  Let $G$ be a compact and connected Lie group. The Hamiltonian $G$-model
functor maps the category of symplectic representations of closed subgroups of
$G$ to the category of exact Hamiltonian $G$-actions. Based on previous joint
work with Y. Karshon, the restriction of this functor to the momentum proper
subcategory on either side induces a bijection between the sets of isomorphism
classes. This classifies all momentum proper exact Hamiltonian $G$-actions (of
arbitrary complexity).
  As an extreme case, we obtain a version of the Eliashberg cotangent bundle
conjecture for transitive smooth actions. As another extreme case, the momentum
proper Hamiltonian $G$-actions on contractible manifolds are exactly the
symplectic $G$-representations, up to isomorphism.
