No Finite Modular Obstructions for the Inverse Collatz Tree

The paper demonstrates a general method for determining if a generalized Collatz-type map (called herein an a, b, c map) has modular obstructions via an exact solution over the accelerated inverse tree formulation. We fully work the case for the Collatz map (3, 1, 2 map) and demonstrate that no finite modular obstructions, equivalently, no modular holes, no profinite obstructions, and that the tree contains infinite representatives at each class.