The Planck Pixel: Spacetime Granularity and the Regularization of Singularities

Classical General Relativity predicts the formation of infinite singularities, a breakdown of physical laws. In the AMDCF framework, we resolve this by treating spacetime not as a continuous manifold, but as a computational grid with a finite minimum resolution: the Planck length (l_p). In this paper, we demonstrate that l_p acts as the "pixel size" of the universe. Using analytical and 3D numerical simulations, we show that the classical gravitational potential (1/r) is naturally regularized to a finite depth when the distance approaches l_p. Furthermore, we introduce the concept of "Spacetime Memory Addressability," showing that information cannot be resolved below this fundamental pixel limit. This geometric, computational explanation provides a natural mechanism for the avoidance of singularities in nature. Keywords: Planck Scale, Spacetime Granularity, Singularity Avoidance, AMDCF, Quantum Geometry, Planck Pixel, Memory Addressability.