Basso–Dixon fishnet determinant conjecture

For integers $n\geq m\geq2$, let $\overline{G}_{m,n}$ be the $m$-row, $n$-column fishnet graph and let $f_{\overline{G}_{m,n}}(z)$ denote its graphical function. Define the $m\times m$ Hankel matrix $H=(H_{i,j})_{i,j=1,\ldots,m}$ by

$$H_{i,j}(z)=(n-m+i+j-2)!(n-m+i+j-1)!f_{\overline{G}_{1,n-m+i+j-1}}(z).$$

Basso–Dixon fishnet determinant conjecture.

$$f_{\overline{G}_{m,n}}(z)=\frac{\det H(z)}{\displaystyle\prod_{k=n-m}^{n+m-1}k!}.$$

This conjecture gives all rectangular fishnet graphical functions with $n\geq m\geq2$ in terms of the one-row ladder functions. The one-row case is known, but the supplied text describes the general fishnets as unsolved and gives no resolution of the determinant formula.