No, Scripture does not state that Peter is the rock upon the church was built. Peter's confession, "You are the Christ, the Son of God," is the rock. I do agree that the apostolic leadership continued, but it is not institutionalized in the Roman Church. It is institutionalized in the Word of God, and the living Word of God, Christ.
The equivalent of your interpretation is, "You are 'rock', and I could really go for a chocolate malt."
Your interpretation implies that Jesus wasn't capable of forming a simple analogy in a complete sentence.
The 'rock' refers to Simon Peter. It doesn't change meaning within the same sentence.
do agree that the apostolic leadership continued, but it is not institutionalized in the Roman Church.
You have no proof that it wasn't, just a fact not in evidence.
So why are you calling Simon "Rock" then? Why does Paul call Simon "Rock"? Why do the Gospel writers call Simon "Rock"? Aren't you YOURSELF refering to a person, rather than a spoken confession?
Christ didn't say "I am rock {Peter}", but "YOU are rock {Peter}"
The Church Fathers also agree with this interpretation, even Eastern Church Fathers, such as St. John Chrysostom. It is only those who refuse to accept authority given by God who make the claim that ONLY Simon's confession is the Rock. IF the confession was the Rock, why didn't Christ call all of the Apostles in the boat of Mt 14 rocks when they called Him the "Son of God"? Or Nataniel in John 1?
Regards