Finite algorithm conjecture for stable graph representations

A stable representation of a graph is an ${\mathcal{M}}$-representation that is a local minimum with respect to the ordering relation defining stability. Finite algorithm conjecture. There exists a finite algorithm to find a stable representation of a given graph. Stable representations provide a framework for studying jammed configurations and maximal disk packings; validating this conjecture would complete the proposed algorithmic strategy for finding such packings. The source does not state whether the conjecture has been resolved.