Michel–Venkatesh mixing conjecture for shifted packets

In the setting of shifted packets $P_D^{\mathrm{shifted}}$ on $X_1\times\cdots\times X_r$, assume individual equidistribution, or assume $k_1=\dots=k_r=1$. For every pair $i\ne j$ with $k_i=k_j$ and $\mathbb{G}_i=\mathbb{G}_j$, require

$$\mathrm{N}\left(t_D^{i}{t_D^{j}}^{-1}\right)\xrightarrow[D\to\infty]{}\infty,$$

where $\mathrm{N}(t)$ is the least ideal norm among invertible ideals in the class $t$. Michel–Venkatesh mixing conjecture. If this condition is satisfied, then $P_D^{\mathrm{shifted}}$ equidistributes to

$$m_{X_1}\otimes\dots\otimes m_{X_r}.$$

The norm-divergence condition excludes bounded-level Hecke correlations and is presented as the only obstruction to product equidistribution in the stated setting.