Conformal GeometroDynamics

We propose Conformal Geometrodynamics (CGD) to describe exploration dynamics in information spaces. Eliminating external parameters, we construct a closed dynamical system governed entirely by six geometric axioms on a thermodynamic contact manifold M(x^i, p_i, S). We derive the Exploration-Exploitation Equilibrium (EEE) theorem, ρ u^j ∇_i p_j = ∇_i(ρ S), as the governing equation of local dynamics, establishing an exact equilibrium between the inertia of conviction and entropic pressure. Furthermore, we demonstrate that thermodynamic irreversibility and the arrow of time autonomously emerge directly from the contact Hamiltonian flow. This framework subsumes conventional information geometry as a local limit, reformulating exploration as pure geometry.