# Leading order in 1/S: first correction dS, m = eps_h (S - dS) + O(1/S)

## Cubic torus, L -> infinity, no push (midpoint sums): dS_3 = (W - 1)/2
L=  64: dS_3 = 0.078304
L= 128: dS_3 = 0.078344
L= 256: dS_3 = 0.078354
Richardson (error ~ L^-2): dS_3 = 0.07836

## Cubic torus with push (exact Gaussian), far site (L/2,L/2,L/2)
L    eta=h_p/(JS)   dS(far)    dS(h)     zero-mode estimate sqrt(2z/(N eta))/2   max|<Q^2>-<P^2>|
  8    0.10        0.31135   0.29896   0.24206                                0.0e+00
  8    1.00        0.15197   0.11065   0.07655                                0.0e+00
  8   10.00        0.11169   0.01999   0.02421                                0.0e+00
 12    0.10        0.20637   0.19853   0.13176                                0.0e+00
 12    1.00        0.11960   0.08897   0.04167                                0.0e+00
 12   10.00        0.09770   0.01863   0.01318                                0.0e+00
 16    0.10        0.16197   0.15613   0.08558                                0.0e+00
 16    1.00        0.10561   0.07974   0.02706                                0.0e+00
 16   10.00        0.09139   0.01805   0.00856                                0.0e+00

## Ring with push (exact Gaussian), eta = 1, far site L/2
L      dS(L/2)    dS(L/2) - (1/pi) ln(L/2)
   64  1.10378    0.00061
  128  1.31488    -0.00893
  256  1.53065    -0.01380
  512  1.74882    -0.01626
 1024  1.96822    -0.01750
slope d dS / d ln L (last three sizes) = 0.31564;  1/pi = 0.31831 (Dirichlet image at the push)