AMU conjecture for surface groups

Let $\Sigma$ be a closed surface of genus at least $2$, let $p=2r$ be an even integer, and consider the quantum representation

$$\rho_p:\pi_1(\Sigma)\longrightarrow \prod_{n=1}^{r-1}\mathrm{PAut}(V_p(\Sigma,n)).$$

Here $V_p(\Sigma,n)$ is the vector space assigned by the $\mathrm{SU}(2)$ Witten–Reshetikhin–Turaev TQFT to $\Sigma$ equipped with a banded point colored by $n$. AMU conjecture. If $\gamma\in\pi_1(\Sigma)\setminus\{1\}$ is not a power of a simple element, then $\rho_p(\gamma)$ has infinite order for all sufficiently large $p$. This conjecture predicts that quantum representations detect the non-simple nature of mapping classes represented by surface-group elements; the paper discusses its application through asymptotics of quantum representations, but the supplied text does not establish the conjecture in full.