Assertedly is a word used to indicate that a statement is claimed to be true, but may not necessarily be the case. Some synonyms for this term include allegedly, supposedly, purportedly, and apparently. Allegedly is commonly used in legal settings, where someone is accused of a crime but it has not yet been proven, while supposed and purported both suggest that the truth of a statement is in doubt. Apparently can be used to indicate that something seems to be true based on evidence, but it is not completely certain. All of these words are useful for adding nuance and uncertainty to a statement, and can be used to avoid making definitive claims without sufficient evidence.