Garcia–Stillman–Sturmfels conjecture for the binary hidden naive Bayes model

Let $n$ be the number of observed variables, each with two states, and let $\mathfrak a(2;2,2,\dots,2)$ be the ideal associated to the hidden naive Bayes model with one hidden variable having two states. For every bipartition of the observed variables, form the corresponding two-dimensional flattening of the $2\times\cdots\times 2$ probability tensor.

Garcia–Stillman–Sturmfels conjecture. The ideal $\mathfrak a(2;2,2,\dots,2)$ is generated by the $3\times 3$ minors of all two-dimensional flattenings arising from bipartitions of the observed variables.

The paper presents this as a special case from which a proof of the full conjecture of Garcia, Stillman, and Sturmfels would follow. The supplied text does not establish whether this special case is resolved, so its database status remains open.