I am glad to see more people thinking about this. The real catch in my opinion is that we’re collectively approaching the problem backwards. Bonding curves are part of a larger theory of scalar functions that remain invariant under legal changes in state.

We don’t need to analyze the bonding curves in isolation; they are just tools. We need to analyze the economic incentive problem at hand, determine what mathematical properties need to be always true and then derive our curves and mechanisms from those requirements.

In my experience, the invariants chosen are a representation of value conservation (despite it changing forms) in the manner of energy conservation as the root law of most the ‘laws’ in Newtonian physics.