LQC is a subset, a symmetry reduced minisuperspace of LQG, which appears to have a Hamiltonian with a good semiclassical limit that reproduces GR. First, Randano papers addresses Witten's earlier paper on Kodama's state being nonrenormalizable. Now, thanks to Marcus, it appears Eyo Eyo Ita paper, Existence of generalized semiclassical Kodama states 1-3, http://arxiv.org/abs/gr-qc/0703052, that LQG apparently with the presence of matter, has GR as part of its semiclassical limit which is deSitter spacetime. If this is true it would appear that LQG has completed a major milestone, and is now a "theory of quantum gravity" -- the Hamiltonian is now able to reproduce GR at distances much larger than the planck distance. The claim has been that string theory is the only game in town, in that its long distance graviton scattering amplitude matches that of GR reframed as a QFT. There are doubts, such as that it is not background independent, that its calculations are down in 10 dimensions with unbroken supersymmetry, but LQG it is alleged does not even reproduce classical spacetime. It appears in these papers that the Kodama state gives LQG reproduction of GR.