  This is the third paper in a series outlining an algorithm to construct
finite states of quantum gravity in Ashtekar variables. In this paper we treat
the case of the Klein--Gordon field quantized with gravity on the same footing.
We address the full theory, outlining the solution to the constraints and the
construction of the corresponding wavefunction of the universe. The basic
method for the full theory is to expand the constraints relative to the
solution for the pure Kodama state and rewrite them in the form of a
generalized nonlinear group transformation of the CDJ matrix, viewed as a
nine-dimensional vector. We then outline a prescription for finding the fixed
point of the flow, and the corresponding generalized Kodama state for the full
theory is constructed. The final solution is expressed in an asymptotic series
in powers of model-specific matter inputs, suppressed by a small dimensionless
constant, relative to the pure Kodama state. We discuss this expansion from
different perspectives. Lastly, we explicitly show how the solution to the
quantized constraints establishes a wavefunction of the universe with a
predetermined semiclassical limit built in as a boundary condition on quantized
gravity in the full theory.
