcup_{i\in\Lambda}\varphi_i(X).$$

A dimension drop means

$$\dim X<\min\{1,\dim_S\Phi\},$$

where $\dim_S\Phi$ is the unique solution $s$ of $\sum_{i\in\Lambda}|r_i|^s=1$ when $\varphi_i(x)=r_i x+t_i$. The system has exact overlaps if there are distinct words $\mathbf{i},\mathbf{j}\in\Lambda^n$ of the same length such that $\varphi_{\mathbf{i}}=\varphi_{\mathbf{j}}$.

Exact overlap conjecture. If there is a dimension drop for $\Phi$, then $\Phi$ has exact overlaps.

For self-similar sets on the real line, exact overlaps were the only known cause of dimension drop at the time of the source. The conjecture is attributed to Simon, with recent progress cited by the authors, but its status is not resolved by the supplied text.