text: ω 
  c  ω 
  c 
  
  (4). The 
  FIG. 1: Schematic behavior of ∆W vs ωc, Eq. 
  is ∆WK given by Eq. (3) 
  limiting value of ∆W at ωc = 
  Depending on the value of ∆WK, there can be either one sign 
  change of ∆W (panels a and c), or no sign changes (panel b), 
  or two sign changes (panel d). 
  
  ∞ 
  
  In our work, we perform direct numerical calculations 
  of optical integrals at T = 0 for a lattice dispersion ex- 
  tracted from ARPES of the cuprates. The goal of our 
  work is two-fold. First, we perform calculations of the 
  optical integral in the NS and analyze how rapidly W (ωc) 
  approaches WK , in other words we check how much of 
  the Kubo sum is recovered up to the scale of the band- 
  width. Second, we analyze the diﬀerence between optical 