Solving the Unsolvable: Where the Cosmic Medium Model Succeeds and Relativity Fails

General Relativity (GR) is undeniably successful in describing gravity within the Solar System, yet it faces critical failures when applied to galactic scales, the entire universe, and extreme conditions. To maintain its validity, it forces physics to postulate invisible entities (dark matter, dark energy) and accept mathematical singularities where physical laws cease to apply. This paper demonstrates how an alternative model based on absolute time and a dynamic cosmic medium resolves these five key paradoxes naturally, without the need for ad-hoc hypotheses. We show that phenomena attributed to dark matter are consequences of the medium's refractive index gradient, that accelerating expansion is interpretable as inertia following a "Great Bounce," and that singularities are replaced by the physical pressure of a compressed medium. Thus, this model not only replicates the successes of GR but also removes its conceptual burdens.