Infinite-order TQFT representation conjecture for pseudo-Anosov mapping classes

Let $\phi$ be a pseudo-Anosov mapping class of a surface of arbitrary genus, and let $k$ denote the level of the associated TQFT representation. Infinite-order TQFT representation conjecture. The matrices representing $\phi$ in TQFT have infinite order for all but finitely many values of $k$. The question concerns whether TQFT representations detect the dynamical complexity of pseudo-Anosov mapping classes at all but finitely many levels; the source provides no resolution of this assertion.