Gravitational Coupling as Emergent Coherence Stiffness presents a closed, non-circular derivation of the quantity conventionally identified as Newton’s gravitational constant G within the Sobolev-Ozok Lattice (SOL) framework. Rather than treating G as a fundamental microphysical constant, the paper shows that it emerges as an effective macroscopic stiffness parameter determined by coherence decoherence imbalance in a discretely resolving lattice. The construction explicitly avoids importing standard Planck relations as inputs. Instead, the analysis proceeds by: (i) defining coherence and decoherence as complementary Sobolev-state functionals under a conserved global budget, (ii) deriving a terminal stable resolution length from a surface–volume stability inequality, (iii) establishing a surface-response bridge between acceleration and boundary degrees of freedom using equipartition together with a kinematic interpretation of the Unruh relation, (iv) constructing a non-Planck reference density based solely on ℏℏ and ccc, and (v) closing the derivation by eliminating the resolution step count to obtain a direct prediction form for GeffG₄₅₅Geff. In this framework, standard gravity is recovered in the homogeneous limit of coherence imbalance, while controlled deviations correspond to coherence gradients. The analysis also clarifies why factors of c4c⁴c4 arise necessarily in curvature–energy mappings, independent of convention. Overall, gravity is reinterpreted as an emergent coherence stiffness of the resolved universe rather than a fundamental local micro-constant. This work is intended as a foundational contribution to the SOL program and is suitable for readers interested in non-circular approaches to quantum gravity, emergent coupling constants, and discrete spacetime frameworks. Declaration of Tools Used: This manuscript was prepared and typeset using LaTeX via Overleaf. Language refinement and stylistic polishing were assisted by the Overleaf AI Editor. All scientific content, mathematical derivations, conceptual development, and conclusions are original and authored by the undersigned.
Ozcan Ozok (Sun,) studied this question.