  In a companion paper we introduced a kinematical arena for the discussion of
the constraints of canonical quantum gravity in the spin network representation
based on Vassiliev invariants. In this paper we introduce the Hamiltonian
constraint, extend the space of states to non-diffeomorphism invariant
``habitats'' and check that the off-shell quantum constraint commutator algebra
reproduces the classical Poisson algebra of constraints of general relativity
without anomalies. One can therefore consider the resulting set of constraints
and space of states as a consistent theory of canonical quantum gravity.
