Tsukioka's generalized Mukai conjecture for Fano manifolds

Let $X$ be a complex $n$-dimensional Fano manifold with Picard number ${\rho}_X$. For every extremal ray $R$ of $X$, define its length by

$$l(R):=\min\{(-K_X\cdot C)\mid C\subset X\text{ is a rational curve with }[C]\in R\}.$$

Let $l_X$ be the minimum of $l(R)$ over all extremal rays $R$ of $X$. Tsukioka's generalized Mukai conjecture. One has

$${\rho}_X(l_X-1)\leq n,$$

and equality holds if and only if

$$X\simeq(\mathbb{P}^{l_X-1})^{{\rho}_X}.$$

This is presented as a generalization and refinement of Mukai's conjecture for Fano manifolds; the supplied source context does not specify whether it is open or resolved.