Fault Localisation in Infinite-Dimensional Linear Electrical Networks

The candidate solution reproduces the paper’s Theorem 2 with the same core ingredients: (i) a block-elimination identity (Definition 3 / Theorem 1) to show exact recovery at the true location ℓ, (ii) a uniform exponential bound on Ψ(Y) from Assumptions 2 and 6 (Lemma 4), and (iii) a Paley–Wiener–type inversion (Proposition 1) with t0 = 3τ to obtain measurable inverse-Laplace signals and time-domain identities. These match the paper’s proof of Theorem 2 (statements (30)–(33)) and its supporting lemmas almost line-for-line, including the growth rate ∥Ψ(Y(s; d))∥ ≤ K e^{3τ Re(s)} on C+_β and the use of Assumption 7 to ensure inversion along Re(s) = β is well-posed . The candidate adds an explicit invocation of the identity theorem to extend equalities from C+_β to C+_α, which is implicit in the paper. A minor clarity issue in the paper is that it casually states Ψ(Y(·; d)) preserves analyticity “by matrix operations,” without noting that Moore–Penrose analyticity requires constant rank; however, the paper’s actual use is restricted to C+_β where constant rank is assumed (Assumption 6), so the argument stands as written .