Third Party (PhotonPUN) Physics/pathfinding running differently on different clients?

Here's the scenario: I am trying to synchronize pathfinding (The A* Project) across multiple clients, so that I don't have to send/recieve a lot of position data. It's just not working: I ensure that the moving objects on all clients start in the exact same place, and that they use the exact same logic, and that they start at nearly the exact same time (frame-time permitting). But there are always these little deviations that cause objects to wind up in noticeably different places, especially if objects bump into each other. How can this be? I've eliminated all the influence of randomness and latency that I can think of. Could it be just the random deviation of floating-point numbers that causes the chaotic spiral?

Any suggestions would be appreciated.

 

This sounds as if you run on unit's pathfinding on multiple clients?
I would suggest you run each unit's pathfinding on one machine and then send the next nodes and when to reach them, so other clients can move the unit there and arrive at the same time?

The problem is so general that it's hard to help at all.

 

Here's a more detailed description of what I've done to try and follow the doctrine outlined in the "1500 Archers" article:

1. Logic on the owner-instance of an object determines that the object should move.
2. The owner instance sends an RPC to remote instances which contains the move destination, the current position of the object on the owning client, the current velocity of the object on the owning client, and a time in the future when the move should start. This time is far enough in the future that even after network latency, there should be some wait-time left over.
3. Remote objects change their position and velocity to that of the object on the owner client (note: I do understand that there is an opportunity for the object on the owner client to move in the interem, but in my testing the objects are stationary, so I don't think that's the cause of this problem).
4. Objects on all clients wait until the start time determined in step 2, using PhotonNetwork.Time as a reference.
5. Objects in all clients use A* Project pathfind logic to generate a path. (note: I have confirmed that the paths generated are the same)
6. Objects propel themselves along this path. After about 0.2 seconds, or four pushes on the rigidbody, a slight deviation emerges in the position/velocity/impulses of these objects. This is the problem.