Canonical lamination realization conjecture for the stretch unit sphere

Let $\Sigma_g$ be a closed surface of genus $g$, let $\sigma\in\mathscr T_g$ be a hyperbolic structure, and let $v$ be a vector in the stretch unit sphere of $T_\sigma\mathscr T_g$. Denote by $v^*$ the lamination associated with $v$. Canonical lamination realization conjecture. For every vector $v$ in the stretch unit sphere of $T_\sigma\mathscr T_g$ there exists a hyperbolic structure $\tau\in\mathscr T_g$ such that $v^*$ is the canonical lamination maximally stretched by the homotopy class of the identity $(\Sigma_g,\sigma)\to(\Sigma_g,\tau)$. The conjecture proposes that every direction in the stretch unit sphere arises as the canonical maximally stretched lamination of an identity map to some hyperbolic structure; the supplied text gives no resolution or further evidence.