Stephenson's conjecture on electrical-network approximation of Riemann mappings

Let a simply-connected, bounded Jordan domain be approximated by a sequence of electrical networks, for instance networks arising from a sequence of disk packings. Choose conductance constants along the edges of each network according to the conductance formula specified in the source. Stephenson's conjecture. The sequence of discrete potentials and currents converges to the potentials and currents induced by the Riemann mapping. The conjecture proposes that electrical behavior in thin conducting planar domains can be approximated by suitably constructed networks, linking discrete electrical models with conformal mappings. The supplied text does not state whether this conjecture has been resolved.