I think it might be useful to mention an analogy between your considerations and actual particlephysics, where people are stuck with a functionally similar problem. They have tried (and so far failed) to make much progress, but perhaps you can find some inspiration from studying their attempts.
The most immediate shortcoming of the Telephone Theorem and the resampling argument is that they talk about behavior in infinite limits. To use them, either we need to have an infinitely large graphical model, or we need to take an approximation.
In particle physics, there is a quantity called the Scattering matrix; loosely speaking, the S-matrix connects a number of asymptotically free "in" states to a number... (read more)
I think it might be useful to mention an analogy between your considerations and actual particle physics, where people are stuck with a functionally similar problem. They have tried (and so far failed) to make much progress, but perhaps you can find some inspiration from studying their attempts.
In particle physics, there is a quantity called the Scattering matrix; loosely speaking, the S-matrix connects a number of asymptotically free "in" states to a number... (read more)