The boundary-format hyperdeterminant conjecture

Let $\Delta_k$ denote the $k$-simplex, and let

$$A=\Delta_{k_0}\times\Delta_{k_1}\times\cdots\times\Delta_{k_r},$$

where $k_0\geq\cdots\geq k_r$. The configuration $A$ is GKZ-rational when its associated GKZ hypergeometric system has the rationality property considered in the source. The boundary-format hyperdeterminant conjecture. The product of simplices $A$ is GKZ-rational if and only if

$$k_0=k_1+\cdots+k_r.$$

The equality case is the boundary format for hyperdeterminants and is known to give GKZ-rational configurations; the converse is posed as a conjecture, with no general resolution supplied.