Integral representation conjecture for the matroid hypergeometric system

Let $M_L(u)$ and $M_L^{\rm hyp}(u)$ be the matroid and hypergeometric $D_Z$-modules associated with the linear space $L$ and parameter $u\in\mathbb{C}^{n+1}$, and let

$$\psi:M_L(u)\longrightarrow M_L^{\rm hyp}(u)$$

be the morphism defined in the source.

Integral representation conjecture. For generic choices of $u\in\mathbb{C}^{n+1}$, the morphism $\psi$ is an isomorphism of $D_Z$-modules.

The conjecture asserts that, for generic parameters, solutions of the matroid hypergeometric system arise from Euler integrals. The source compares this with the non-resonant toric case and records several consequences that would follow if the conjecture holds.