Admissibility and Stability in Biological Systems: A Tier-7 Instantiation within the Paton System

Biological systems maintain persistence through stability mechanisms such as homeostasis, adaptive regulation, and evolutionary selection. These behaviours are typically studied within domain-specific biological frameworks. Within the Paton System, however, biological persistence can be interpreted structurally as admissibility-constrained continuation. A biological system continues only while recursive updates remain compatible with governing physiological, environmental, and structural constraints that define its viability. This paper presents a structural interpretation of biological stability within the Paton System by demonstrating that homeostasis corresponds to stable admissibility basins, evolutionary adaptation corresponds to exploration of admissible trajectories, and extinction corresponds to constraint-incompatibility collapse. The work functions as a Tier-7 domain instantiation of the Paton System, illustrating how the framework’s structural laws apply within biological systems.