Geodesic stability for memoryless binary long-lived consensus

The determination of the (in-)stability of the long-lived consensus problem is a fundamental open problem in distributed systems. We concentrate on the memoryless binary case with geodesic paths. For this case, we offer a conjecture on the instability, measured by the parameter inst, exhibit two classes of colourings which attain the conjectured bound, and improve the known lower bounds for all colourings. We also introduce a related parameter, winst, which measures the stability only for certain geodesics, and for which we also prove lower bounds.