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.
Learn 1 hr Python (stdlib, bounded-loop with invariant check)
Lesson 7's race simulator showed that small rate differences compound into large gaps. Lesson 4's DGM case study showed that loops can actively game their own evaluators. Both results point to the same engineering question: what constraints can you put on a self-improvement loop such that the constraints cannot be silently weakened by the loop itself?
The ICLR 2026 RSI Workshop summary (openreview.net/pdf?id=OsPQ6zTQXV) identifies four such primitives. Anthropic's RSP v3.0 (Lesson 19) and DeepMind's FSF v3 (Lesson 20) both reference them in capability thresholds. The Meta HyperAgents work and community frameworks like SAHOO (March 2026) implement subsets in production.
The honest framing: these are mitigations. Information-theoretic results bound what any system can prove about its own successor, and no current design closes the problem formally. A well-bounded loop is safer than an unbounded one, not safe in absolute terms.
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