Penner's conjecture on powers of pseudo-Anosov mapping classes

Let $S_{g,n}$ be an orientable surface of genus $g$ with $n$ punctures, and let $f\in\mathrm{Mod}(S_{g,n})$ be a pseudo-Anosov mapping class, meaning that it has a representative preserving a pair of transverse invariant measured foliations and scaling their transverse measures by factors $\lambda>1$ and $\lambda^{-1}$. A mapping class arises from Penner's construction if it is a product of positive Dehn twists about one multicurve and negative Dehn twists about another filling multicurve, with every twist appearing at least once. Penner's conjecture. Every pseudo-Anosov mapping class has a power that arises from Penner's construction. The conjecture asserts that Penner's construction captures every pseudo-Anosov mapping class after passing to a positive power, despite the construction's restriction that the resulting map fix the singularities and separatrices of its invariant foliations.