text: We considered four models: a BCS model with impu- 
  rities, a model of fermions interacting with an Einstein 
  boson, a phenomenological MFL model with impurities, 
  and a model of fermions interacting with collective spin 
  ﬂuctuations. 
  In all cases, we found that ∆WK is neg- 
  ative, but how it evolves with ωc and how much of the 
  sum rule is recovered by integrating up to the bandwidth 
  depends on the model. 
  
  It is also instructive to understand the interplay be- 
  tween the behavior of ∆W (ωc) and the behavior of the 
  diﬀerence of the kinetic energy between the SCS and the 
  NS, δKE. We computed the kinetic energy as a function 
  of λωsf and present the results in Fig. 23 for λ = 1 and 
  10. For a relatively weak λ = 1 the behavior is clearly 
  BCS like- δKE > 0 and increases with increasing λωsf . 
  However, at large λ = 10, we see that the kinetic energy 
  begin decreasing at large λωsf and eventually changes 
  sign. The behavior of δKE at a truly strong coupling is 