New Formulation of Physics based on a Complex Terrain Model — III: The Weak Equivalence Principle and the Geometric Origin of Gravity —

In this third report, we present a geometric derivation of the Weak Equivalence Principle(WEP), one of the foundational assumptions of General Relativity stating the equivalenceof inertial and gravitational mass.Within our projection framework, the WEP emerges naturally in the static limit, corre-sponding to a small projection angle η. We derive the relationMg = Mi cos2 η,which implies that the classical form of the WEP is recovered as η → 0.The identity further suggests that deviations from exact equivalence may not occur inhighly relativistic regimes where η → π/2. In addition, we show that the projection equationprovides a geometric explanation for the factor-of-two enhancement in gravitational lightdeflection