We establish a sharp threshold on variable occurrences that guarantees polynomial‑expected‑time convergence of the Moser–Tardos (MT) algorithm and the pure random‑walk WalkSAT on 3‑CNF formulas. Specifically, if a formula with $m$ clauses has each variable appearing at most twice, both algorithms finish in $O(m)$ expected updates. This bound is tight: we construct an infinite family where each variable appears at most three times and both algorithms need $2^{\Theta(\sqrt{m})}$ expected updates. Remarkably, this dynamical transition occurs strictly below the classical NP‑completeness threshold at occurrence degree four. Moreover, we prove exponential separations on satisfiable 3‑CNF instances. On one family WalkSAT terminates after $O(m^4)$ expected flips while MT requires $2^{\Omega(m)}$ resampling steps; on another family MT finishes in $O(m)$ expected resamplings whereas WalkSAT needs $2^{\Omega(m)}$ flips. The constructions exploit the distinct ways single‑variable flips and simultaneous resampling propagate local violations, showing that the expected runtimes of the two algorithms are incomparable even up to polynomial factors on the same inputs.\n\nReview: The paper precisely characterizes how variable‑occurrence limits affect MT and WalkSAT performance and provides concrete families that exhibit exponential gaps, offering fresh insight into the fundamental differences between local search and resampling methods.