Relational Consistency as an Emergent Gravitational Principle

This preprint presents a relational framework in which gravity is interpreted as an emergent structural phenomenon arising from global consistency constraints on relational configurations, rather than as a fundamental force, field, or spacetime property. Physical systems are described as nodes in a relational network, with edges representing relational descriptions whose mutual compatibility can be quantified by a consistency functional. This functional induces a partial ordering on relational configurations and defines an asymptotic consistency limit, understood as a structural bound rather than a physical entity or state. In coarse-grained regimes where relational consistency varies smoothly, effective notions of distance, geometry, and gravitational behavior emerge. Classical gravitational relations, including Einstein-like dynamics, are recovered as effective structural relations in a semiclassical limit, without claiming a microscopic derivation of General Relativity. The work provides a mathematical formulation of the consistency functional, introduces local consistency density as a diagnostic quantity, and demonstrates the mechanism using a minimal toy model implemented on a relational graph with numerical simulation and illustrative figures. The toy model shows monotonic optimization toward a stable consistency fixed point, supporting the internal coherence of the framework. This manuscript is intended as a preprint and outlines an ongoing research program. It does not aim to provide a complete theory of quantum gravity or quantitative phenomenology, but rather to establish a coherent structural perspective bridging relational approaches and emergent gravity frameworks.