Fetching details from the dictionary...
conclusive evidence; positive proof; definite proof; confirmation
犯人だという確証はまだない。
There is no conclusive proof yet that he is the culprit.
確証を得てから行動に移すべきだ。
You should act only after obtaining definite proof.
科学的な確証に基づいて判断する。
I make judgments based on scientific evidence.