Recursive Load Distribution in Control Systems: A Tier-7 Instantiation of the Closed vs Distributed Recursion Law

This technical note presents a Tier-7 domain instantiation of the recursion-under-load principle formalised at Tier-6 within the Paton System. It demonstrates that classical control systems exhibit the same structural distinction identified in numerical stability theory: closed recursion under sustained amplification leads to boundary collision, while distributed feedback constraint preserves bounded continuation. Using spectral radius conditions and feedback stabilisation, the work shows that control engineering implements the Tier-6 inequality in operational form. No new operators are introduced and the foundational admissibility spine (Gate → Datum → ∞) remains unchanged. The document functions as a structural overlay reinforcing domain invariance between abstract recursion theory and physical feedback systems.