No operational criteria currently distinguish understanding earned by a system through its own ongoing dynamics from competence received through prior optimisation. We define understanding as organisational structure earned through a system's history of interaction, and argue that such structure must satisfy five necessary properties: emergence, stability, integration, operational impact, and transfer. On this basis, we classify systems along a spectrum defined by whether the feedback loop between learned structure and future dynamics is active, continuous, and undirected during operation. At the critical boundary between externally directed and undirected systems, we propose a formal path-dependence test. We further introduce the Earned Understanding Battery, comprising five provenance-constrained instruments for distinguishing earned understanding from advanced self-organising learning. The framework is falsifiable, system-agnostic, and useful even under null results. The unresolved question is whether these properties identify a distinct organisational regime or instead formalise a sophisticated form of adaptive learning. That question can only be settled empirically.

v2: Added Foxworthy (2026) as closest empirical neighbour in §6. Rewrote §6 for clarity. Added Chollet (2019) to §3.6. Added Levin (2022) to §7. Added multiplicity note to §5. Added conflicts/funding statement and DOI to first page. Added glossary entry for consolidation-dependent persistence. Corrected abstract ("five" instruments). Added missing DOIs to references.