Contact Geometry of Renormalization Group Flow: A Miniversal Unfolding of the A2 Fold Catastrophe

We construct a dynamical system on the exponential constraint manifold S={∑e−Ti=1}S={∑e−Ti=1} equipped with a deformed information metric. We derive the full contact Hamiltonian structure, compute the curvature explicitly, and prove that entropy production is the geodesic divergence rate. We derive the RG flow from the coarse-graining operator and show that the system reduces to an A₂ fold catastrophe with miniversal unfolding. The moduli space is one-dimensional, generated by u=c1ϵ2−c2Ω2u=c1ϵ2−c2Ω2. The contact structure is rigid up to contactomorphism. This establishes a complete universality class for non-equilibrium RG flows.