When does static correlation scale to the high-density limit as exchange does?

In density functional theory, the exchange-correlation energy is usually decomposed as the sum of exchange and correlation contributions. In the absence of static correlation, this decomposition can be made by uniform coordinate scaling to the high-density limit, because the exchange part dominates in this limit. The estimate of static correlation provided by semilocal, global hybrid, and some more-advanced approximate exchange-correlation functionals scales up as exchange does in this limit. Here we argue that a proper estimate of static correlation should scale up in magnitude less strongly than exchange in the high-density limit, except in special circumstances. Such a special circumstance can occur when there is an exact degeneracy at the non-interacting Fermi level, or when another limit is taken first, in which a degeneracy develops between occupied and unoccupied Kohn-Sham orbital energies. Examples of the latter case are the H2 molecule as the bond length is stretched to infinity, and the four-electron atomic ion as the nuclear charge tends to infinity.