Identifiability of Differential-Algebraic Systems

The paper’s Theorem 2 states a rank condition for local identifiability and proves it via a 1-fullness linear-algebra criterion applied to a lifted map Ψ, then invokes the Constant Rank Theorem to pass from linearized uniqueness to local nonlinear uniqueness . The candidate solution establishes the same rank condition and proves identifiability by showing that the level set S = {(θ,z): G(θ,z)=const} is a submanifold with vertical tangents, forcing the θ-projection to be locally constant; equality of outputs on an interval gives equality of finite jets, hence membership in S, which implies θ′=θ0. This differs in style from the paper (geometric level-set argument vs. the paper’s 1-fullness/Ψ argument) but is logically consistent with the paper’s hypotheses and conclusion. Both are correct under the same local smoothness and consistency assumptions (e.g., x0 ∈ L, smooth F and h) .