IDENTIFIABILITY OF LINEAR COMPARTMENTAL TREE MODELS

The paper proves the exact classification for SISO bidirectional tree models (identifiable iff the input and output are equal or adjacent and there is at most one leak) and supplies a leaf-attachment framework plus a coefficient-counting criterion to show necessity and sufficiency. The candidate solution reaches the same classification via a different proof flavor (forest/minor expansions with a reparametrization by node-sums and 2-cycle products, plus an induction/leaf-attachment step and a rank defect argument when the input–output distance is ≥2). Minor issues in the candidate solution include a slightly misstated count of the number of coefficients in the leakless case and an unnecessary ‘move the leak’ step during induction, but these do not affect the final conclusion.