Rational connectedness conjecture for klt pairs with strictly nef anti-log canonical divisor

Let $(X,\Delta)$ be a projective klt pair. A divisor is strictly nef if it has positive intersection with every complete curve. A projective variety is rationally connected if two general points can be joined by a rational curve.

Rational connectedness conjecture. If $-(K_X+\Delta)$ is strictly nef, then $X$ is rationally connected.

This is a particular case proposed in the paper of the singular Campana–Peternell conjecture. It is motivated by rational connectedness results for smooth projective varieties, but the general klt-pair statement remains open.