Deep Dives into AI Governance Architecture

Recursive Self-Improvement Under Governance Constraints: Governed Recursion via Contraction Mapping and Lyapunov Stability

How MARIA OS's Meta-Insight turns unbounded recursive self-improvement into convergent self-correction while preserving governance constraints

Recursive self-improvement (RSI) — an AI system improving its own capabilities — is both promising and risky. Unbounded RSI raises intelligence-explosion concerns: a system improving faster than human operators can evaluate or constrain. This paper presents governed recursion, a Meta-Insight framework in MARIA OS for bounded RSI with explicit convergence guarantees. We show that the composition operator M_{t+1} = R_sys ∘ R_team ∘ R_self(M_t, E_t) implements recursive improvement in meta-cognitive quality, while a contraction condition (gamma < 1) yields convergence to a fixed point instead of divergence. We also provide a Lyapunov-style stability analysis where Human-in-the-Loop gates define safe boundaries in state space. The multiplicative SRI form, SRI = product_{l=1..3} (1 - BS_l) * (1 - CCE_l), adds damping: degradation in any one layer lowers overall autonomy readiness. Across simulation and governance scenarios, governed recursion retained 89% of the unconstrained improvement rate while preserving measured alignment stability.