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The Geometry of Interaction

This monograph develops a new geometric framework for decision, cognition, and interaction, motivated by the systematic failure of functional models of rationality. Expected Utility, Cumulative Prospect Theory and related approaches succeed only locally; across scales they break down into preference reversals, context effects, instability, and abrupt regime shifts. We argue that these failures are not empirical anomalies but ontoUtwórz pliklogical mismatches: functional models attempt to represent field-like interaction using single-scale functions. We introduce the General Theory of Signature Space (GTSS), in which interaction is modeled as a geometric field characterized by three invariants: scale flow, orientation, and intermittency. These invariants define a signature space  whose regions correspond to distinct regimes of rationality. Rational behavior emerges as a phase of the interaction field rather than as a universal normative property of agents.