Investigated is a hypothetical mathematical framework describing a dynamical crossing between two otherwise orthogonal and causally unbridged (n)-dimensional spaces or spacetimes, interpreted here as distinct universes. The crossing is represented by a localized, time-dependent kernel that temporarily modifies the effective mode spectrum of the coupled system.The central object is a non-homogeneous para-topological crossing kernel which induces a transient mixing between the two spaces without requiring a permanent geometric bridge. In an effective field description, the crossing may generate a temporarily negative effective squared frequency,, thereby producing a transient tachyonic regime. Shown is, that this does not necessarily imply a persistent tachyonic degree of freedom after the crossing. Instead, the process can be represented by a Bogoliubov transformation characterized by coefficients and . Subsequently introduced ergo is an effective entropy/information sector and investigated is its feedback on the crossing dynamics. The resulting system admits stabilizing, destabilizing and potentially symmetry-breaking regimes. In particular, entropy transport between the two universes can be distinguished mathematically from entropy production, allowing the possibility of asymmetric post-crossing states even when the initial configuration is symmetric. May be, that the phenomenon of matter transportation or of radiation energy could occur between the two space manifolds over the crossing zone ("skip effect") but this special situation is discussed in a later paper. Two similiar crossing zones between the same universes then will be defined as a u201econgruence".The present work however concentrates on and constitutes a phenomenological mathematical framework rather than a claim of an established physical theory. Its principal purpose is to identify the necessary dynamical structures, stability criteria and falsifiable mathematical consequences of such a crossing scenario. Some more treatises to this theme discussing intesively these sort of phenomena, will follow.