The Kh-Stiffness Formalism: A Unified Mechanical Resolution to the H_0 Tension and the 10^122 Vacuum Catastrophe

This paper presents an expansion of the Kh-Stiffness formalism, a novel theoretical framework that reinterprets the ontology of spacetime not merely as a smooth geometric manifold, but as an elastic medium characterized by a fundamental stiffness modulus, Kh = c^2/G. By shifting away from the rigid manifold assumption of standard General Relativity, we introduce a tripartite conceptual symmetry termed the "Khaghani Triangle" which mathematically links temporal flux (Δτ), energy density (ρ), and quantum wave-states (Ψ). Through the Density-Induced Rigidity (DIR) mechanism, we demonstrate that spacetime achieves perfect rigidity in high-density regimes—recovering standard Einsteinian field equations—while undergoing mechanical relaxation in cosmic voids. This foundational reinterpretation provides a dynamic resolution to two severe crises in modern cosmology: it resolves the H_0 tension by predicting a local expansion rate of H_0 = 73.14 ± 0.22 km/s/Mpc in alignment with recent JWST data, and it resolves the 10^122 vacuum energy discrepancy by treating Planck-scale density as dynamic potential stiffness rather than divergent curvature energy. Additionally, the model offers an entropic, thermodynamic derivation of gravity and a torsion-based alternative to dark matter in galactic rotation curves, establishing a falsifiable mechanical infrastructure for modern physical cosmology.