MUT Theory v6.8: Mass Curvature Rate, Cosmic Scales, and Hierarchy

This paper develops the Mass Curvature Rate (MCR) framework as a curvature-based reformulation of mass and gravitational scaling. The theory introduces a master relation connecting a generalized microscopic mass parameter to energy through a curvature-rate constant. From this foundation, gravitational coupling and curvature radius are redefined in a manner consistent with dimensional analysis.The framework is extended to cosmological scales by deriving the Hubble mass directly from the Friedmann equation and demonstrating consistency between the MCR curvature radius and the Hubble radius. This establishes a natural bridge between microscopic mass parameters and large-scale cosmic structure.An action principle formulation is proposed in analogy with the Einstein–Hilbert action, providing a variational structure for the theory. Although the exact form of the curvature scalar remains formal, the construction indicates compatibility with standard field-theoretic methods.Finally, the theory reveals a natural UV–IR hierarchy, where microscopic mass scales and cosmic horizon scales are connected without additional fine-tuning. The resulting structure suggests that curvature-based mass definitions may offer a coherent framework linking gravitational dynamics across scales.