Description
This monograph presents Cognitive Signature Field Theory (CSFT), a geometric and field-theoreticframework for cognition that reinterprets decision, belief, time, psychopathology, and collectivedynamics as phase-dependent phenomena. Moving beyond functional and axiomatic models ofrationality, CSFT treats cognition as motion in a structured space whose curvature, topology, andrenormalization dynamics determine which representations are possible - and when they fail. At the core lies the General Theory of Signature Space (GTSS), parameterized by a control variable (with auxiliary shape parameters). GTSS yields three ontological regimes: a probabilistic phase, where measures exist and optimization is meaningful; a critical phase, where additivity breaks while normalization survives, producing contextuality; and a field phase, where normalization collapses, negative curvature appears, and behavior is governed by potentials,barriers, and phase transitions rather than functions. Exact renormalization-group flow in signaturespace explains why rationality is stable in some environments, fragile at boundaries, and impossiblebeyond them. Within this geometry, major decision traditions are unified as phase-local descriptions: Savage andde Finetti characterize the infrared attractor of probabilistic rationality; Kahneman describesstructured fluctuations within that phase; Busemeyer’s quantum cognition captures the criticalboundary where probability gives way to amplitude and contextuality; and Birnbaum’s empiricalfindings map the field phase in which functional representation provably fails. The framework extends to time, explaining hyperbolic discounting and time inconsistency as negative temporalcurvature; to psychopathology, deriving AMPD severity as curvature depth and therapyas curvature operators; and to society and markets, modeling bubbles, crises, polarization, andinstitutional breakdown as collective field dynamics. CSFT reframes anomalies as phase effects, relocates normativity from agents to structures, andrecasts institutions as geometry-stabilizing operators. The result is a unified, mathematicallygrounded paradigm - the geometry of mind - in which rationality is a phase, probability a locallanguage, and cognition a field with identifiable transitions, diagnostics, and limits.