Bounded integer spectral norm conjecture for pseudo-rotations

Let $(M,\omega)$ be a monotone symplectic manifold admitting a pseudo-rotation. Here $\gamma_\mathbb{Z}$ denotes the spectral norm over the integers, and $\phi^k$ denotes the $k$-th iterate of $\phi$. Bounded integer spectral norm conjecture. Any pseudo-rotation $\phi\in\operatorname{Ham}(M,\omega)$ satisfies

$$\sup_{k\in\mathbb{Z}}\gamma_\mathbb{Z}(\phi^k)<+\infty.$$

The conjecture proposes that the integer-coefficient spectral norm remains uniformly bounded along all iterates of every pseudo-rotation on a monotone symplectic manifold. The source proposes it as a generalization of a preceding theorem, but the supplied context records that the conjecture is disproved.