I just skimmed through it so maybe I'm missing something, but it also appears to be incomplete. It even says "the completion of the rigorous derivation of the above results will be presented in a companion paper". He brings up equation 1.6 but I don't see a rigorous handling of its asymptotics, nor any precise statement of what the growth rate of zeta on or near the critical line is expected to be. The conclusions section also says about as much. I hope it works out and we will see the conclusion, but I'd really like to see some precise growth rates so we can at least compare it to known bounds and example.