====== Overview ======

There are three approaches, 
  * Daping's canonical skeleton using $\omega = Im(\Omega)$. 
  * Constructing Kahler potential by extending (after modification) standard KP on $(\C^*)^n$. 
  * Semi-Tropicalize the cluster variety, put the main torus on some flat region. Let  trickle down from 

They each need to solve some technical problems. 

===== Canonical Skeleton =====
There is a canonical subspace, that is easy to specify,  and easy to check that it is a skeleton. The trouble is, how to show there is a Liouville flow that realize this as a Liouville skeleton. 
  * (OK) One can engineer the flow near the skeleton, that is a local gluing / plumbing problem
  * (Hard) Find a Morse function whose critical manifold is as the skeleton.