The Failure of Decomposition in Recursively Self-Conditioned Systems - Structural Conditions and Implications for Consciousness

Decomposition—the analytic strategy of partitioning a system into subsystems whose local dynamics and interaction terms suffice to reproduce the whole—is among the most productive methods in science. This paper identifies a class of systems for which decomposition necessarily fails. When a system’s activity is recursively self-conditioned, preserves its own ongoing identity under perturbation, and is continuously and globally integrated through the physical interactions that realize it, any attempt to factor its coordination into separable subsystems either breaks the recursive identity-preserving structure, introduces covert global variables that vitiate the decomposition, or fails to reproduce the system’s trajectory under perturbation. The failure is not practical but structural: it follows from the conjunction of conditions, not from measurement limitations. The class of systems satisfying these conditions is characterized, the proof of decomposition failure is developed, and the empirical signatures of non-decomposability are specified. The paper concludes by identifying the regime in which these conditions jointly obtain.