As a TL;DR, we came up with two alternative protocols for Ark, which have the following properties:
“Erk”: no user interactivity for rounds offline refresh (server can refresh for a user) perpetual offline refresh (server can keep refreshing for a user indefinitely) works best with single input and single output vtxo requires CTV + CSFS
“hArk”: no user interactivity for rounds very efficient, also for multiple inputs no offline refresh possible (so far) requires CTV only