Collatz-Root Hypothesis: A Framework Towards the Collatz Conjecture

The Collatz conjecture asks whether every natural number eventually reaches 1 underiteration of the map f (n) = n/2 if n is even and f (n) = 3n + 1 if n is odd. Despite extensivecomputational verification up to 268, a general proof remains elusive. In this paper, Iintroduce the Collatz-Root Hypothesis (CRH), a structural framework based on backwardexpansion of 1 via predecessor sets. I define Collatz and Collatz roots, construct depth levelsDb up to D100, and present evidence of non-repetition and infinite expansion. CRH assertsthat every number has a distinct Collatz root, that the Collatz root tree expands withoutmerging, and that all numbers ultimately collapse to 1. If CRH holds globally, it implies theCollatz conjecture. My aim is to establish CRH as a base concept for future work towardresolving the conjecture.