The tropical web-function conjecture for four flags

Let $n$ be a positive integer and let $a,b,c,d$ satisfy $1\leq a,b,c,d<n$, $a+b>n$, and $a+b+c+d=2n$. Let $F$ be the cluster-algebra function on $\operatorname{Conf}_4 \mathcal{A}_{SL_n}$ constructed from the corresponding invariant web, and let $F^t$ denote its tropicalization. For points $x_1,x_2,x_3,x_4$ in the affine building for $PGL_n$, write $d_k$ for the corresponding distance function indexed by $k$. The tropical web-function conjecture. $F^t(x_1,x_2,x_3,x_4)$ is given by the minimum, over points $p$ and $q$ in the affine building for $PGL_n$, of

$$d_a(p,x_1)+d_b(p,x_2)+d_{a+b-n}(q,p)+d_c(q,x_3)+d_d(q,x_4).$$

This extends the paper's higher-lamination intersection framework to a cluster function arising from a web beyond the results established in the paper. The parser supplies no evidence that the statement has been proved or refuted, so its status remains open.