One thing to keep in mind when reading this article is that human cognition always halts after some number of decades. “Finite” does not mean small or insignificant, and it’s easy to read too much into even the best-reasoned impossibility arguments.
-edit- Also, this logic would lead us to believe that category B and C programs can't exist in our universe since, according to our best current understanding, the universe will end eventually, presumably ending any program running within the universe as well, therefore we can "prove" that every program is a category A program that will come to a halt.
Ok, but the intelligent entity in question isn't the program, it's the program-running-on-the-hardware. A mere description of your brain is totally inert.