Valuation-Mean Classification for the Accelerated Collatz Map: A Conditional Lyapunov Criterion, the Critical Boundary log2 3, and the Cycle Window

Ongoing formalization and the latest developments in this research program are available in the EOC Lean verification repository: https://github.com/innerlightr-wq/eoc-lean-verification This revised note studies the accelerated odd-only Collatz map using the logarithmic Lyapunov potential V(m)=\log_2 m. The main rigorous result is a conditional convergence criterion: if the global Cesàro mean of the 2-adic valuation discharges satisfies \liminf \bar D_N>\log_2(10/3), then the orbit reaches 1 in finite time. The paper does not prove the Collatz conjecture. Instead, it identifies the valuation profile that any hypothetical non-terminating orbit would have to maintain: such an orbit must satisfy \liminf \bar D_N\leq\log_2(10/3). The revision clarifies the distinction between exact algebra, uniform-residue heuristic drift, leakage-coordinate reparameterization, and the remaining pointwise orbit obstruction.