Landsberg–Weyman conjecture on generators of tangential ideals of Segre varieties

Let $X$ be a Segre variety, and let $I(\tau(X))$ denote the homogeneous ideal of its tangential variety. The relevant Schur-module factors are expressed using exterior powers $\bigwedge^k$ and Schur functors $S_{\lambda}$. Landsberg–Weyman conjecture. The ideal $I(\tau(X))$ is generated by the submodules of quadrics which have at least four $\bigwedge^{2}$ factors, the cubics with four $S_{(2,1)}$ factors and all other factors $S_{(3)}$, the cubics with at least one $\bigwedge^3$ factor, and the quartics with three $S_{(2,2)}$ factors and all other factors $S_{(4)}$. This gives an explicit representation-theoretic description of the generators of the ideal of the tangential variety in the Segre case; the surrounding paper presents it as the next goal after determining the coordinate ring of tangential varieties, and the supplied text gives no resolution status.