Let nonnegative coefficients $c_S$ be supported on sets of size at most $\ell$, with $\sum_S c_S^2\leq1$. For every $m$, the sum of $\prod_{j=1}^m c_{S_j}$ over double-cover tuples is bounded by a constant depending only on $\ell,m$, not on the underlying coordinate set. We give the explicit, nonoptimal bound $1+3^{\ell(2m+1)2^m}$.

This is the normalized form of Lemma 4.15 needed for the small-coefficient analysis. The proof uses a centered variable equal to 3 with probability 1/4 and -1 otherwise. Its moments vanish at order one and are at least one at every order at least two. Representing it on two Boolean coordinates allows the low-degree moment bound to control all double-cover terms.