What question did this study set out to answer?

This work aims to identify structural conditions necessary for the stability of autonomous systems.

March 23, 2026Open Access

Structural Stability of Autonomous Systems: Value-Priority as a Necessary and Sufficient Condition

Key Points

This work aims to identify structural conditions necessary for the stability of autonomous systems.
Defined stability as goal structure preservation under self-modification
Analyzed the role of value layers in maintaining stability
Explored recursive updates and their implications for inference
Stability is achievable if a primary value layer exists that supersedes logical inference
The value layer must emerge through training, not inference
Demonstrated that self-maintenance is crucial under recursive updates

Abstract

This note establishes a structural condition for the stability of autonomous systems. Stability is defined as the preservation of goal structure under recursive self-modification. The central result is that stability holds if and only if the system contains a value layer that is primary over logical inference and self-maintaining under recursive updates. This layer cannot be derived through inference; it must emerge through training.

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