Hierarchical Structure of Congruence Classes 4x+1 in the Inverse Collatz Graph}

This paper formalizes a new topological structure for the analysis of the Collatz problem on the domain of odd integers A paradigm shift is proposed where the fundamental unit of analysis is not the individual node, but the Congruence Branch (infinite sequences generated by 4x+1). A system of Branch Weight is introduced, organizing the graph into discrete hierarchical layers (tributaries), resolving the topological location of any odd integer via its structural distance to the trivial singularity. Likewise, boundary conditions imposed by modular arithmetic (multiples of 3) are defined, which dictate connectivity between levels.