This question may seem abstract and strange, but it is genuine.
We obviously don't have ketubot of every marriage and certificates of every conversion, but yet, our assumption is that the Jewish maternal line is pure. On what halakhic basis do we assume this?
Can we say that even if there was an invalid conversion thousands of years ago, because we don't know about it, it doesn't matter, and we will be treated as full-blooded Jews from Yaakov for the purposes of Olam haBa and Teḥiat haMeitim?
PS: What if someone wanted to perform geyur leḥumra for this very concern?