  The bulk distribution of the topological charge density, constructed via HP^1
sigma-model embedding method, is investigated. We argue that the specific
pattern of leading power corrections to gluon condensate hints on a particular
UV divergent structure of HP^1 sigma-model fields, which in turn implies the
linear divergence of the corresponding topological density in the continuum
limit. We show that under testable assumptions the topological charge is to be
distributed within three-dimensional sign-coherent domains and conversely, the
dimensionality of sign-coherent regions dictates the leading divergence of the
topological density. Confronting the proposed scenario with lattice data we
present evidence for indeed peculiar divergence of the embedded fields. Then
the UV behavior of the topological density is studied directly and is found to
agree with our proposition. Finally, we introduce parameter-free method to
investigate the dimensionality of relevant topological fluctuations and show
that indeed topological charge sign-coherent regions are likely to be
three-dimensional.
