The Ulrich bundle existence conjecture for polarized varieties

Let $(X,L)$ be a polarized pair, meaning a projective variety $X$ equipped with a polarization $L$, and let an Ulrich bundle mean a vector bundle satisfying the Ulrich conditions with respect to this polarization. Ulrich existence conjecture. Ulrich bundles exist on any polarized pair $(X,L)$. This conjecture is presented as mathematical folklore, and the source expresses skepticism about it; examples are known for many specific polarized varieties, but the general existence question remains open.