Moving on to the problem of ST in LQG: Hamiltonian formulation of GR in an attempt to apply canonical quantization; belief is that resultant Hilbert basis is spin network basis, and these spin networks provide the fundamental 3-d spatial structure [and these networks can be considered eigenstates of geometrically-interpreted operators]

Thus: space comes out as superposition of spin network eigenstates — i.e., no well-defined geometric properties