Hello,
I was recently comparing Orthodox & Catholic translations of the Divine Liturgy and a small but peculiar difference between translations stood out in the commemoration of he hierarchs during the anaphora.

In most English translations, the text reads something like a petition so that the hierarchs may faithfully teach the “word of your truth”. In the current Ruthenian (and Antiochian Orthodox) text, it seems to take for granted that the hierarchs would just automatically be faithfully imparting the “word of your truth”.

Here is the full text from the Pittsburgh Metropolita:

Among the first, O Lord, remember our holy father (Name), Pope of Rome, our most reverend Metropolitan (Name), our God-loving Bishop (Name). Preserve them for your holy churches in peace, safety, honor, and health for many years as they faithfully impart the word of your truth.

I am curious about the underlying Greek and Slavonic if it could shed any light on the original meaning of text. Does it presume the hierarchs are faithfully teaching the word or is it a petition that they may teach the word faithfully?

I'm not expert in any of this so my opinion is that of an ignorant layman. But based on what you've presented, I would assume it's the latter.

Well, technically, it is neither. This is a quote/reference to 2 Timothy 2:15. The word in Greek means "to cut straight; to set forth truthfully, without perversion or distortion". In older translations it would be rendered "to divide rightly (correctly)". Here, grammatically, it is an present active participle (accusative singular masculine), which is describing the (arch)bishop (or in this case Pope and (arch) bishop). The text can be rendered (from Greek):

Among the first be mindful, O Lord, of our Archbishop (name), whom grant-for thy Churches in peace-(that he be) safe, honored, healthful, increasing in days, and dividing rightly the word of thy truth.

I would say that (if I read rightly) that this a petition that he teach the word rightly, although in St Paul, this is an attribute he should already possess, so it would be a petition for him to retain the attribute. It a way, it is asking for both-that they are teaching rightly and that they continue to do so.