  Collider events with multi-stage cascade decays fill out the kinematically
allowed region in phase space with a density that is enhanced at the boundary.
The boundary encodes all available information about the spectrum and is well
populated even with moderate signal statistics due to this enhancement. In
previous work, the improvement in the precision of mass measurements for
cascade decays with three visible and one invisible particles was demonstrated
when the full boundary information is used instead of endpoints of
one-dimensional projections. We extend these results to cascade decays with
four visible and one invisible particles. We also comment on how the topology
of the cascade decay can be determined from the differential distribution of
events in these scenarios.
