The folklore conjecture on the lower bound of Seshadri constants

Let $X$ be an irreducible projective variety, and let $L$ be a nef and big line bundle on $X$. Here, $\b5(L)$ denotes the Seshadri constant of $L$.

Seshadri lower-bound conjecture.

$$\epsilon(L)\geq 1.$$

This lower bound is known in dimension two, but remains open in higher dimensions.