Mixing of the Collatz Block-Shift Map via Descent Decorrelation: A Complete Autonomous Proof

We prove that the Collatz block-shift map Φ : ℤ₂ → ℤ₂ is mixing in L²(ℤ₂, μ) with an explicit exponential rate. The proof reduces to two independent lemmas: a lower bound δ ≥ 5/8 on the frequency of descent events (Lemma A) and full decorrelation across every descent (Lemma B, with exact zero covariance for t ≥ r and explicit bound 2-t/2 for t < r). Exponential mixing of Φ follows by a renewal argument. Mixing implies ergodicity of the accelerated Collatz map T₃, and unique ergodicity of Φ (via topological mixing on the compact space ℤ₂) forces every positive integer into the classical Collatz cycle (1,4,2). All steps are fully rigorous and autonomous.