Meaning of Papal Descriptions

Here's the challenge to Roman Catholics. State what the following expressions (I-IV) mean, preferably from some sort of authoritative source. Try to do so positively. (Please note, this post is a carry-over from a previous comment box discussion between Louis and Sean Patrick - I've slightly expanded on the original challenge there).

I realize that this is a big challenge, and that it is much easier sometimes to explain what an expression does not mean than to explain what an expression does mean. So, for those unable (or unwilling) to meet the primary challenge, I offer a secondary challenge of explaining why these titles cannot be understood as a fulfillment of 2 Thessalonians 2:3-4, bearing in mind that the passage doesn't say that the man of sin (the son of perdition) is not specifically described as calling himself God.

I. "Christ on Earth"

John Paul II:

Against this background of love towards Holy Church, "the pillar and bulwark of the truth" (1 Tim 3:15), we readily understand the devotion of Saint Francis of Assisi for "the Lord Pope",the daughterly outspokenness of Saint Catherine of Siena towards the one whom she called "sweet Christ on earth",the apostolic obedience and the sentire cum Ecclesia of Saint Ignatius Loyola,and the joyful profession of faith made by Saint Teresa of Avila: "I am a daughter of the Church".We can also understand the deep desire of Saint Theresa of the Child Jesus: "In the heart of the Church, my mother, I will be love".These testimonies are representative of the full ecclesial communion which the Saints, founders and foundresses, have shared in diverse and often difficult times and circumstances. They are examples which consecrated persons need constantly to recall if they are to resist the particularly strong centrifugal and disruptive forces at work today.A distinctive aspect of ecclesial communion is allegiance of mind and heart to the Magisterium of the Bishops, an allegiance which must be lived honestly and clearly testified to before the People of God by all consecrated persons, especially those involved in theological research, teaching, publishing, catechesis and the use of the means of social communication.Because consecrated persons have a special place in the Church, their attitude in this regard is of immense importance for the whole People of God. Their witness of filial love will give power and forcefulness to their apostolic activity which, in the context of the prophetic mission of all the baptized, is generally distinguished by special forms of cooperation with the Hierarchy.In a specific way, through the richness of their charisms, consecrated persons help the Church to reveal ever more deeply her nature as the sacrament "of intimate union with God, and of the unity of all mankind".

- John Paul II, Vita Consecreta, Chapter II, Section 46 (25 March 1996)

John Paul II:

With the same vigour, Catherine addressed Churchmen of every rank, demanding of them the most exacting integrity in their personal lives and their pastoral ministry. The uninhibited, powerful and incisive tone in which she admonished priests, Bishops and Cardinals is quite striking. It is essential—she would say—to root out from the garden of the Church the rotten plants and to put in their place “new plants” which are fresh and fragrant. And strengthened by her intimacy with Christ, the Saint of Siena was not afraid to point out frankly even to the Pope, whom she loved dearly as her “sweet Christ on earth”, that the will of God demanded that he should abandon the hesitation born of earthly prudence and worldly interests, and return from Avignon to Rome, to the Tomb of Peter.

- John Paul II, Proclamation of the Co-Patronesses of Europe, Section 7 (1 October 1999)

Tarcisio Bertone, SDB (Archbishop Emeritus of Vercelli):

The twentieth century was one of the most crucial in human history, with its tragic and cruel events culminating in the assassination attempt on the “sweet Christ on earth”. Now a veil is drawn back on a series of events which make history and interpret it in depth, in a spiritual perspective alien to present-day attitudes, often tainted with rationalism.

- Bertone, Introduction to The Message of Fatima (apparently 26 June 2000)

Professor Maria Antonietta Falchi Pellegrini:

Your Eminencies, Excellencies, reverend and dear priests, I feel especially honoured to provide this small service to you, whom St. Catherine of Siena defines as "Ministers of the Blood of Christ", in this patriarchal Basilica, centre of Catholicism, housing the Chair of he who is the "Sweet Christ on earth".

...

Only the Pope could correct the defects of the priests, and not the laity who should always revere them, since Christ left to the Apostle Peter and his successors the key of His Blood, from which all the Sacraments gain life. The Pope, with ardent faith recognised by Catherine as "sweet Christ on earth" and called with tender affection "My kindest daddy" is asked to work strongly for the reform of the Church. "Intervene to eliminate the stink of the ministers of the Holy Church; pull out the stinking flowers and plant scented plants, virtuous men who fear God".

