Entropic Quantum Gravity - The Topological Origin of Mass and Physical Constants

In this paper, I propose a fundamental revision of the description of matter, replacing the point-particle model with a model of topological solitons (Gaussons) in higher-dimensional spacetime. By combining the concept of entropic gravity with relativistic quantum mechanics, I derive the Logarithmic Klein-Gordon Equation as a natural description of matter stabilization. The model yields precise geometric predictions: (1) the proton-to-electron mass ratio is derived with an accuracy of 0.0019% as a topological invariant 6π⁵, interpreting mass as knot complexity in phase space; (2) the fine-structure constant α⁻¹ ≈ 137.0356 emerges as the difference between the holographic capacity of a 5D sphere and the vacuum defect (0.0002% error); (3) a geometric prediction for the muon mass based on a π³ structure is proposed. Significantly, this structure exhibits a striking duality with the geometry of Calabi-Yau manifolds and T-duality in Superstring Theory. This suggests that the presented model constitutes an effective, thermodynamic description of the non-perturbative string vacuum, where physical constants are emergent features of π-geometry.