The distinction between the local coulomb integral and the non-local exchange integral is a foundational definition in quantum chemistry and electronic structure theory that does not require citation.
The claim is a definitional statement in quantum chemistry regarding the spatial nature of Coulomb and exchange integrals (Coulomb operator depends on local charge density, whereas exchange involves nonlocal coordinate-dependent electron correlation). None of the retrieved papers directly address or test this fundamental physical definition, making it common knowledge within the domain.