Resolution of Schwarzschild Singularities: via Atomic-Scale Rebound Forces

General Relativity predicts a physical singularity at the center of black holes, where density and spacetime curvature diverge to infinity. This paper proposes a resolution to the singularity paradox by introducing a high-order repulsive potential (n=11) that becomes dominant at the atomic scale (10^-10 m). We demonstrate that this modification—termed the "Atomic Seed'' model—preserves standard Schwarzschild dynamics at macroscopic scales, maintaining strict consistency with the 43'' per century perihelion precession of Mercury. By arresting gravitational collapse at a finite radius, the model provides a testable prediction for secondary gravitational wave echoes. For a 30 solar mass binary merger, we calculate a characteristic echo frequency of 20 Hz, offering a specific pathway for observational verification via LIGO-Virgo-KAGRA data.