However, essential disparity can arise since a superposition of localized objects inherits the properties of isolated objects while the superposition of defects in the initially homogeneous ordered background brings some disorder and merely refines the overall properties of the background. For instance, the superposition of infinitely many instantons and anti-instantons is not a configuration with a finite classical action but it maintains the property to have integer-valued topological charge. On the contrary, the configuration obtained by implanting infinitely many domain wall defects into the Abelian covariantly constant (anti-)self-dual field can have any real value of the mean topological charge density as well as any real value of topological charge fraction per domain [@NK3]. Both configurations can be seen as lumps of the topological charge density distributed in the Euclidean space-time like in Fig.\[Fig:kink\_network\] or in the lattice configurations [@Moran:2008xq; @Ilgenfritz:2007xu]. However, in the instanton picture each lump carries an integer charge while in the treatment of global minima the charge is any real, irrational, for instance, number. This can have dramatic consequences for the fate of $\theta$ parameter in QCD and the natural resolution of the strong CP-problem [@NK3].

In the Euclidean formulation, the statement of the problem starts with 