You are again incorrect.  I'm speaking of the succession of popes -  Linus, Cletus, Clement and so on.  Apostolic Succession certainly wasn't modeled after the imperial state now, was it?  Especially when the imperial state was murdering them all.  They lived and led the Church 2 hundred years before Constantine.  That's not a circular argument, it's an historic, linear one.
Perhaps you might read the works of the Early Fathers from the 2nd and 3rd centuries.  You know, Tertullian, or even perhaps  St. Cyprian, who, BTW wrote "On the Unity of the Church",  in which he states, "those who start their own 'churches' are deceiving with serpent’s tongue, and artful in corrupting the truth, vomiting forth deadly poisons from pestilential tongues” (AD 250).
It is interesting being accused of "revisionist history" by someone who doesn't know the first thing about it.