This supplemental paper to MUT v5.8 presents the first formal derivation of the Newtonian gravitational constant � from the fundamental Awareness Constant �. Within the Myo Min Aung Unified Theory (MUT) framework, gravity is interpreted as an emergent phenomenon resulting from the resistance of awareness flux at the cosmological scaling limit �. The derivation bridges consciousness-based substrate dynamics and classical gravitation, yielding a numerical value of �, consistent with empirical observations. This work demonstrates that the gravitational constant is not fundamental but emerges from a deeper awareness flux structure, providing a unifying mathematical framework for mass, force, and cosmic scaling. In this version, the term “Awareness” is formally interpreted as an effective background scalar field (EBSF), clarifying its role within the physical framework of the theory.