Lang's intermediate pseudo-conjectures

Let $k$ be an algebraically closed field of characteristic zero, let $X$ be a projective variety over $k$, and let $pgeq 1$ be an integer. The notions of general type, pseudo-Mordellicity, pseudo-algebraic hyperbolicity, and pseudo-algebraic boundedness are those defined in the paper. Lang's intermediate pseudo-conjectures. The following conditions are equivalent: $X$ is of general type; there is a proper closed subset $\Delta\subsetneq X$ such that every subvariety $Y\subset X$ of dimension at least $p$ not contained in $\Delta$ is of general type; $X$ is pseudo-Mordellic over $k$; $X$ is pseudo-$p$-Mordellic over $k$; $X$ is pseudo-algebraically hyperbolic over $k$; $X$ is pseudo-$p$-algebraically hyperbolic over $k$; $X$ is pseudo-bounded over $k$; $X$ is pseudo-$p$-algebraically bounded over $k$; $X$ is $\dim(X)$-Mordellic over $k$; $X$ is $\dim(X)$-algebraically-hyperbolic over $k$; and $X$ is $\dim(X)$-algebraically-bounded over $k$. The paper records several implications and special cases, but the equivalence as a whole is not resolved there.