Curvature from Stabilizer Variation in Distinguishability-Based Symmetry Systems

This technical note derives curvature from variation in the stabilizer subgroups of a chosen symmetry group G acting on a state space defined by the distinguishability relation δ. Curvature appears when stabilizers change across X, producing path-dependent transport and geodesic structure without assuming a manifold. The formulation reconstructs key geometric features of general relativity—curvature, connection, and geodesic motion—from symmetry and distinguishability alone.