Correlation functions in linear chaotic maps

For the core claim—vanishing of connected two-point functions of local operators at nonzero time separation in the spatiotemporal cat map—the paper gives a correct proof via a Green’s-function/light-cone expansion and sitewise character orthogonality, yielding factorization ⟨Fn,t Gm,0⟩ = ⟨Fn,t⟩⟨Gm,0⟩ (their Eqs. (4.10)–(4.18)) . The candidate model provides a different, also correct, proof based on integer light-cone coefficients and eliminating Fourier modes using “corner” sites; it also correctly notes the equal-time same-site caveat. Where the paper offers a belief (not a full proof) about multipoint factorization, the model sketches a recursive corner-elimination proof; that sketch needs an additional non-degeneracy condition ensuring at least one unshared corner at each descent step. Thus, on the main two-point statement, both are correct with different proofs; on general multipoint factorization, the paper is intentionally noncommittal and the model’s extension is plausible but under-justified.