  We extend the theory of diffeomorphism-invariant spin network states from the
real-analytic category to the smooth category. Suppose that G is a compact
connected semisimple Lie group and P -> M is a smooth principal G-bundle. A
`cylinder function' on the space of smooth connections on P is a continuous
complex function of the holonomies along finitely many piecewise smoothly
immersed curves in M. We construct diffeomorphism-invariant functionals on the
space of cylinder functions from `spin networks': graphs in M with edges
labeled by representations of G and vertices labeled by intertwining operators.
Using the `group averaging' technique of Ashtekar, Marolf, Mourao and Thiemann,
we equip the space spanned by these `diffeomorphism-invariant spin network
states' with a natural inner product.
