Emergent Relational Geometrodynamics: Tensorial Stability, Structural Conservation, and Scaling Breakdown in Discrete Networks

This work introduces a tensorial formulation of emergent gravity in discrete relational systems. Extending previous results on scaling degradation in small-world networks, we propose a relational field equation based on discrete Ricci curvature and structural conservation. Finite-size numerical simulations demonstrate that gravitational scaling collapses under increasing topological disorder, correlating with a measurable violation of a conservation identity analogous to the Bianchi identity. These results suggest that gravity is not a fundamental interaction, but a stability property of geometrically coherent networks.