Research proof index

Let $u$ and $u'$ be distinct forest tops at level $(k,n,j)$. If a tile $p$ belongs to the tree rooted at $u'$ and its spatial cube lies below the spatial cube of $u$, then its phase center is quantitatively far from that of $u$ at the scale of $p$:

$2^{Z(n+1)}<d_p(\mathcal Q(p),\mathcal Q(u)).$