Hmmm. I think you might be on to something…. but this is going to take a looong time to digest.
My brain got as far as “Note that there are K ∗ J states for the array elements…” and segfaulted… Why isn’t that J**K states? But maybe it’s just I haven’t finished my morning coffee….
So I’m doing a Bad Thing. Making a bookmarking comment to come back to when I have digested it.
I am adding the state set counts of modules when the system is factored. So K elements of J states each. If we construct the product, we get J^K.