We consider hypersurfaces in (P1)n that contain a generic
sequence of small dynamical height with respect to a split map and project onto
nβ1 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 nβ1
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