Manifold Dynamics Model of Cognitive Functions: A Topological Construction Based on Jungian Cognitive Functions and the Free Energy Principle

This paper proposes a novel modeling framework for cognitive functions, shifting the representation of human personality traits from traditional static probability distributions toward high-dimensional dynamic manifolds. By introducing a topological-morphological perspective, this study explores the shaping process of individual cognitive manifolds from childhood to adulthood and puts forward the concept of "pathological attractors" to distinguish personality variations from psychological disorders. Through the language of geometric topology, this model aims to provide a unified explanation for the evolution of cognitive functional efficiency, sensitivity, and self-consistency.