I have no problem with the definition of "Apostolic Succession", though I don't agree it is necessary or that it is shown from Scripture to be a requirement. But that's another story. :-)
Well, yes there is a published list of "Popes" and "Anti-Popes" going all the way back to Peter. It is this list which I believe is imaginative if nothing else.
Fair enough, but can I ask why? Eusebius and other early historians give the list from Peter to the 300s A.D., and from then on I'm pretty sure we have contemporary documentation in every century till the present.