The Geometric Origin of Mass: Closed Surface Closure, Reaction Amplitude, and Frequency

This paper presents a geometric theory of mass based on closed surface dynamics. Mass is shown to arise only when a surface remains closed, maintaining uniform pattern density under the condition that tangential velocity equals the speed of light (C). The paper describes mass as the inverse of reactive amplitude in response to external force, interpreted as the surface’s stiffness. This stiffness is a function of vibrational frequency ν. As ν decreases, pattern uniformity degrades, the surface weakens, and mass cannot be defined. Scalar field coupling is also shown to be inversely proportional to inter-surface reactive amplitude. Together, these results provide a purely geometric foundation for mass, density, and coupling strength.