Bounded Self-Improvement Designs

Research has converged on four primitives for bounding a self-improvement loop. Formal invariants that must hold across every edit. Alignment anchors that cannot be modified. Multi-objective constraints where every dimension (safety, fairness, robustness) must hold, not just performance. Regression detection that pauses the loop when historical metrics suggest capability loss. None of them is a proof of safety — information-theoretic results (Kolmogorov complexity, Lob's theorem) bound what any system can prove about its own successors. They are mitigations that raise the cost of silent failure.