Farb–Leininger–Margalit symmetry conjecture for small stretch factors

Let $S_g$ be a closed orientable surface, let $f\in\operatorname{Mod}(S_g)$ be pseudo-Anosov with stretch factor $\lambda$, and let $C$ be the constant appearing in the small-stretch-factor bound. Symmetry conjecture. If

$$g\log\lambda<C,$$

then $f$ is the product of a finite-order element and a reducible element, and the absolute value of the Euler characteristic of the support of the reducible element is bounded above by $C$, independently of $g$. The source notes partial progress when the stretch factor is less than $3/2$, but the full conjecture remains open.