"The project is exploring a replicated-kernel OS model for the Linux operating system. In this model, multiple Linux kernel instances running on multiple nodes collaborate each other to provide applications with a single-image operating system over the nodes. The kernels transparently provide a consistent memory view across the machine boundary, so threads in a process can be spread across the nodes without an explicit declaration of memory regions to share nor accessing through a custom memory APIs. The nodes are connected through a modern low-latency interconnect, and each of them might be based on different ISA and/or hardware configuration."

Intuitively, I would think that the way to do this would be as follows:

First, we have the memory hierarchy, disk at the bottom, increasingly faster (but smaller) regions of memory closer to the CPU.

Now, if let's say a process shares memory across nodes, then what seems to make sense would be moving chunks of that memory, as needed, as "cache blocks" to the local machine that needs it.

Observation: That pattern is really not very different than what OS's do with swap files / virtual memory, except that the "swap file" is actually a larger memory region located on a remote node, across the network...

Of course there may be other issues with respect to locking, synchronization objects in memory, thread scheduling, etc., etc., but if you got the above memory access pattern right, then you'd go a long way to enabling such an OS...