Wha tis the threshold, Is there an example of how this would work? It's pretty vague.
@vandeberg's deep dive on the topic should help explain this better: https://steemit.com/steem/@vandeberg/reward-curve-deep-dive
The idea is to gain the benefit of having a curve without moving far away from linear that we currently have. It's being described as convergent linear because you quickly converge into mostly linear, it could also be described as minimally superlinear. This is drastically different than the n^3 or n^2 that we had prior to linear.
No solution will ever be exactly perfect, but we may be able to attain something much better than we have and promote the type of behavior that most user's would like to see (by making it more economically advantageous to do so).