Systematic Failure of the Markov Assumption Under Operational State Constraints

This manuscript presents a unified and non-compressible analysis of the limitations of the Markov assumption under explicit operational constraints on state representations.We consider modeling settings in which states are required to be finite, observable, locally updatable, and free of external or hidden memory. Under these constraints, we show that the Markov assumption fails systematically at multiple levels:(1) interface-level dynamics,(2) information sufficiency,(3) methodological validity of state augmentation,(4) predictive optimality, and(5) responsibility attribution. In particular, we demonstrate that commonly invoked recovery strategies based on unrestricted state augmentation are non-falsifiable and non-operational within the assumed modeling interface.All results are presented as an explicit proof chain that cannot be collapsed into a single state-extension argument. The work does not deny the formal existence of Markovian embeddings under unrestricted assumptions.Rather, it establishes that, under operationally meaningful constraints, Markovianity should be treated as a contingent modeling choice with explicit costs and consequences, rather than as a default structural principle.