My mathematical point to Risto is that the relatively lesser fit of 0.73 for the log-logistic exponential model is entirely meaningless because precisely the choice of model is what matters. So aminorex and Peter R have supported my argument.
Not only implicitly but explicitly as well, yes: A bad fit of a structurally representative model is far more predictive than a good fit of an unrepresentative model, because it is a compressive attractor. There are some statistical tests you can use to discriminate, but knowing structure beforehand gives you a lot more leverage than structural estimation after the fact, because noise.
There are certainly some intuitions to support log-logistic, but they aren't compelling to me. Still have not taken time to think this one through properly, after all this time. Summer has been crazytown. And I've been indulging myself with distractions.
Yet, events in the world will never be entirely modeled by anything so simple. COIN will be a liquidity event at a magnitude far larger, relative to current market cap, than was the advent of exchanges - which precipitated the superbubble.