You've also averred that science cannot answer the question of what the source is by studying the program - ie the answer to the question of the source of the program is not embedded in the program itself.
When it goes beyond the "toolkit" of science and math - the question should be put in the hands of the theologians and philosophers.
Nevertheless, I'm very sincere in asserting that science - and math - should pursue the origin questions, all of them - as far as it can go.
Lack of curiosity is poisonous. Christians understand that God wants us to look and see. (Psalms 19:1-3, Romans 1:20)
My statement about God's copyright notice on the cosmos being the "unreasonable effectiveness of math" is my own speculation.