  The Gopakumar-Vafa conjecture predicts that the BPS invariants of a
symplectic 6-manifold, defined in terms of the Gromov-Witten invariants, are
integers and all but finitely many vanish in every homology class. The
integrality part of this conjecture was proved by Ionel and Parker. This
article proves the finiteness part. The proof relies on a modification of Ionel
and Parker's cluster formalism using results from geometric measure theory.
