>[!warning] >This content has not been peer reviewed. # Homeostasis (the identity loop) — RST application **Homeostasis** is the maintenance of a stable internal state despite external perturbations. In RST this is the **identity loop**: the system maintains the request I by regulating workload Omega against noise N so that the rendered output equals the target. The Main Equation I = Omega * mu(Omega/N) is exactly this: given a target signal I and ambient noise N, the substrate delivers output Omega such that the effective delivered signal (projection I = Omega^2/W) equals the request. --- ## I. Mapping to the relational axioms | Homeostasis | Relational identity | RST axiom | |:---|:---|:---| | Set point (target) | Request I | A1 (Format) | | Regulation | Adjusting Omega so that I = Omega * mu(Omega/N) | A2, A4 | | Perturbation / noise | N | A2, Noise Floor | | Stable state | Equilibrium: I = Omega^2/W, W^n = Omega^n + N^n | Resource Triangle | --- ## II. The identity loop in code - **Forward:** Given I and N, solve for Omega = solve_omega(I, N). - **Inverse:** Given Omega and N, I = source_from_rst(Omega, N). - **Round-trip:** I from (Omega,N) then solve_omega(I,N) should recover Omega. The script rst_homeostasis_identity_loop.py verifies this. --- ## Links - **Applications Roadmap:** [[../../Applications Roadmap]] - **Code:** [[Homeostasis Identity Loop - Code]] - **Results:** [[Homeostasis Identity Loop Results]] - **Resource Triangle:** [[expanded theory/Resource Triangle]]