Logarithmic bound for confluent-edge-free flows

Let $G$ be a rich flow admissible graph with maximum degree $\Delta$. A pair of edges is confluent when the relevant flow values coincide in the sense used by the paper; a nowhere-zero $k$-flow is a $\mathbb{Z}$-flow with nonzero edge values of absolute value less than $k$.

Confluent-edge-free flow conjecture. Every rich flow admissible graph with maximum degree $\Delta$ has a nowhere-zero $O(\ln(\Delta))$-flow containing no pair of confluent edges.

The source contrasts this with the linear behavior obtained when both confluent and contrafluent pairs are forbidden. It gives no proof or resolution of the proposed logarithmic bound.