Hubble-Weighted Cosmological Fractal Recursion: A Discrete Planck-Time Dynamical System for Cosmological Evolution

This paper presents a discrete Planck-time dynamical system for cosmological evolution derived directly from the Friedmann kinematic relation . The model defines a conformal recursion map acting on a five-component cosmological state vector encoding spatial scale, vacuum energy density, matter density, radiation density, and scalar field amplitude.The recursion operates geometrically on the scale degree of freedom while densities evolve via standard conservation laws. The Friedmann equation is imposed as an explicit closure relation, making the system dynamically self-contained. A physical admissibility gate enforces Planck-scale bounds, providing natural regularization at the boundary where semiclassical physics breaks down. Three theorems are established: exact FRW recovery at every Planck step, self-consistent preservation of the Friedmann constraint by induction, and exact reproduction of the standard inflationary e-fold relation without parameter tuning.The formalism constitutes a parameter-free, physically regulated discrete conformal flow over cosmological phase space, offering a novel unified framework for cosmological evolution at Planck resolution.