Derivation of Gravitational Constant from Sobolev Ozok Lattice Model

This work presents a first-principles derivation of Newton’s gravitational constant within the Sobolev–Ozok Lattice (SOL) model, a discrete spacetime framework in which curvature and energy emerge from coherence tension across Planck-scale lattice cells. Two independent approaches are developed: a variational derivation from the coarse-grained SOL action, and a thermodynamic route based on surface degrees of freedom, equipartition, and the Unruh effect. Both yield the same value for the gravitational constant directly from the lattice’s fundamental geometry, without empirical fitting. This distinguishes SOL from other emergent or induced gravity theories, where the constant remains an adjustable parameter. The paper discusses the physical interpretation of the result, its relation to known thermodynamic gravity links, and implications for theoretical and analogue gravity research.