The Catholic Understanding of the Papacy

When thea ten northern tribes seceded from the union and set up their rival temple, some of them said, you know, we need to worship at jerusalem. And in the same way, if it's established that god set up within the church a petrine institution for its government, then most likely to guide people who are in communion with that institution into a correct understanding of it as opposed to people who have separated from it. So i would make a primafacial case on that basis, for a, the catholic understanding of the papacy is more likely to be true than orthodox understanding or lutheran understanding.