Conjecture on the facets of the network model cone

Let $B$ denote the model matrix for the directed random graph network model with reciprocation, and let $\mathrm{cone}(B)$ be its cone. For a network on $n$ nodes, the facets conjecture. $\mathrm{cone}(B)$ has $3n$ facets: $2n$ correspond to patterns of zeros leading to a zero row or column margin, and the remaining $n$ correspond to patterns of zeros that cause the maximum-likelihood estimate not to exist without inducing zero margins. This conjecture is based on computations in \texttt{polymake} for networks of size up to $n=10$; a general proof is not provided in the source.