Simon's dimension conjecture for self-similar measures on the line

Let $\mu$ be the self-similar measure on $\mathbb{R}$ associated to an IFS $\{\varphi_i:i\in\Lambda\}$ without exact overlaps and a probability vector $\{p_i\}$. Let $\lambda_i$ be the contraction factor of $\varphi_i$. Simon's measure-dimension conjecture. Then

$$\dim\mu=\min\left(1,\frac{\sum_i p_i\log p_i^{-1}}{\sum_i p_i\log\lambda_i^{-1}}\right).$$

This is the measure counterpart to the dimension conjecture for self-similar attractors: it predicts that, without exact overlaps, the expected entropy-over-Lyapunov-dimension formula is valid up to the ambient bound. The source does not specify the conjecture's resolution status.