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 $30 M_{\odot}$ binary merger, we calculate a characteristic echo frequency of $20$ Hz, offering a specific pathway for observational verification via LIGO-Virgo-KAGRA data.