Thanks for the correction on nuclear state. It's hard to imagine anything having absolutely no state - but I guess a nucleus is not a "thing" as such, even if surrounded by lots of similar non-things. Does state not subsist in the total assembled mass in my example of near-critical collection?

Just answering myself after some reading today.

No, not really Because fission caused by free neutrons (which are rare) is something different from more common "spontaneous" radio-decay.

That does beg the question; what is the cause that we don't yet understand, what lies behind little bits of the universe falling apart?