where C represented a covering of a lattice by nearest neighbor dimers. Each such covering is weighted equally. In a mean field approximation, the RVB state can be written in terms of a Gutzwiller projection, and displays a superconducting phase transition per the Kosterlitz–Thouless mechanism. However, a rigorous proof for the existence of a superconducting ground state in either the Hubbard or the t-J Hamiltonian is not yet known. Further the stability of the RVB ground state has not yet been confirmed.