Is crystallizing honey a sign of purity, or quite the contrary?

I mean honey that is sold in liquid form and crystallizes over time. Sometimes, labels are not very clear about the origin of honey, so it could be a mixture of different kinds.

I know I can re-liquefy it by placing the jar in warm water. That's not the subject of this question.

Is crystallizing honey a sign of purity, or quite the contrary?
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