The term AS FACT STATE can be broken down into three crossword solutions: CLAIM (5 letters), AVOW (4 letters), and AVER (4 letters). All three words have similar meanings, which is to declare something as true. CLAIM is the most general of the three words, meaning to state something as true without providing evidence. AVOW is a stronger statement, meaning to declare something as true with confidence and conviction. AVER is the strongest of the three, meaning to assert something as true with certainty.