Informational Geometry: Curvature Without Spacetime

This paper develops an informational geometry in which curvature, geodesics, and connection structures arise without assuming a geometric spacetime or a metric background. Building on an ontology where distance is defined as informational work and dynamics as informational pressure, we introduce informational connections, informational curvature, and informational geodesics as purely relational constructs. The resulting framework provides a structural analogue to differential geometry and curvature phenomena in general relativity, while remaining fully independent of metric assumptions. Informational curvature is shown to emerge from pressure gradients and divergence patterns, offering a non-metric interpretation of gravitational-like behavior.