Maximal rank conjecture for varieties with a hypersurface secant variety

Let $X \subset \mathbb{P}^N$ be a smooth non-degenerate projective variety, and let $g$ be the generic $X$-rank. Denote by $r_{\text{max}}$ the maximum $X$-rank and by $r_{\text{max},g-1}$ the maximum $X$-rank achieved on the secant variety $\sigma_{g-1}(X)$. Assume that $\sigma_{g-1}(X)$ is a hypersurface. Maximal rank conjecture.

$$r_{\text{max}}=\max\{r_{\text{max},g-1},g\}.$$

This conjecture refines the preceding upper bound on the maximal $X$-rank by asserting that the maximum is attained either on $\sigma_{g-1}(X)$ or at the generic rank. Its status is not resolved in the supplied source.