Economic Phase Transitions as Derivation, Not Causation: A Stuart-Landau Framework

Mainstream economics seeks causal explanations for crises: why do bubbles form? Why do markets crash? We argue this question is malformed. Following Newton—who described gravitation without explaining why masses attract—we propose that economic phase transitions require description, not causal explanation. The Stuart-Landau equation dA/dt = αA − β|A|²A, describing universal dynamics near bifurcation points, provides an axiomatic foundation for economic dynamics. Unlike mathematical axioms posited a priori, these axioms are empirically discovered—extracted from three centuries of convergent physical investigation from Newton through Landau, Kuramoto, and Vicsek. The sense of 'because' we feel when connecting economic events arises from prediction error minimization in the brain (Friston, 2010), not from features of economic reality itself. Building on prior analysis of AI investment narratives (Ishibashi, 2025), we generalize the saturation parameter β as the key to systemic stability. When institutional constraints maintain β > 0, growth self-limits. When deregulation, leverage, or narrative excess drives β → 0, the system approaches pure linear instability—collapse becomes not caused but derivable. We demonstrate this framework through the 2008 financial crisis, Asian currency crises, and technology bubbles. The hierarchy Movement-Field-Attraction-Resonance-Synchronization, derivable from Stuart-Landau structure, applies across these cases. The framework generates testable predictions: critical slowing down and increasing variance as β → 0. Economics should shift from asking 'why do markets crash?' to 'under what conditions is collapse derivable from axioms?' The answer is mathematical, not causal.