So you are not satisfied because a law defining common knowledge does not exist.
Whether I am satisfied or not is irrelevant. Over the last 150 years since adoption of the 14th Amendment’s citizenship clause, there has been nothing stopping any Congress from writing down “common knowledge” in a statute.
When there are challenges to a candidate’s eligibility, the challengers have tended to use the courts as the primary locus for petitioning the government for redress of grievances. Courts look to the letter of the law of the land to make their determinations.
“So you are not satisfied because a law defining common knowledge does not exist”
Your view of this matter is not common knowledge.
It was common knowledge at the time.