Collatz-Root Hypothesis: A Framework Towards the Collatz Conjecture

The Collatz conjecture asks whether every natural number eventually reaches 1 under iteration of the map f (n) = n/2 if n is even and f (n) = 3n + 1 if n is odd. Despite extensive computational verification up to 268, a general proof remains elusive. In this paper, I introduce the Collatz-Root Hypothesis (CRH), a structural framework based on backward expansion of 1 via predecessor sets. I define Collatz and Collatz roots, construct depth levels Db up to D100, and present evidence of non-repetition and infinite expansion. CRH asserts that every number has a distinct Collatz root, that the Collatz root tree expands without merging, and that all numbers ultimately collapse to 1. If CRH holds globally, it implies the Collatz conjecture. My aim is to establish CRH as a base concept for future work toward resolving the conjecture.