Deterministic diffusion in dynamical systems with a tiled phase space

The paper’s 2D proof relies on small-λ Taylor expansions of the Fourier multiplier matrix, then (incorrectly) upgrades them to the exact all-λ identity ρ̃n(λ) = e^{-(5/4)n|λ|^2}ρ̃0(λ) (its Eq. (3.5)), yielding an exact Gaussian at every n. That step is unjustified and false for a finitely supported kernel. By contrast, the model gives the exact convolution formulation on the triangle-center lattice, derives the correct small-λ behavior φ(λ) = 1 - (5/4)|λ|^2 + O(|λ|^4), and invokes the (local) CLT to obtain the Gaussian limit with diffusion constant D = 5/4. The model also correctly frames the hexagon case (odd Λ) via an isotropic finitely-supported step set and CLT. The paper’s main qualitative claim (normal deterministic diffusion) is plausible, but the presented argument is incomplete and contains the above critical step error.