Information as Geometry: A Computational Verification of Entropic Gravity

Abstract: This repository contains the high-performance Python simulation framework used to validate the Emergent Gravity hypothesis (Verlinde, 2016) in the context of galactic rotation curves. The suite implements an N-Body symplectic integrator (Velocity Verlet) with a modified effective potential that incorporates the entropic acceleration scale $a_0$. Key Features: Symplectic Integration: Ensures energy conservation for orbital dynamics. Entropic Interpolation: Implements the full acceleration transition function $g_{obs} = (g_B + \sqrt{g_B^2 + 4g_B a_0})/2$. Lensing Validation: Includes modules for calculating effective refractive index and deflection angles in the weak-field limit Usage: This software supports the results presented in the paper "Numerical Validation of Galactic Rotation Curves in an Emergent Gravity Framework" (Submitted, 2025).