Open questions
One question, and what would settle it.
What did the khaz neumes of Armenian chant instruct a singer to do?
Why it is open. Khaz signs were written above Armenian chant texts from about the ninth century and grew steadily more elaborate, but they did not fix pitch and appear to have cued gestures a singer already knew. When that oral knowledge lapsed the signs stopped being readable. Komitas Vardapet worked on the problem for years without reaching a reading, and Robert At'ayan's systematic study did not produce an agreed decipherment. There is no camp to argue against; the work simply stopped.
What would resolve it. A manuscript pairing khaz with a notation whose values are known, or a securely dated source setting Armenian signs beside Byzantine ones for the same melody, would give the system the external check it has never had. Comparative work on the earliest strata, before the signs multiplied, may also be able to fix a small core of them.
Field. Musicology and Armenian palaeography