I'm familiar with the MT.. I have Matsumoto & Nishmura's paper on it right here, in fact. Yes, it has a huge period (on the order of 2^19937), its spectral distribution is good up to 263 dimensions, and the analysis looks great. But its mechanism is totally different from the one I'm talking about here.

I'm not looking for a long-period RNG per se. If I want one of those, yeah, I'll probably use the Twister. The itch I'm trying to scratch here is theoretical. This particular machine strikes me as interesting, and I want to learn what makes it tick.