>[!warning] >This content has not been peer reviewed. # Homeostasis identity loop — Code Script: `rst_homeostasis_identity_loop.py`. ## Purpose Verifies the **identity loop** at the heart of RST homeostasis: - **Forward:** Given workload \(\Omega\) and noise \(N\), delivered signal is \(I = \Omega \cdot \mu(\Omega/N)\) = `source_from_rst(Omega, N)`. - **Inverse:** Given request \(I\) and noise \(N\), equilibrium workload is \(\Omega = \text{solve\_omega}(I, N)\). - **Round-trip:** For many \((\Omega, N)\), compute \(I = \text{source\_from\_rst}(\Omega, N)\), then \(\Omega' = \text{solve\_omega}(I, N)\); check \(\Omega' \approx \Omega\). ## Engine Imports from `rst_engine`: `source_from_rst`, `solve_omega`. Path: workspace root = two levels up from this script. ## Output - Prints number of trials, max relative error, and PASS/WARN. No figure; verification only. ## Links - **Application:** [[Homeostasis (RST)]] - **Results:** [[Homeostasis Identity Loop Results]] - **Roadmap:** [[../../Applications Roadmap]]