The Gromov–Yomdin type conjecture for categorical entropy

Let $X$ be a smooth projective variety over $\a0\mathbb{C}$, and let $\a0\Phi \in \operatorname{Aut}(D^b(X))$ be an autoequivalence. Write $[\Phi]: K_{\mathrm{num}}(X) \to K_{\mathrm{num}}(X)$ for the induced linear map on the numerical Grothendieck group of $X$, and let $\rho([\Phi])$ denote its spectral radius. Gromov–Yomdin type conjecture. One has

$$h_{\mathrm{cat}}(\Phi)=\log\rho([\Phi]).$$

This proposes a categorical analogue of the Gromov–Yomdin formula, extending the previously stated equality for pullbacks by surjective endomorphisms. The source provides no resolution of the conjecture.