Campana's Kobayashi pseudo-distance conjecture for the core

Let $X$ be a projective manifold, let $c_X:X\to\mathcal C(X)$ be its core, and let $\Delta(c_X)$ denote the orbifold divisor on the core induced by this fibration. Let $d_X$ be the Kobayashi pseudo-distance of $X$.

Campana's core-distance conjecture. The Kobayashi pseudo-distance is the pullback of the orbifold Kobayashi pseudo-distance on the core:

$$d_X=c_X^*\delta_X,\qquad \delta_X=d_{(\mathcal C(X)/\Delta(c_X))}.$$

This refines the preceding description of the Kobayashi pseudo-distance by identifying the distance on the core with its orbifold Kobayashi pseudo-distance. Its resolution is not given in the source and remains open.