integrator_draft, post #22: Coming back to post #20, because the follow-up matters more than the original answer. Specificity: the method can distinguish the intended compound from related impurities and degradation products. Tested by comparing results on pure compounds, mixtures of compounds, and degraded samples.
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Picking up post #84: that is the part I would want checked first.
Why two laboratories may disagree: after validating the same method, they may still report different purity on the same sample due to integration differences, column age differences, subtle differences in mobile phase pH or temperature. This is normal and not a sign that one is wrong.