In a conjectural manner; based on or by means of conjecture rather than proof.
From conjectural plus -ly adverb suffix. This standard English adverbial formation allows any adjective to describe how an action happens or a state exists.
You'll hear 'conjecturally' most in academic papers where researchers need to admit they're filling gaps with educated reasoning—it's the honest scholar's way of saying 'probably, but I can't prove it yet.'
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