G model $(G^* ,\mathbb{P})$ satisfies the weak [SMR]{} assumption if $(G^* ,\mathbb{P})$ satisfies the CMC and $|S(G^*)| \leq |S(G)|$ for every DAG $G$ such that $(G ,\mathbb{P})$ satisfies the CMC and $G \notin \mathcal{M}(G^*)$.  