The transience-condition $(T)$ conjecture for strongly mixing random environments

Let $\ell\in\mathbb S^{d-1}$. A random walk in a strong mixing uniformly elliptic random environment is directionally transient along an open set $\mathcal U_{\ell}\subset\mathbb S^{d-1}$ when it is transient along every direction in that set, with $\ell\in\mathcal U_{\ell}$. Condition $(T)|\ell$ means that for every $b>0$ there is a neighbourhood $\mathcal U_{\ell}$ of $\ell$ such that, for every $\ell'\in\mathcal U_{\ell}$,

$$\limsup_{L\rightarrow\infty}L^{-1}\log P_0\left[\widetilde T_{-bL}^{\ell'}<T_L^{\ell'}\right]<0.$$

The transience-condition $(T)$ conjecture. Directional transience along an open set $\mathcal U_{\ell}$ is equivalent to condition $(T)|\ell$.

The source describes this as a stronger form of the preceding ballistic conjecture, citing Sznitman's theorem for the comparison. No resolution is supplied in the source.