Collatz as a Renewal Process on Trailing Bits: Chain Structure, Bit Consumption, and the Ergodic Threshold

We reformulate the Collatz conjecture as an ergodic problem on a renewal process indexed by the trailing 1-bit counter of odd integers under the Syracuse map. We prove eleven structural results, including: (1) a complete characterization of k=1 chains via trailing binary bits; (2) a geometric distribution (with mean 3) for the post-chain 2-adic valuation, independent of chain length; (3) a Zero Carry Lemma that decouples high and low bits at chain boundaries, yielding exact intra-stratum equidistribution; (4) a Bit Consumption Theorem showing that consecutive stays at any renewal state are bounded by the 4-adic valuation; and (5) a critical threshold p_crit ≈ 0.7075 below which convergence is guaranteed, with a 41.5% margin from the standard value. The remaining gap is a quantitative frequency bound (π₅ > 0.085 along every trajectory). A previous claim of deterministic self-limiting behavior is refuted with explicit counterexamples. All results are verified computationally on millions of transitions.