That seems like a very hard problem. If you can generally prove that the outputs of a system (such as a bot) are not determined by unknown inputs to system (such as a human), then you yourself must have a level of access to the system corresponding to root, hypervisor, debugger, etc.
So either moltbook requires that AI agents upload themselves to it to be executed in a sandbox, or else we have a test that can be repurposed to answer whether God exists.