Strong Lang–Vojta conjecture IV

Let $k$ be an algebraically closed field of characteristic zero. For a projective variety $X$ over $k$, consider strong pseudo-Brody and pseudo-Kobayashi hyperbolicity, pseudo-Mordellicity, pseudo-arithmetic hyperbolicity, pseudo-grouplessness, pseudo-algebraic hyperbolicity, pseudo-boundedness, pseudo-$1$-boundedness, pseudo-geometric hyperbolicity, and being of general type. Strong Lang–Vojta conjecture IV. All ten listed properties are equivalent. The source identifies several implications as known, but the full equivalence is presented as conjectural.