How can we know which person is a valid Pope, and which persons might be antipopes (a false claimant to the papacy)? The answer is simple and dogmatic: the Church is indefectible. Therefore, God’s providence and grace NEVER permits anyone to be accepted by the body of Bishops as the Roman Pontiff, the Head of the Church, other than a valid Pope. There have been many antipopes in the history of the Church. Not a single one was a Head accepted by its Body, the Church.
What factors make a papacy valid?
There are only three factors needed for a papacy to be valid:
1. The person must be validly elected.
2. The person must freely accept the papal office.
3. The person must be ordained as a Bishop.
Some commentators add that the candidate for the papacy must be an adult male. But those requirements are included in the condition that he must be ordained as Bishop (before or after his election). Only adult men can be ordained to the episcopal degree.
You might think that, once all three conditions for a valid Pope are met, the candidate must be installed in some type of ceremony before he is actually the Pope. But technically, this ceremony is not essential. The three factors needed for a valid Pope are explained by Pope Saint John Paul II in the Apostolic Constitution Universi Dominici Gregis:
Pope Saint John Paul II: “While it is indeed a doctrine of faith that the power of the Supreme Pontiff derives directly from Christ, whose earthly Vicar he is, it is also certain that this supreme power in the Church is granted to him ‘by means of (1) lawful election (2) accepted by him, together with (3) episcopal consecration’.” [Universi Dominici Gregis; inner quote from Canon law]
The ceremony for the inauguration of the Roman Pontiff is traditional, and should be observed. But it is not required for validity. Indeed, the ceremony used to include a literal coronation. The last to be crowned with the papal tiara was Pope Paul VI. Each of his successors opted to omit that portion of the ritual.
Proof of Validity
But I suppose that malicious persons are always able to invent a set of fictitious accusations, sufficient to rise to a level that would, if true, invalidate an election. So how can we know that such a case has not occurred? The answer is simply the same as for the other questions already resolved above. God protects the Church, making Her indefectible. The Ark of Salvation can never sink. The Rock on which the Church is founded can never fail.
Therefore, if the Bishops and dioceses of the world accept the election of anyone as Pope, then this work of the Holy Spirit confirms the validity of his election and his papacy. For if the Bishops as a body were to accept an invalid Pope, the Church would no longer be indefectible. She would have gone astray by having an invalid leader. Therefore, the acceptance of any Pope by the body of Bishops dispersed in the world confirms the validity of his election and his papacy.
Much more on this point in my book: In Defense of Pope Francis.
Please take a look at this list of my books and booklets, and see if any topic interests you.