RETΦ / RETΩ runtime architecture
Recursive Ethical Topology (RETΦ) and second-order damping (RETΩ) form the formal foundation of the constitutional runtime and evidence control layer. This page describes the public-safe architecture spine. Formal tuning constants and per-turn governance evidence remain private.
What RETΦ is
RETΦ is a recursively governed, cryptographically verifiable, constraint-regularized, graph-coupled, closed-loop learning control system with spectral damping. It derives governance properties from first principles: state-space dynamics, constrained optimization, graph theory, and spectral analysis.
| Symbol | Meaning |
|---|---|
| xt | System state at time t (operational context, governance state, accumulated evidence) |
| ut | Control action (agent decision) |
| f | State transition function, assumed Lipschitz continuous |
| εt | Stochastic disturbance |
The governance layer maintains a belief state over latent variables; not all components of xt are directly observable. Spectral damping ensures bounded perturbations decay rather than amplify across the supervisory layer.
What RETΩ is
RETΩ is the second-order stability surface over RETΦ. When the governance graph or the directive hierarchy is itself updated, RETΩ damps the transition so the system does not oscillate between rule sets. RETΩ is what keeps recursive ethical topology stable under appended directives.
What is public-safe and what stays private
| Surface | Disposition |
|---|---|
| Architecture spine (this page) | Public-safe; allowed. |
| Public anchor. | |
| First-principles math (state-space, Lipschitz, spectral damping) | Public-safe; allowed. |
| Formal tuning constants of the spectral damping operator | Private; protected. |
| Per-turn governance evidence payloads | Private; protected. |
| Trustlock RETΦ record | Private; protected. |