Mathematical Resolution of the Hubble Tension and Singularity Regularization through Dynamic Vacuum Coupling (DVCH)

This technical report introduces the Dynamic Vacuum Coupling Hypothesis (DVCH) as a mathematical solution to the Hubble Tension. The model proposes a dynamic interaction between matter density and vacuum energy. A key feature of this framework is the implementation of a Planck-scale regulator [1 + \alpha(l_P/R)^2], designed to prevent gravitational singularities and provide finite, consistent solutions for high-energy density environments. The hypothesis is aligned with the latest cosmological data observations of 2026.