Other forms: baselessly
If something's baseless, it can't be proven or justified. A baseless accusation of cheating, for example, has no facts or evidence to back it up.
Baseless facts in a research paper don't have sources — they may have simply come from the writer's own imagination. A baseless allegation is when one person accuses another of doing something wrong, without having any solid proof or reason for the accusation. The sense of base that baseless comes from is "foundation," from the Greek basis, "step or pedestal."