According to assertion; allegedly or supposedly, as claimed by someone.
From 'asserted' (past participle of 'assert') plus '-ly' (adverbial suffix). The form suggests something that has been claimed but not necessarily proven true.
This adverb carries subtle meaning: calling something 'assertedly true' means someone claimed it without your endorsement, functioning much like 'allegedly' or 'supposedly'—it's a linguistic hedge that lets speakers report claims without confirming them.
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