Linear-resolution conjecture for maximal minors of Jacobian dual matrices

Let $S=k[x_1,\dots,x_n]$ be a polynomial ring, let $I=(f_1,\dots,f_r)$ be a linearly presented $\operatorname{\mathfrak{m}}$-primary ideal of $S$, and let $\Theta$ be the Jacobian dual matrix of a presentation matrix of $I$. Linear-resolution conjecture. The ideal of maximal minors $I_n(\Theta)$ has a linear resolution. The conjecture concerns the homological structure of the maximal-minor ideal associated with a Jacobian dual matrix. The supplied text gives no resolution status or supporting result beyond its presentation as one of the paper's conjectures.