A Generalized Modulo-m Extension of Collatz-Type Maps

This paper introduces a generalized modular arithmetic framework extending the classic 3n+1 Collatz mapping to arbitrary modulo-m base systems. Using a probabilistic heuristic distribution, we analyze the long-run branching mechanics of these maps and prove that the expected geometric growth factor satisfies G(m) < 1 for all m ≥ 2. While formulated independently by the author, this framework shares structural equivalence with generalized multi-branch systems explored in prior number theory literature.