Hironaka's golden ratio conjecture for minimum dilatations

For each genus $g$, let $\delta_{g,0}$ denote the minimum dilatation among pseudo-Anosov maps on the closed surface of genus $g$, and let $\mu$ be the golden ratio. Hironaka's golden ratio conjecture. The minimum dilatations satisfy

$$\lim_{g\to\infty}\delta_{g,0}^{2g-2}=\mu^4.$$

This conjecture predicts the asymptotic minimum normalized dilatation for pseudo-Anosov maps on closed surfaces. The source notes that examples with a uniformly bounded number of singularities support an approach to proving it, but the conjecture remains open in the supplied text.