MUT v6.18: Quantum Embedding Contradicts Hierarchy Scaling in the MCR Framework

This paper develops the Mass Curvature Rate (MCR) framework as a unified structure connecting quantum-scale physics with cosmological-scale phenomena. It examines the Quantum Embedding Contradiction of Hierarchy Scaling, demonstrating that directly embedding quantum parameters—such as atomic radii and fine-structure variations—into cosmic-scale dynamics produces measurable deviations from classical hierarchy scaling assumptions.
At the atomic level, small variations in the fine-structure constant lead to shifts in the Bohr radius and hydrogen spectral transitions, providing potential spectroscopic observables. At galactic scales, the framework modifies rotational velocity profiles without invoking dark matter, while at black hole cores, the scalar field structure prevents singular curvature by introducing a finite effective density.
The model provides explicit falsifiability conditions through spectroscopy, galaxy rotation measurements, and black hole gravitational profiles. By embedding quantum structure into cosmic dynamics, the MCR framework challenges naive scale separation and proposes a predictive, testable bridge between atomic physics and cosmology.