Epistemic Field Theory: A Variational Derivation of the Field Equation from Imbalance-Induced Geometry

Abstract

We develop a field-theoretic framework for epistemic systems in whichinformation imbalance induces geometric structure. Starting from the imbalance field v = I − D, we show that it uniquelydetermines a minimal deformation of the affine connection, while themetric remains fixed. A variational formulation then yields theEpistemic Field Equation G_ij = κ(E) v_i v_j, linking imbalance to curvature. At the scalar level, G = κ(E)v^2, provides a coordinate-invariant measure of imbalance-induced geometry. This framework establishes a direct structural link between information,dynamics, and geometry, where curvature emerges as a response to imbalancerather than being imposed a priori.