  We calculate the lattice two-point function of topological charge density in
pure-glue QCD using the discretization of the operator based on the overlap
Dirac matrix. Utilizing data at three lattice spacings it is shown that the
continuum limit of the correlator complies with the requirement of
non-positivity at non-zero distances. For our choice of the overlap operator
and the Iwasaki gauge action we find that the size of the positive core is ~2a
(with a being the lattice spacing) sufficiently close to the continuum limit.
This result confirms that the overlap-based topological charge density is a
valid local operator over realistic backgrounds contributing to the QCD path
integral, and is important for the consistency of recent results indicating the
existence of a low-dimensional global brane-like topological structure in the
QCD vacuum. We also confirm the divergent short-distance behavior of the
correlator, and the non-integrable nature of the associated contact part.
