Geometric Coupling and Area-Dependent Gravitational Fall in an Atmospheric Pal-Riemann Manifold

In classical mechanics, the acceleration of a falling body in a vacuum is independent of its mass and shape. However, in an atmospheric medium, observations suggest that the time of fall is significantly influenced by the two-dimensional (2D) projection area formed by the farthest points of the object parallel to the gravitational field. We propose that this phenomenon is a macroscopic manifestation of the Pal-Riemann Manifold. By treating the atmosphere as a high-density information medium, we demonstrate that the object's cross-sectional area acts as a "coupling constant" to the entropic force of gravity. This experiment provides empirical support for the theory of gravity as an emergent entropic phenomenon F = T \nabla S.