Structural Invariance Theorem: A Tier-6 Formalisation within the Paton System

This paper formalises the Structural Invariance Theorem within the Paton System. Building on cross-domain instantiations across financial systems artificial intelligence systems and healthcare systems it establishes that any admissible system must follow a common lifecycle defined by admissibility datum stabilisation recursive continuation constraint drift and boundary closure. The theorem demonstrates that this lifecycle is a necessary structural condition of system existence rather than an empirical observation.