I was trying to follow the math as well, but didnt get it. Maybe due to my limited understanding of making a very easy bitcoin calculation so difficult in formulas 
I tried to reverse the idea, and think about attack vectors and the validation of the system (nodes validations and miner validations, where a single wrong tx makes also end up in an invalid block, destroying potential revenues). There is no view on this from the bottom, instead it postulates a model, and derives limits of blockchain. Without links to reality. So I believe it is a speculative paper to prove at a scientific level, that bitcoin cannot scale. And this smells like fiat banks or big blockers behind the paper...
I tried to reverse the idea, and think about attack vectors and the validation of the system (nodes validations and miner validations, where a single wrong tx makes also end up in an invalid block, destroying potential revenues). There is no view on this from the bottom, instead it postulates a model, and derives limits of blockchain. Without links to reality. So I believe it is a speculative paper to prove at a scientific level, that bitcoin cannot scale. And this smells like fiat banks or big blockers behind the paper...
I *think* the author is trying to say that bitcoin cannot grow due to the fact that if it will, the incentive to do a 51% attack would become too big.
To counter this his argument is that the transaction value of each block must be atleast X amount of $, ( to make it unprofitable to do such an attack, (Right?)), which means that relative small transactions will become impossible, ( due to the high fees and limited blocks) and thus bitcoin would never "work" on a larger scale/be adopted due to the fact that there are much better/cheaper options out there.
I've skimmed through the text, so i might be completely wrong here though.
I'm not too sure if his math checks out either. We've seen bitcoin work reasonably well at a marketcap of >200 billion, so i'm not quite sure how accurate all his statements are.