I think we've *only* got the mechanism, not the implications.

Compare with fluid dynamics; it's not hard to write down the Navier–Stokes equations, but there's a million dollars available to the first person who can prove or give a counter-example of the following statement:

  In three space dimensions and time, given an initial velocity field, there exists a vector velocity and a scalar pressure field, which are both smooth and globally defined, that solve the Navier–Stokes equations.