  We study the trace of the incipient infinite oriented branching random walk
in $\mathbb{Z}^d \times \mathbb{Z}_+$ when the dimension is $d = 6$. Under
suitable moment assumptions, we show that the electrical resistance between the
root and level $n$ is $O(n \log^{-\xi}n )$ for a $\xi > 0$ that does not depend
on details of the model.
