There’s no such thing as a formal correction of the Pope. The Pope is the highest, supreme authority in the Church and answers to Jesus Christ alone.
The Eighth Ecumenical Council:
"We believe that the saying of the Lord that Christ addressed to his holy apostles and disciples, Whoever receives you receives me, and whoever despises you despises me, was also addressed to all who were likewise made supreme pontiffs and chief pastors in succession to them in the catholic church. Therefore we declare that no secular powers should treat with disrespect any of those who hold the office of patriarch or seek to move them from their high positions, but rather they should esteem them as worthy of all honour and reverence. This applies in the first place to the most holy pope of old Rome, secondly to the patriarch of Constantinople, and then to the patriarchs of Alexandria, Antioch and Jerusalem. Furthermore, nobody else should compose or edit writings or tracts against the most holy pope of old Rome, on the pretext of making incriminating charges, as Photius did recently and Dioscorus a long time ago. Whoever shows such great arrogance and audacity, after the manner of Photius and Dioscorus, and makes false accusations in writing or speech against the see of Peter, the chief of the apostles, let him receive a punishment equal to theirs.
“If, then, any ruler or secular authority tries to expel the aforesaid pope of the apostolic see, or any of the other patriarchs, let him be anathema. Furthermore, if a universal synod is held and any question or controversy arises about the holy church of Rome, it should make inquiries with proper reverence and respect about the question raised and should find a profitable solution; it must on no account pronounce sentence rashly against the supreme pontiffs of old Rome.”
papalencyclicals.net/councils/ecum08.htm
Pope Gregory VII:
“He himself may be judged by no one.”
en.wikipedia.org/wiki/Dictatus_papae
Saint Thomas Aquinas:
“The administration of this kingdom, therefore, is entrusted not to earthly kings, but to priests, so that spiritual and earthly things may be kept distinct; and in particular to the Supreme Priest, the successor of Peter, the Vicar of Christ, the Roman Pontiff, to whom all the kings of the Christian people should be subject, as if to the Lord Jesus Christ Himself.”
[(name removed by moderator).uw.edu.pl/mdsie/Polit…%20Aquinas.pdf](
http://www.(name removed by moderator).uw.edu.pl/mdsie/Polit…%20Aquinas.pdf)
Pope Boniface VIII:
“But if the highest power of all err, it can be judged only by God, and not by man.”
papalencyclicals.net/bon08/b8unam.htm
Saint Catherine of Siena:
“For divine obedience never prevents us from obedience to the Holy Father: nay, the more perfect the one, the more perfect is the other. And we ought always to be subject to his commands and obedient unto death. However indiscreet obedience to him might seem, and however it should deprive us of mental peace and consolation, we ought to obey; and I consider that to do the opposite is a great imperfection, and deceit of the devil.”
drawnbylove.com/Scudder%20letters.htm
Pope Pius II:
“Do you not know, you miserable man, that only divine authority binds the Roman Bishop? The Pope is only subject to Holy Scripture, revealed by the hand of God, and he is not bound by decrees of men. ”But we say that the pope is subject to reason, and the power of the Church is given for edification and not for destruction.” But even if you believe the Bishop of Rome to be in error, that does not give you the right to judge him, for only God can judge the Pope. No mortal man may accuse him of faults. Oh, how wrong is the opinion of many men: though they do not allow a king’s subjects to have any say against the king, they would allow it in the case of the pope even if God has given him power over all mortal men. Those stupid men are unconcerned that the Holy Apostolic Church has, from Saint Peter to this day, never been heard to teach anything that is contrary to orthodox faith. This privilege it has received from the Lord that it shall never succumb to wrong teachings for the gates of hell shall not prevail against it. Let this suffice concerning your praise of the Apostolic See.”
hal.archives-ouvertes.fr/hal-01184531/document
Code of Canon Law:
“No appeal or recourse is permitted against a sentence or decree of the Roman Pontiff.”
vatican.va/archive/ENG1104/__P16.HTM