Regarding 7, the definition of correlation functions with respect to real-space sites is natural for lattice models and specific systems such as well-localized µ-oxo-bridged transition metals. However, such a construction is more challenging to systematically define for, e.g., Be 2 at short interatomic separation, and (more obviously) atoms like cerium with complicated low-lying states. Regarding 8: As mentioned in our response to point 5, in this work we are interested in quantities and properties of the exact wavefunction or quantities derived from the 2-RDM which can, in principle, be exactly mapped to the exact wavefunction. Although the size-consistency of GHF and subsequent low-order perturbation theories indeed enables qualitatively correct energies at that level of theory to signal correlation regimes in which energies can be predicted tractably, this metric is out of the scope of this work since we are interested in physical properties of exact eigenstates (which, like spin-entanglements, can persist even when the correlation energy is zero). Additionally, there are many ways to break low-order single-reference perturbation theory that are not (at least directly) physically meaningful, including the idea of "artificial" symmetry breaking in the HF reference. In an effort to report on physically-meaningful, i.e. "essential", symmetry breaking, in this work we will report numerical values of ⟨S 2 ⟩ from an unrestricted CCSD wavefunction (vide infra). Finally, we note that, GHF aside, redefining the 0th order Hamiltonian can often lead to qualitatively correct energies from low-order perturbation theories, as in CASPT2 or NEVPT2.