Hacon–McKernan's uniformity conjecture for the Iitaka fibration

Let $X$ be a smooth projective variety of dimension $n$ and Kodaira dimension $\kappa$, and let $\phi_{|mK_X|}$ denote the rational map defined by the pluricanonical linear system $|mK_X|$. The Iitaka fibration of $X$ is the fibration associated with its pluricanonical sections, and a positive integer is sufficiently divisible when it satisfies the divisibility conditions required for this map to be defined. Hacon–McKernan's conjecture. There is a positive integer $m_{n,\kappa}$ such that for any $m\geq m_{n,\kappa}$ sufficiently divisible, $\phi_{|mK_X|}$ is birationally equivalent to the Iitaka fibration of $X$ for all smooth projective varieties $X$ of dimension $n$ and Kodaira dimension $\kappa$. This conjecture asserts uniformity of the pluricanonical realization of the Iitaka fibration across varieties with fixed dimension and Kodaira dimension; the supplied source does not indicate whether it has been resolved.