Type D Chan–Robbins–Yuen volume conjecture

Let $K_n^D$ be the complete signed graph with vertex set $[n]$, containing all edges $(i,j,\pm)$ with $1\leq i<j\leq n$, and let

$$CRYD_n=\mathcal{F}_{K_n^D}(2,0,\ldots,0)$$

be its flow polytope. Let $Cat(k)=\frac{1}{k+1}\binom{2k}{k}$ denote the $k$th Catalan number. Type D Chan–Robbins–Yuen volume conjecture. The normalized volume of $CRYD_n$ is

$$\operatorname{vol}(CRYD_n)=2^{(n-2)^2}\prod_{k=0}^{n-2}Cat(k).$$

The conjecture is motivated by computed values and a constant-term expression for the volume; the paper gives no proof or resolution of the product formula.