By constructing a Lyapunov potential function based on 2-adic measure, this paper demonstrates the convergence of the Collatz mapping[1] (the 3n+1 conjecture) in the domain of positive integers[2]. We prove that the mapping operator exhibits a negative drift expectation in the logarithmic measure space and rule out the existence of non-trivial closed cycles through phase analysis of (mod 6) congruence classes. The final results indicate that any orbit starting from n∈N+ must intersect with the attractor set of powers of two, S={2k}, within finite steps, leading to a collapse toward the identity element 1. Keywords: Collatz Conjecture; 2-adic Valuation; Lyapunov Stability; Ergodicity of Integer Sequences; Logarithmic Drift; Phase Transition in Arithmetic Dynamics; Attractor Basins.