Non-mixed dual distance for dually uniquely ergodic trees

Let $T\in\partial cv_N$ be an $\mathbb R$-tree with dense orbits, and suppose that its dual lamination $L(T)$ is uniquely ergodic; then $T$ is dually uniquely ergodic. In this case the associated dual distance $d_*$ is defined up to rescaling. Non-mixed dual distance conjecture. If $T$ is dually uniquely ergodic, then the dual distance $d_*$ is not mixed: it is not the case that some pairs of points have zero, infinite, or positive finite distance in the mixed sense. The claim concerns the possible metric behavior arising from the unique ergodic measure on the dual lamination; the supplied text gives no resolution, so its status remains open.