Introduction

Stability and resilience metrics are widely used to characterize complex systems in fields such as physiology, ecological monitoring, infrastructure, and machine learning.
In many implementations, stability estimates are emitted even when the underlying dynamics cannot be uniquely inferred from observations.
This creates a structural problem: numerical estimates are produced even when parameters are not identifiable.

Such emission of synthetic stability metrics creates false certainty. In high‑stakes systems, medicine, infrastructure monitoring, and automated decision systems incorrect stability estimates may be more harmful than the absence of a metric.

This paper proposes a recovery‑based framework in which stability is inferred only when disturbance–recovery dynamics are observable.

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