The Infinite Descent A Fractal Model of Cosmological Singularity and Subatomic Self-Similarity

Current cosmological models struggle to reconcile the deterministic laws of General Relativity with the probabilistic nature of Quantum Mechanics, particularly at the event horizon of black holes. This paper proposes a novel theoretical framework based on Scale Invariance and Infinite Hierarchical Nesting. We hypothesize that the fundamental geometric form of energy concentration—the sphere—acts as a topological threshold between scales. We argue that when matter reaches a critical density within a spherical volume, it does not collapse into a zero-dimensional singularity but undergoes a phase transition into a sub-scale universe. Furthermore, we propose that the speed of light ($c$) is a scale-dependent limit, permitting superluminal velocities at sub-Planck scales. This fractal cosmology offers a unified solution to the singularity problem, defining the Big Bang not as a unique temporal origin, but as a recurring, scale-dependent event of spherical collapse.