  Long-range order of a specific kind has recently been found directly in
configurations dominating the regularized QCD path integral. In particular, a
low-dimensional global structure was identified in typical space-time
distributions of topological charge defined via the overlap Dirac matrix. The
presence of the order has been concluded from the fact that the structure
disappears after random permutation of position coordinates in measured
densities. Here we complete the argument for the reality of this structure
(namely the conjecture that its existence is a consequence of QCD dynamics and
not an artifact of the overlap-based definition of lattice topological field)
by showing that the structure ceases to exist after randomizing the space-time
coordinates of the underlying gauge field. This implies that the long-range
order present in the overlap-based topological density is indeed a
manifestation of QCD vacuum, and that the notion of the fundamental structure
(structure involving relevant features at all scales) is viable.
