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I'm sorry about this! Generally, we recommend using a wide variety of backlink tools to get the most illustrative picture of how your site's backlink profile looks. OSE and Ahrefs index differently and have different purposes. Ahrefs is good for quantity while OSE is great for finding higher quality links. You could always try Ahrefs to compare and potentially give your client the peace of mind that the links are still there. Domain Authority is our own proprietary metric that is closely correlated to Google rankings, so our customers often use OSE to research influential sites to build links. (E.g. which links to try and target)