Rationality Collapses and Shifts

This monograph develops a unified geometric theory of decision, belief, polarization, and inequality by extending the boson-fermion distinction from quantum statistics to cognitive and social systems. We introduce the General Theory of Signature Space (GTSS), in which systems are characterized by a low-dimensional signature  encoding local curvature (exclusion versus coherence), coupling strength, and memory. Within this framework, rational choice, belief formation, market dynamics, and social polarization emerge not as properties of agents or preferences, but as statistical phases of a curved state space.