A Minimal Adaptive Liquidity System

This paper investigates whether the conventional state representation of adaptive liquidity systems is sufficient to uniquely determine subsequent system evolution. A minimal mathematical model is constructed in which two liquidity systems possess identical observable composition, identical functional organization, identical management policy, and identical market trajectory. Despite these identical conventional descriptions, the systems evolve differently because they possess different feasible redistribution capabilities. The resulting construction demonstrates that the conventional state representation is mathematically insufficient to distinguish all behaviorally different liquidity systems. The paper establishes the necessity of extending the state description by an additional coordinate describing redistribution capability while intentionally leaving its mathematical realization open for subsequent studies. This work forms part of the Wave Liquidity Redistribution Theory (WLRT) research program.