There are only two marks of unity given to the one holy Roman Catholic and apostolic Church:
Okay, I'll make the obvious and obligatory retort (I'm sure pax has already lined up an answer, and I'd like to see his cards).
I thought it was a clear teaching of the Church that there are
four marks of unity. You've already identified them in your post, and the same words also appear in the Nicean Creed which is read at every mass. The Church is:
1. One. That is to say, the Church is united by common teaching, common sacraments, common liturgy, and common obedience to a single pontiff. (This
one classic point seems to include, by itself, the
two novel points you've introduced.)
2. Holy. This Church (and only this Church) was founded by Christ (and only by Christ). Therefore it is biconditionally holy. It is the continuation of Christ's incarnation on earth. It has been granted a divine promise of infallibility, and the grace of God Himself is present in the sacraments.
3. Catholic, i.e. universal. The Church (potentially) includes everybody, living or dead or not yet born, independent of race or class, or any other natural constraint.
4. Apostolic. Only those prelates who stand in the line of apostolic succession actually constitute the clergy; the graces, blessings, and fitness to confect the sacraments attach only to them. No divine promise, no guarantee of saving grace, is explicitly given to any other Church or clergy.
Interestingly, these for marks are collectively logically necessary for a consistent and complete ecclesiology. They are the Four Pillars of Truth. If you remove any one, then the Church becomes subject to diffusion and revision. Given their logical character, it is possible that a Syballine intellect could have articulated something like them even before Christ founded the Church. She would not have been able to point to a True Church, but she would have been able to say "These are the features the True Church will have when it shows up." The exact circuмstances of the Incarnation could not, of course, have been predicted in advance by
the human intellect alone. A prophecy would have been required for that, and even the Old Testament prophecies of Christ's advent were not specific in every detail. But this proves that an Incarnation "event" was analytically necessary for salvation. If Christ did not come, then man could not be saved. Therefore Christ's coming would have been expected by every man of primitive faith. He would not know what form it would take, but he knew he would know it when he saw it.
"Abraham rejoiced to see my day..." is the corollary of
"Let earth receive her King." The Lord's coming was surely to be expected. Those who recognized Him would be saved. Those who did not were damned already.
The truth of any proposition is proved when it harmonizes with all of the facts, whereas a false proposition quickly runs at varience with them. The four marks of the Church harmonize with everything else we have been given concerning ecclesiology, christology, and natural revelation. Therefore it is just and right that we should accept them. And if that's not enough, let's not forget that they are in the Creed after all, which does not mention either the Eucharist or the pope.