  Quantum holonomy theory is a candidate for a non-perturbative theory of
quantum gravity coupled to fermions. The theory is based on the QHD(M) algebra,
which essentially encodes how matter degrees of freedom are moved on a
three-dimensional manifold. In this paper we commence the development of a
lattice-independent formulation. We first introduce a flow-dependent version of
the QHD(M) algebra and formulate necessary conditions for a state to exist
hereon. We then use the GNS construction to build a kinematical Hilbert space.
Finally we find that operators, that correspond to the Dirac and gravitational
Hamiltonians in a semi-classical limit, are background independent.
