it’s not like that aren’t people who dispute the existence of a monarchial episcopate in the first century,
I am sure there are; however, the early 1st century Church stood firm on the infallibility and leadership of Peter and his successors. There have been anti-popes and heretics since the beginning of Christianity; this does not mean there is not a valid office of the papacy.
I refer you to the Council of Jerusalem, where Peter spoke to end discussions and the assembly fell silent. If you do not accept this as convincing evidence because it is from the Acts of the Apostles and not considered divinely inspired or historical then we have another issue.
it’s not like there weren’t any interregnums and dispute over the papal office in the history of popes
It is interesting to note that for over 250 years, the Roman Empire tried to exterminate Christianity by brutal persecutions. Within the first 31 popes, 28 of them were martyered. The Roman emperors sure knew who to go after to end Christianity: kill the leaders.
When a pope was martyred, there is time in between his death and the appointment of the next papal seat. For logisitic reasons, the turnaround can not be within a day or immediately.
St. Peter was the first pope and was martyred and his successor was St. Linus. It would be reasonable to believe there was a time when Peter was dead, and thus not the pope, and Linus had not yet been elected. So would this in-between-time constitute a “breaking” in the chain of apostolic reign to you?
Look at St. Dionysius (r. 260-268), who was martyred December 26, 268 A.D. His successor was not elected until January 5, 269. There are 10 days in between these two papal reigns.
Do these instances constitute as “breaking” the chain of authority to you? And if they do, how would you address that the Church should have fixed their issue so that no time lapsed inbetween the passing of one pope to the next? Have a few on reserve just in case something happens? Information did not travel instantaneously in the 200’s as it does today.
I think you are confused by the “unbroken chain” in terms of time vs. valid apostolic succession. The “unbroken chain” does not refer to time passed between papal reigns, as it would be impossible to predict when a pope would die. A pope would have to have a few backup popes with him wherever he went, just in case he were to die or become incapacitated and would need a new successor.
Rather, this “unbroken chain” refers to the laying on of hands by a validly consecrated bishop. One pope was validly consecrated by the laying on of hands by a validly consecrated bishop, who was ordained by the laying on of hands by another validly consecrated bishop, etc. all the way back to the original apostles. This is the “unbroken chain” of successors that Catholics are referring to.
