Does the Jacobian Hypothesis ask if the Jacobian is a valid map?

Question

It appears that the JH is equivalent to asking whether the jacobian determinant itself is a valid map, I would appreciate any related research on this and confirmation of this equivalence.

Answer 1

You're incorrect. The determinant is always well-defined whenever the partials exist. It is about the inverse of the function that you are looking at the Jacobian determinant of.