Orbifold fundamental group finiteness conjecture for slope rationally connected pairs

Let $(X,D)$ be a smooth connected orbifold pair as above, with $D$ integral, and let $\pi_1(X,D)$ and $\pi_1^{\mathrm{alg}}(X,D)$ denote its topological and algebraic orbifold fundamental groups. Write $D(+\infty)$ for the union of components of $D$ having multiplicity $+\infty$.

Orbifold fundamental group conjecture. The group $\pi_1(X,D)$ is almost abelian, finite if $(X,D)$ is klt, and trivial if $(X,D)$ is purely logarithmic or if $h^0(X,\Omega^1(X,\operatorname{Log}(D_1)))=0$; the same assertions hold for $\pi_1^{\mathrm{alg}}(X,D)$.

The claim is presented as a consequence of the preceding special-orbifold fundamental-group conjecture, since slope rationally connected orbifold pairs are special. Its resolution status is not given in the supplied text.