“...the definition of natural born citizen is still undefined.”
Why would the writers of the Constitution insert an undefined word? Yes, it is defined in the legal theory of the day, and specifically in the Naturalization Act of 1790.
The Constitution does not provide a glossary of its words; it depends on the generally accepted definitions of the English language at that time, and they really haven’t changed much. For example, does “infringe” still mean the same?
No, it was defined in English common law prior to the adoption of the Constitution. The reading in the law of 1790 was actually an aberrant definition, and one which Madison succeeded in removing a mere five years later.
Here I sort of disagree. It's meaning was the axiomatic extension of the "natural law" foundation of the nation.
As the nation was founded on "natural law", the meaning of "natural citizen" derives from that body of philosophical work.
It may not be defined to your satisfaction, but it is defined. A natural born citizen is one whose claim to citizenship derives naturally from the circumstances of his or her birth so that there is a natural and abiding connection between the child and the society and nation into which he or she is born.