Who died on the cross?

Brenda asked Matt Yester on Veritas 2020-12-07.

If Jesus died on the cross, did his human nature or his God nature died? Did God die? Is the father the son?

During the discussion, M. Yester said all of the following:

The conclusion is that Matt Yester admits that there are separate wills, but his caveat is that the wills are “identical”. Ultimately, our conclusion is that separate wills, separate bodies, and so on, indicate separateness.

Here are a few starting points for this:

Follow-up questions

Q: So if Jesus's human nature (only) died on the cross, why couldn't any human being do it?

Some of these are trivial to refute, such as “after the order of melchizedek” which was given to Abraham and does not represent Jesus. Others, such as a value proposition, are assumptions and not mentioned in the text (even the existance of such an “only begotten” son of god is found nowhere in scripture).

Q: When we say that only Jesus' human nature died on the cross, does this imply that only Jesus' human nature kept the law perfectly? Or is there some link between the two (such that they are not separate, perhaps) to the point where God granted Jesus grace to keep the law, in order to consecrate him as a perfect or righteous sacrifice?