AS API gives no way to tell ASes about state resolution, so their view of room state can diverge over time.

This is equivalent to https://github.com/matrix-org/synapse/issues/2735 but for AS API rather than /sync.

The proposed solution is to extend the AS API so pushed transactions can be decorated with any state updates which have happened due to resets at the point of the event being sent.

I'm a bit unclear on why this has to be a decoration rather than just inserting copies of the restored events in the right place in the series of transactions (which is basically the approach that https://github.com/matrix-org/synapse/issues/2735 seemed to be converging on)?

Start by reading the AS API context in this issue and the linked Synapse issue 2735. Compare decorating pushed transactions with state updates against inserting restored events into the transaction sequence. Done means the AS API specifies how reset-related state updates reach application services without their room-state view diverging.

Written by the indexing model from the issue text.