Mental wellbeing emerges from the continuous integration of perception, decision-making, and social regulation. We propose a unified mathematical framework based on the Field Theory of Representation (FTR), in which these interacting processes are modeled as a variational field defined over a learned semantic manifold.

Within FTR, an agent’s cognitive state evolves according to a Lagrangian density whose potential term V (E, U, N) captures the coupled influence of epistemic evidence E, utilitarian objectives U, and normative constraints N. These three components represent complementary forces that jointly shape adaptive cognition and behavior.

Inference is formulated as trajectories on a latent manifold 𝓜 ⊂ ℝᵈ, where the geometry encodes the semantic organization of experience. Mental wellbeing corresponds to stationary solutions of the associated action functional, balancing representational efficiency, accurate environmental modeling, goal-directed behavior, and normative coherence.

FTR therefore provides a geometric framework for studying how cognitive systems maintain stable representations while continuously adapting to changing sensory, behavioral, and social demands. The theory generates quantitative hypotheses for large-scale neurocognitive dynamics, cognitive resilience, stress adaptation, and dysregulation associated with neurological and psychiatric disorders.

By expressing these phenomena within a common variational formalism, FTR offers a principled bridge between mathematical models of cognition, computational neuroscience, and future artificial intelligence systems whose adaptive behavior remains aligned with human wellbeing.