Structural Identifiability of Series-Parallel LCR Systems

The paper proves that a two-type series–parallel LCR network is locally identifiable iff the number of non-monic coefficients equals the number of parameters (Theorem 1.1), deducing RL via viscoelastic results and RC via duality, and establishing LC by a dedicated alternating-shape factorization and a full-rank matrix argument (Theorem 6.9) . The candidate solution, while reaching the same headline equivalence, relies on a “peeling lemma” based on Euclidean division of impedance/admittance that contains algebraic mistakes (notably for a series-added capacitor) and unjustified structural claims (e.g., that the number of coefficients increases by exactly one at every leaf addition, which is contradicted by the LC tables) . It also asserts an incorrect equivalence between a network and its same-type collapsed reduction. Hence the paper’s result stands, but the model’s proof is flawed.