Fair enough; it's true that I don't have a rigorous mathematical model, nor do I expect to have one anytime soon. My current best sketch at an explanation is that it's a combination of:

1. P != NP, i.e. the familiar exponential difficulty of finding solutions given only a way to evaluate them - I think this is the part that contributes the overall exponential shape.

2. The general version of Amdahl's law, if subproblem X was only e.g. 10% of the overall job, then no improvement in X can by itself give more than a 10% overall improvement - I think this is the part that makes it so robust; as I mentioned in the subthread about algorithmic improvements, even if you can break the curve of capability in a subproblem, it persists at the next level up.