The Main Question on birational minimal models

Let $X$ be an algebraic variety. A variety is of semi-negatively curved or Kodaira--Iitaka type if $\int_C c_1(X)\leq 0$ for every curve $C\subset X$ and there is a unique morphism $I_X:X\to I(X)$ such that $\int_Cc_1(X)=0$ if and only if $C$ is contained in a fiber of $I_X$. It is of positive fiber type if there is a unique morphism $m_X:X\to M(X)$ such that $M(X)$ is semi-negatively curved and $c_1(X)$ is positive on all the fibers, with $\dim M(X)<\dim X$.

The Main Question. Every algebraic variety $X$ is birational to a variety $X^{\rm m}$ that is either of semi-negatively curved or Kodaira--Iitaka type, or of positive fiber type.

This is presented as the precise version of the first Main Question and as a proposed birational simplification of arbitrary varieties. The excerpt does not state whether it has been resolved.