The historical documented evidence is in Book III, Chapter 3 of the book by St. Irenaeus against heresies mentioned in the original post.
This is a legitimate work recognized by modern scholars. Irenaeus wrote circa 175-185 A.D. and cannot be dismissed as an illegitimate source.
Research Against Heresies for yourself, don’t take my word for it; you will find that his list of the earleist Popes is legit
The longer one studies looking for real truth the more it becomes evident that the history the Catholic Church claims is pure fiction. There is not indication whatsoever that Linus was even a Bishop.
Very little is known about Linus. St. Irenaeus of Lyons (d. 200) and the historian Eusebius of Caesarea (d. ca. 339) identified him with the companion of Paul who sent greetings from Rome to Timothy in Ephesus (2 Timothy 4:21), but Scripture Scholars are generally hesistant to do so...It should be remembered that contrary to pious Catholic belief--that monoarchical episcopal structure of church governance (also known as the monarchical episcopate, in which each diocese was headed by a single bishop) still did not exist in Rome at this time (McBrien, Richard P. Lives of the Popes: The Pontiffs from St. Peter to Benedict XVI. Harper, San Francisco, 2005 updated ed., pp. 33-34).
That would be Richard P, McBrien, priest, editor of the Catholic Encyclopedia.