Infinite Fractal Descent and the Geometric Origins of Prime Distribution: A Topological Derivation of Goldbach's Conjecture

Abstract: For nearly three centuries, Goldbach's Conjecture has remained an unproven pillar of additive number theory. This paper proposes a novel resolution by re-framing prime distribution as a geometric requirement of a discrete, recursive spatial substrate defined as Infinite Fractal Descent (IFD). Operating under the postulate that the vacuum is a dense mechanical plenum of nested, rotating spheres, we treat even integers as discrete computational volumes corresponding to the Universal Tick (). By deriving the Prime Fractal Density formula () from the IFD mass-density relation, we demonstrate that the Hardy-Littlewood twin prime constant represents a geometric requirement for maintaining topological continuity. Under this framework, Goldbach's Conjecture is reinterpreted as a mandatory structural symmetry requirement of a discrete universe, mathematically precluding the existence of "topological holes" within the prime additive field.