Traditional astrophysical models rely on scale-dependent approximations, such as exponential Silk damping in the early universe and fluid-dynamic thermal dissipation in galactic structures. This paper introduces the Infinite Fractal Descent (IFD) framework, proposing that macroscopic cosmological structures are not classical continuums but strict, infinitely descending geometric projections of Quantum Electrodynamics (QED). By replacing scale-dependent smoothing with a fixed fine-structure constant () acting as a universal, non-running scaling operator, IFD bridges General Relativity and Quantum Mechanics. We propose four observational tests utilizing raw telemetry from the Chandra X-ray Observatory, the Juno spacecraft, the Parkes radio telescope, and the Planck satellite. By applying the -operator to the acoustic pressure waves of the Perseus cluster, the magnetic micro-pulse architecture of the Vela pulsar, the recursive plasma dispersion of the Jovian magnetosphere, and the high-multipole angular power spectrum of the Cosmic Microwave Background (CMB), this framework provides strict falsifiability criteria to determine if macroscopic physical systems possess unbroken harmonic continuity into the quantum foam.