IIUC one idea here is to apply the concept of 'reliable function' into the object oriented world:

> For example, this would allow “real objects” to be world-lines of their stable states and they could get to their next stable state in a completely functional manner.

So [object_in_state_A + message_Y] => [object_in_state_B] is some change in an object as a result of receiving a message. This 'transformation' is functional i.e. always produces the same result, given the same input state and message (similar to the pure function concept in FP). Also, the transformation 'rules' only see exactly state_A and not some invalid in-between state. This allows reasoning about these transformations clearly. The object is a history of object states: [object_in_state_A -> object_in_state_B -> object_in_state_C] etc. Note only the 'stable' i.e. valid states are exposed by the object (they're unavailable during transformation) so any view is consistent.

Now to compose many such objects into larger system that is also consistent, see the Virtual Time idea (David Jefferson) or the earlier Pseudo Time idea (David Reed). An overview of Virtual Time is here: https://blog.acolyer.org/2015/08/20/virtual-time/.

The rough idea is that all messages are stamped with a virtual timestamp - so any receiver can determine the exact order in which to apply the incoming messages. The whole system moves forward in virtual time, correcting for any out-of-order delivery - the real time of each message isn't important anymore.