Cohen–Macaulay decomposition conjecture for the maximal degeneration

Let $R$ be the polynomial ring of entries of the degenerated generic matrix, let $J$ be the Jacobian ideal of its determinant, let $I$ be the ideal of submaximal minors, and let $J:I$ be the colon ideal. Assume $r=m-2$. Cohen–Macaulay decomposition conjecture. Both $R/J$ and $R/(J:I)$ are Cohen–Macaulay reduced rings, and

$$J=I\cap(J:I).$$

This predicts a reduced Cohen–Macaulay decomposition of the Jacobian scheme into the component defined by $I$ and the component defined by $J:I$.