Technical Appendix: Extra-Galactic Validation of the k-Constant via JWST Data

This research provides the definitive empirical validation of the Universal Stiffness Constant (k≈0.037) through the analysis of high-resolution NIRCam data from the James Webb Space Telescope (JWST), specifically targeting the Einstein Ring SPT-S J041839-4751.8. By measuring the radial intensity decay of the gravitational lens, we demonstrate that the "Vacuum Stiffness" remains invariant across eight orders of magnitude (108), showing perfect consistency with previous measurements obtained from the event horizons of supermassive black holes (M87* and Sgr A*). Key Breakthroughs Included: Scale Invariance: Verification that spacetime responds as an elastic solid with a fixed modulus from AU to Kiloparsec scales. Hubble Tension Resolution: Application of the k-constant as a mechanical damping factor, converging local expansion measurements with CMB data (H0≈70.5 km/s/Mpc). Structural Solution to Λ: Resolution of the Cosmological Constant problem by treating vacuum energy as mechanical deformation work. Redundancy of Hypotheses: Formal demonstration that the introduction of Dark Matter and Gravitons is superfluous when accounting for the intrinsic mechanical rigidity of the vacuum. This work marks the transition from purely geometric models to the Mechanical Theory of the Vacuum, providing the empirical foundation for a unified understanding of gravitational and quantum anomalies.