Operator Stability and Failure: Admissibility Breakdown Under Sequential Constraint

This paper defines operator stability within the Paton System and formalises how admissibility breaks down under sequential constraint. Building on the Paton Operator Calculus, this work establishes how admissible execution paths degrade over time through cumulative strain, boundary approach, and cascading failure. It shows that systems may remain admissible step by step while progressively exhausting their tolerance, leading to eventual breakdown. The framework introduces no new domain-specific laws and does not modify governing equations. It operates as a pre-theoretical layer determining when admissible sequences lose viability through accumulation. This paper is part of the Paton Operator Layer and is structurally linked with: - The Paton Operator Calculus: Composition, Sequencing, and Admissible Execution Paths - Admissible Operator Optimisation: Selection and Efficiency Within Constraint Boundaries Together, these define how systems execute, degrade, and select paths under constraint. CONCEPT DOI (use this public link) https://doi.org/10.5281/zenodo.19604966