I have trouble with the most basic statements in that paper. I find your writing confusing, which I hope is not intentional. The answers to several questions might help. Could you define “active information”? Why have you chosen that as the term? Is this information in any technical sense? Do you think that transition/transversion bias demonstrates active information? How do you choose what distribution to consider “random”? Does changing the rate of mutations while keeping the same distribution constitute active information?
Do you agree that much (perhaps 90%) of the human genome is junk? If so, would the mutation spectrum in junk DNA be a good one to choose as a random distribution?