Campana's numerical cotangent bound for special manifolds

Let $X$ be a compact Kähler manifold that is special, and let $p>0$. For every rank-one coherent subsheaf $L\subset\Omega_X^p$, the numerical cotangent bound conjecture. One has

$$\nu(X,L)<p.$$

This was proposed as a relation between numerical and Kodaira dimensions and is presented as a conjectural strengthening relevant to special manifolds; no proof or disproof is supplied here.