Ratification is irrelevant. If Nazi Germany was bound by unwritten laws of war, than so are we. We helped engineer the Nuremberg trials; we can't now claim to be immune from its requirements.
The Congress shall have Power ...To define and punish ...Offences against the Law of Nations"
The court agreed with you that the Constitution means nothing.
All titles of treaties and US laws are followed by four digits which allude to its date of enforcement. The Geneva Convention has the four digits 1949 and the Nuremberg trials have the four digits 1945.
Hint :- subtract the lower from the higher, then refer back to your post.
Or, you can read a history book on the American Revolution, and reflect on the legal authority which General Washington used to try, convict, and then hang Major John Andre, the contact for General Benedict Arnold in the intended betrayal of the garrison at West Point.
The government is obeying the Law of War, here. It is the Court which ignored the Law of War in this decision, primarily by running away from its own unanimous decision in Quirin. You have a lot of reading to do before you will demonstrate an understanding of what you are posting about.
John / Billybob