This is way over my head, but I believe the Armenian Catholics belong to the Oriental Orthodox, to make matters confusing.
What? I don't think so - the Armenian Catholic Church is under the Pope, not the Catholicos of the Armenian Apostolic Church in Etchmiazdin, the other Catholicos in Cilicia or any other Oriental Orthodox patriarch.
And apart from Oriental Catholics, there are Chaldean Catholics who intercommune with the Assyrian Church of the East. This has sparked some controversy among Catholics, because the Chaldean Church lacks an institution narrative. IIRC.
Most interesting that. The Chaldean Catholic Church is the only Eastern Catholic church in the world that is bigger than its parent, the Assyrian Church (Church of the East, formerly known as Nestorian), and so has a good claim to be the Church of Iraq.
The Assyrian Church's liturgy indeed lacks an institution narrative but I think is also the oldest eucharistic liturgy still in use. It's also in a form of Aramaic, the language Jesus spoke.
The Catholic Church came out with a curious statement a while back that said basically 1) it is forced to acknowledge that the Assyrian Liturgy of SS. Mari and Addai is 'valid' as is (given the rite's antiquity, it could do nothing else), 2) that Chaldean Catholics are free to use it in its pure form without the tacked-on institution narrative they'd been using (an example of latinization, the needless bastardization of the Eastern Rites by some Catholics) and 3) in a weird instance of passive-aggressive doubletalk, 'warmly inviting' those in question to use the institution narrative.
I reckon that really means 'OK, your Mass is real, but we really don't like it and wish you wouldn't use it (or else)'.