I find it useful to give such a disclaimer when stating something from memory or personal knowledge but which I would not guarantee to be correct.
However, saying, e.g., "according to my knowledge" or "if I remember correctly" is also wordy and can be distracting.
There must be a one-word adverb that has a similar meaning or connotation (to one or both of these prhases), and I would appreciate if you could point it out.
I tried looking up 'recallingly' [which would be somewhat analogous to 'allegedly'], but it seems the word does not exist.
Edit: Of course, one could say 'perhaps' or 'maybe', but that has a somewhat different meaning because one could say 'perhaps' or 'maybe' without having any personal knowledge or memory of the thing in question. I would like to convey that I am not merely speculating or opining in the moment but that I have processed the information and now am passing it on to others as I have it in my mind.