  We propose and support the possibility that the shape of topological density
2-point function in pure-glue QCD is crucially, and possibly entirely,
determined by the space-time folding (geometry) of the double-sheet
sign-coherent structure of Ref.[1], while the distribution of topological
density within individual sheets only determines the overall magnitude of the
correlator at finite physical distances. A specific manifestation of this,
discussed here, is that the shape of the correlation function (encoding e.g.
the masses of pseudoscalar glueballs) is reproduced upon the replacement q(x)
-> sgn(q(x)), i.e. by considering the double sheet of the same space-time
geometry but with constant magnitude of topological density. Combined with
previous results on the fundamental topological structure, this suggests that a
collective degree of freedom describing topological fluctuations of QCD vacuum
can be viewed as a global space-filling homogeneous double membrane. Selected
possibilities for practical uses of this are discussed.
