I need to digest this more. I've just been playing around with iterated sigmoid curves and they get more pronounced with a steeper inflection; maybe that's the discovery sweet spot.

On dispersive discovery generally I could point out that Fosset's plane was outside the 'container'. Also what is happening now with oil, gas and metals is technology enabling of already discovered reserves, some of the acronyms being EOR, ISL and UCG.

With the damped exponential or gamma forms, there is no strict "container", it just becomes more and more improbable as you go along the profile.

So if you are referring to Steve Fosset, the analogy is that there is a slight probability that they could have found his plane all the way on Mars -- it is just a very, very, very slight possibility using an exponential distribution. Yet the fact that it took this long to discover it makes sense to me, as the rate is effectively very slow in exploring outside of the zone they initially started searching. As you radiate outward, you effectively go that much more slowly as you have more ground to cover.

... EOR, ISL and UCG.

Sounds good. To first order, at least some of these may be the equivalent of the long tails in the dispersive profile. They don't get reported until now so have gotten deferred from the reserve accounting for quite some time. Yes, it could be that one of these technologies could turn into a Black Swan event. Yet, in general, you should make the new enabled regions exponentially more difficult or slower to process since that is a historically accurate observation.