Minimality of the counterexample construction

Determine whether the twelve-node and forty-two-independent-coefficient construction provides minimal node and edge counts for a counterexample in which generic local identifiability fails to imply generic global identifiability for linear networks with fixed topology, independently unknown edge coefficients, and partial excitation and measurement.

Background

The paper constructs a twelve-node linear network with forty-two independent edge coefficients that has generic local identifiability but fails generic global identifiability, including under a common spectral-radius bound. The authors explicitly describe these node and edge counts as constructive upper bounds rather than minimal values.

Determining whether a smaller network or a network with fewer independent unknown edges can exhibit the same separation would clarify the smallest possible counterexample within the scalar linear-network formulation considered in the paper.