Kaan Particle as the Fundamental Quantum Cell of Vacuum Elasticity: A Mathematical Derivation

This work presents the concept of the Kaan particle, defined as the smallest structural unit of spacetime within the Vacuum Elasticity Model. In this model, spacetime behaves like an elastic medium, and its curvature is interpreted as a mechanical response of the vacuum. Because an elastic medium cannot sustain infinite stress or singularities, the theory requires spacetime to have a minimum discrete structure rather than being perfectly continuous. The Kaan particle represents this fundamental vacuum cell and defines the smallest meaningful scale at which spacetime can deform. Its introduction provides a new perspective on the microscopic structure of the vacuum and offers a discrete foundation for understanding gravitational and cosmological behavior.