IDENTIFICATION OF A REVERSIBLE CATENARY SYSTEM BY THE MEASURE OF ONE COMPARTMENT

The paper asserts that a reversible catenary compartmental system is identifiable from measuring only the primary compartment and sketches an algorithm based on decomposing x1(t) into a sum of exponentials, introducing Δ-moments, and then recursively recovering parameters (Theorem 3.4) . However, two issues undermine completeness: (i) a key formula used to compute k1e from x1(t) is misstated in the text (the paper writes k1e = −a ∑ β1_i/λ_i instead of the dimensionally consistent k1e = −a / ∑ (β1_i/λ_i)), and this misstatement is then used in the algorithm to compute k12 and hence k21 ; (ii) the step “determine β1_i and λ_i by minimizing J” is invoked as if it established structural identifiability, but no uniqueness argument is provided for that inverse problem (beyond asserting recoverability of eigenvalues and β1 from a single output) . By contrast, the candidate solution gives a complete, constructive identifiability proof via the (1,1) resolvent, a finite J-fraction decomposition, and a backward recursion that uniquely recovers all rates under the stated reversible catenary assumptions. The result established by the model matches the paper’s main claim, but with a cleaner, fully self-contained argument.