With the practical prospect of second order perturbation theory in mind, we now want to ask the question: Are there regularisers on this manifold, which recreate the exact correlation energy at second order? Not only is there a manifold of regularisers fulfilling this property, they are also derivable from the ground state density alone. We present a formal proof of this theorem in the appendix. Their construction requires no knowledge of t-amplitudes, orbitals or any other wavefunction properties. Compare this to a hypothetical coupled-cluster doubles (CCD) scheme, whose equation for the doubles amplitudes is modified to always yield the exact amplitudes: Since the full coupled-cluster (fCC) doubles are explicitly dependent on triples and quadruples amplitudes (which in turn depend on higher excited amplitudes), any modified CCD scheme emulating the behaviour of these terms would need access to all information contained within triples, quadruples and higher amplitudes. The amount of required information to generate the exact ground state energy is thus much lower in a regularised second-order perturbation theory than in an equivalent CCD theory.