Unimodality conjecture for Betti tables of powers

Let $I\subseteq R$ be an equigenerated homogeneous ideal generated in degree $r$. For each pair of indices $(i,j)$, consider the graded Betti numbers $\beta_{i,j+dr}(I^d)$ as $d$ varies. Unimodality conjecture. There exist integers $1\leq D_1\leq D_2\leq\infty$ such that

$$\beta_{i,j+dr}(I^d)\neq 0$$

for every $d$ with $D_1\leq d\leq D_2$, while

$$\beta_{i,j+dr}(I^d)=0$$

for every $d<D_1$ or $D_2<d$. This proposes that, for each Betti-diagram position, nonvanishing occurs on a single interval of powers. The claim is presented as a general pattern for powers of equigenerated homogeneous ideals; no proof or resolution is supplied in the source, so it remains open.