Current uniqueness conjecture for biased random networks on lattices

Let $({\mathbb{Z}}^d,\, \mathbf{C}_{\lambda_1},\, \mathbf{C}_{\lambda_2},\,p)$ be a biased disordered random network, with $d\geq 3$ and $0<\lambda_1\leq 1<\lambda_2$. A network is current unique when its associated electrical current is unique. Current uniqueness conjecture. Almost surely, every transient biased $({\mathbb{Z}}^d,\, \mathbf{C}_{\lambda_1},\, \mathbf{C}_{\lambda_2},\,p)$ is current unique. The conjecture is presented as a natural question about uniqueness of currents in transient biased networks; no resolution is given in the source.