That seems to speak to "proximity" and "affinity", with regards to "coherency", and "mobility". To "move" state, about state & scope or the contents of (some of) memory and registers, of a process or task, here is described as "re-seating" which is also the usual enough idea in programming like C and C++.
Perhaps the most usual example is pre-emptive multithreading itself, about basically the state as a stack, and "process control block" and "thread control block" usually enough, about context-switching.
In this "Critix" concept, or "DeepOs" (or "BeepOs/DeepOs"), the idea of the "re-routine" as a model of asychronous concurrency, is a little different than the usual idea of a co-routine, which is usually enough a fork in the process model, then about signals as IPC with PID and PPID, vis-a-vis, fibers and threads or events and task queues, basically the re-routine never "blocks" and has no "yield" nor "async" keywords in the source text, instead any call to a re-routine implicitly yields, and then the re-routine is run again later, the re-run, where as the re-routine is filled in, then then the re-routine adds a penalty of basically n^2 in time to be completely non-blocking and where asynchrony is modeled in the language as the normal procedural flow-of-control.
Then, as that's only in the kernel itself, that n^2 might seem a huge penalty, yet, it's actually quite under that, since as the re-routine its data (in a stack) is filled in, then most of its routine is cache hits, the "memoized" calls to the re-routine.
About the allocator, then this design concept basically is for making use of virtual memory, to be able to "re-seat" the memory of a process without changing a process' view of the memory. This can help avoid both syscalls and memory fragmentation, since memory paging basically is performed by the user-space process in its time instead of by the kernel. This has the usual guarantees of process memory that it's to be visible only to the process itself unless explicitly shared, that then being treated as a usual sort of shared resource in the distributed sense.
The syscalls by a process essentially yield (the process yields to the scheduler), about ideas like round-robin and fairness and anti-starvation and incremental-progress in the scheduler, while it's so that until a process gets any other signal and only touches its own memory that's non-yielding, then about the machinery of pre-emptive multithreading or context-switch and as with regards to hyper-threading or the interleaved contexts on the double-pipeline CPUs, the idea being that context-switching is along the lines of basically a periodic signal interrupt.
Notions of "Orange Book" and "mandatory access control" then are considered "more than good ideas" with regards to the allocator and scheduler of resources in computation.