To no one's surprise, Verizon has appealed the FCC's misguided net neutrality rules. In its petition for review in the DC Circuit, among the other reasons for vacating the FCC's rules, Verizon asserts, in the words of the APA's judicial review provision, that the regulations are "contrary to constitutional right."
By this, I assume that Verizon means that the rules violate the First Amendment. I was one of the first, if not the first, to argue that net neutrality mandates are inconsistent with the First Amendment. You can find my law review article, "Net Neutrality Mandates: Neutering the First Amendment in the Digital Age," here.
I hope Verizon presses this argument on appeal.