  We consider hypersurfaces in $(\mathbb{P}^1)^n$ that contain a generic
sequence of small dynamical height with respect to a split map and project onto
$n-1$ coordinates. We show that these hypersurfaces satisfy strong coincidence
relations between their points with zero height coordinates. More precisely, it
holds that in a Zariski-open dense subset of such a hypersurface $n-1$
coordinates have height zero if and only if all coordinates have height zero.
This is a key step in the resolution of the dynamical Bogomolov conjecture for
split maps.
