  In the Approval Participatory Budgeting problem an agent prefers a set of
projects $W'$ over $W$ if she approves strictly more projects in $W'$. A set of
projects $W$ is in the core, if there is no other set of projects $W'$ and set
of agents $K$ that both prefer $W'$ over $W$ and can fund $W'$. It is an open
problem whether the core can be empty, even when project costs are uniform. the
latter case is known as the multiwinner voting core.
  We show that in any instance with uniform costs or with at most four projects
(and any number of agents), the core is nonempty.
