The tropical duality conjecture for tropical linear spaces and quotients

Let $p$ be a valuated matroid of rank $d$ on $\mathbb{T}^n$, let $L_p$ be its corresponding tropical linear space, and define

$$Q_p \coloneqq \mathbb{T}^n/\mathpzc{B}(L_p^\perp).$$

Here $L_p^\vee$ denotes the tropical dual of $L_p$. Tropical duality conjecture.

$$L_p^\vee = Q_p.$$

This asserts that the tropical dual of the tropical linear space associated to a valuated matroid agrees with the corresponding tropical quotient. The supplied text gives the definitions but does not state whether the claim has been resolved.