Research proof index

Let $u_1\ne u_2$ be forest tops with $\mathcal I(u_1)\le\mathcal I(u_2)$. If a tile $p$ belongs to either tree and its spatial cube overlaps $\mathcal I(u_1)$, then the two top frequencies are separated at the scale of $p$ by

$2^{Zn/2}\le d_p(\mathcal Q(u_1),\mathcal Q(u_2)).$