Vacuum Elastic Spacetime Framework: A Unified Derivation of G, Λ, g, and the Planck Scale from a Single Modulus

This work introduces the Vacuum Elastic Spacetime Framework, a unified model in which spacetime behaves as an elastic medium characterized by a single vacuum modulus Es. Using only its fundamental elastic-field equations, the framework derives four key physical quantities the gravitational constant G, the gravitational acceleration g, the Planck length, and the cosmological constant Λ without adjustable parameters. All derived values match experimental measurements with high precision. The results suggest that elastic properties of the vacuum may unify gravitational strength, quantum-scale geometry, and cosmic acceleration within one physical principle.