- Pellegrini, St. Catherine and the Priests: a Message for the Church of the Third Millennium (17 May 2000)

II. "Christ and His Vicar constitute one only Head" (Unum solummodo Caput constituere Christum eiusque Vicarium)

Pius XII:

But we must not think that He rules only in a hidden or extraordinary manner. On the contrary, our Redeemer also governs His Mystical Body in a visible and normal way through His Vicar on earth. You know, Venerable Brethren, that after He had ruled the "little flock" Himself during His mortal pilgrimage, Christ our Lord, when about to leave this world and return to the Father, entrusted to the Chief of the Apostles the visible government of the entire community He had founded. Since He was all wise He could not leave the body of the Church He had founded as a human society without a visible head. Nor against this may one argue that the primacy of jurisdiction established in the Church gives such a Mystical Body two heads. For Peter in view of his primacy is only Christ's Vicar; so that there is only one chief Head of this Body, namely Christ, who never ceases Himself to guide the Church invisibly, though at the same time He rules it visibly, through him who is His representative on earth. After His glorious Ascension into Heaven this Church rested not on Him alone, but on Peter, too, its visible foundation stone. That Christ and His Vicar constitute one only Head is the solemn teaching of Our predecessor of immortal memory Boniface VIII in the Apostolic Letter Unam Sanctam; and his successors have never ceased to repeat the same.

They, therefore, walk in the path of dangerous error who believe that they can accept Christ as the Head of the Church, while not adhering loyally to His Vicar on earth. They have taken away the visible head, broken the visible bonds of unity and left the Mystical Body of the Redeemer so obscured and so maimed, that those who are seeking the haven of eternal salvation can neither see it nor find it.

- Pius XII, Mystici Corporis Christi, Sections 40-41 (29 June 1943)

III. In Persona Christi as a Specific Sacramental Identification of the Priest with Christ

John Paul II:

The priest offers the holy Sacrifice in persona Christi; this means more than offering 'in the name of' or 'in place of' Christ. In persona means in specific sacramental identification with 'the eternal High Priest' who is the author and principal subject of this sacrifice of His, a sacrifice in which, in truth, nobody can take His place.

- John Paul II, Letter titled "Dominicae Cenae" (24 February 1980)

IV. "Lord Pope"

See the first item from Section I above. And additionally:

Pius XII:

The Seraphic Father commanded that the Rule and the Life of the Friars Minor should be the following: to observe the "holy Gospel of Our Lord Jesus Christ" living in obedience, without possessing any property, and in all chastity, and this not according to one's own whims or individual interpretation of the Rule, but according to the commands of the Roman Pontiffs, canonically elected. For those who eagerly longed "to follow this manner of life. . . they had to be, first, diligently examined by the Father Ministers concerning their Catholic Faith and their reception of the sacraments of the Church; whether they believed all these things and were firm in their intention to profess them until death." Those who had already become members of the Order must for no reason leave except it be "by order of Our Lord, the Pope." To the clerics of the Order it is prescribed that they celebrate "the divine office according to the calendar of the Roman Church"; to the friars in general it was commanded that they should not preach in the territory of a bishop without his permission, and that they should not enter, not even for reasons of their ministry, the convents of sisters without a special faculty from the Apostolic See. No less reverence and docility towards the Apostolic See is shown by the words which St. Francis uses in commanding that a Cardinal Protector should be appointed for the Order: "In obedience, I enjoin the Ministers to ask the Lord Pope for one of the Cardinals of the Holy Roman Church to be the guide, protector and corrector of this Brotherhood; so that subordinate at all times and submissive, at the feet of the same Holy Roman Church, and thus firm in the Catholic Faith, . . . we shall observe, as we have faithfully promised to do, the holy Gospel of Our Lord Jesus Christ." (Rule of Friars Minor, passim)

- Pius XII, Rite Expiatis, Section 25 (30 April 1926)

Benedict XVI:

I welcome you with great joy at this happy and historical event which has gathered you: the eighth centenary of the approval of the "Protorule" of St Francis by Pope Innocent III. Eight hundred years have passed and that dozen Friars has become a multitude, scattered across every part of the world and today here, is worthily represented by you. In the past few days you have been meeting in Assisi for what you have chosen to call the "Chapter of Mats", to recall your origins. And at the end of this extraordinary experience you have come together to see the "Lord Pope", as your Seraphic Founder would have said.

- Benedict XVI, Address to the Franciscan Family (18 April 2009)

Conclusion

So, there you go. As to each of the four descriptions you can either explain what they mean or explain why these titles cannot be understood as a fulfillment of 2 Thessalonians 2:3-4, bearing in mind what is noted above. Thus, there are tons of ways to respond (ranging from responding to just one explanation of one of the four descriptions to both explanations of all four, about 2,481 permutations of possible responses). People who are not Roman Catholics are also welcome to chime in, though the challenge is primarily for Roman Catholics.