I wrote a random number generator with an unbounded state size. I don't know where to begin proving it to be (or proving it isn't) disjunctive. What would be a property of a disjunctive sequence, besides that it simply must contain all finite sequences? I cant find a finite sequence that my PRNG definitely won't produce given infinite output and infinite memory to store the state.
My best guess is that it is disjunctive, because the state size will always eventually grow to dwarf every finite sequence. Additionally, I was able to prove that it is aperiodic. This is of course no proof of it being disjunctive or normal, just a conjecture.