>Very importantly, there doesn’t seem to be any “input” into this routine. It doesn’t pop anything from the stack, nor does it care about any register values passed into it. Which can only mean that the result of this routine is completely constant!

This is not necessarily a fair assumption (though it worked this time). It could be some sort of a rolling code, where the reply is not constant but changes, and remains verifiable. Example: garge door openers have no input from the garage, but the sent signal differs every button click, and the garage can verify its correctness