Tropical Hirzebruch signature conjecture for tropical surfaces

Let $X$ be a compact tropical surface. Let $K_X^2$ denote the square of its canonical class and $c_2(X)$ its top tropical Chern class. Write $H_{1,1}(X)$ for the tropical $(1,1)$-homology group, and let $\mathbf{Sign}_{1,1}(X)$ be the signature of its intersection form.

Tropical Hirzebruch signature conjecture.

$$3\mathbf{Sign}_{1,1}(X)=K_X^2-2c_2(X).$$

This is the proposed tropical counterpart of Hirzebruch's signature formula. The preceding corollary establishes additivity of the right-hand side under tropical sums, but the source does not state that the conjecture has been proved.