Resolution Ceiling Operator: Structural Limits of System Representation in the Paton System

Systems persist through recursive evolution of states that remain compatible with governing constraints. However, every system also possesses limits to the complexity, resolution, or informational detail it can represent while maintaining persistence. This paper introduces the Resolution Ceiling Operator, a formal construct that defines the maximum structural resolution a system can sustain without violating constraint compatibility. When system representation exceeds this limit, recursive continuation fails due to overload, instability, or incompatibility between state complexity and governing constraints. The Resolution Ceiling Operator therefore establishes an upper boundary on admissible system states. By formalising these limits, the framework provides a unified explanation for computational limits, cognitive capacity limits, observational limits in physics, and structural limits in organisational systems. The operator completes the mathematical core of the Paton System by defining the upper boundary of admissible system evolution.