This kind of pdf is what you get when your genius startup doesn't have a single engineer with half a brain and everybody does enough coke to believe you can beat physics with sheer enthusiasm.
That, or it is calculated fraud.
I should really get an AI to remake Guesstimate as a self-hostable site...
I am btw. not even sure if thermal conductivity is the limiting factor here, they still need to radiate that out and that is a function of surface area if I remember correctly.
Edit: Higher thermal conductivity helps with the thermal dissipation within the radiator, it does not affect the area of the radiator needed. Although it could affect weight if you roll it out thin enough. Still, this is quickly becoming the opposite of "simply putting a data center into space" and more like "decades of research on other topics". And AI is the vehicle to sell that.