Who is it that you are addressing as claiming God, gods, supernatural designers, etc. are proven not to exist by science?Many people mostly atheists believe that God has been disproven or has being shown to be non-existent. But if you knew the definition and explanation of intelligence, or its variants, or synonyms, you will never claim such illogical claim. Thus, intelligence protects the existence of God from those non-intelligent persons.
I hope that before those who claim that God does not exist, let them define "intelligence" first in the usage of God = Intelligent Creator or Intelligent Designer.
Proof is not a standard of science. Science works with evidence and belief-based claims are without objective evidence and not within the scope of science. Science is not the means to determine whether God exists or does not.
I see a lot of claims from you but no evidence or coherent explanation for those claims. Your papers and books are not science literature. They are your essays about your beliefs with allusions to aspects of science.
Intelligent design is not science, since there is no objective evidence for supernatural intelligent agencies or the actions of such an agency in nature. Modern intelligent design as practiced in the United States was a mechanism to get religion (specifically Christianity) into public education under the authority of government and at taxpayer expense. Whatever you think you are doing, who can say. I assume you want to replace science with your version of religion. I have seen nothing that you have posted that I could reasonably call science and nothing that would make me conclude that intelligent design is supported.