Self-rational-map conjecture for very general quintic threefolds

Let $X$ be a very general quintic threefold in $\mathbb{P}^4$, and let $\phi\colon X\dashrightarrow X$ be a rational self-map. Self-rational-map conjecture. The map $\phi$ cannot have degree greater than one, that is, there is no such map with

$$\deg \phi>1.$$

This conjecture extends the paper's result on the triviality of self-rational maps for a general K3 surface to quintic Calabi–Yau threefolds. Its resolution is not given in the supplied text.