python 3.13.5 numpy 2.3.1 decimal precision 170
Part A: integer identity (sigma+2)^2 (sigma+1)^3 - sigma (sigma^2+3 sigma+3)^2
  coefficients sigma^0..sigma^4: [4, 7, 7, 4, 1] (expected [4, 7, 7, 4, 1])
Part B: Lemma 2.2 -- K(|dz + mu dzbar|^2) = 4 Re d^2 mu + O(|mu||D^2 mu| + |D mu|^2)
  round metric: max |K - 1| = 1.62e-10
  t=0.1: max|K - 4 Re d^2 mu| / t^2 = 7.8655   max|K|/t = 9.8933
  t=0.01: max|K - 4 Re d^2 mu| / t^2 = 8.3209   max|K|/t = 10.3426
  t=0.001: max|K - 4 Re d^2 mu| / t^2 = 8.3691   max|K|/t = 10.3891
Part C: formulas for d psi, dbar psi (FD in 170-digit arithmetic) and the jets at 0
  P1 k=1 eps=0.0125: annulus a<=|z|<=b: max abs.err of (3),(4) vs FD = 7.5e-12
  P1 k=1 eps=0.0125: max rel.err of (3),(4) vs FD = 1.3e-60; d^(k+1)(phi-id)(0) = -3.9773746373 (formula -(k+1)!(2+eps c_delta) = -3.9773746373); d^k log|phi_z|(0) = -1.9886873187 (half of it: -1.9886873187)
  P1 k=2 eps=0.0125: annulus a<=|z|<=b: max abs.err of (3),(4) vs FD = 4.2e-12
  P1 k=2 eps=0.0125: max rel.err of (3),(4) vs FD = 1.4e-54; d^(k+1)(phi-id)(0) = -11.9321239119 (formula -(k+1)!(2+eps c_delta) = -11.9321239119); d^k log|phi_z|(0) = -5.9660619560 (half of it: -5.9660619560)
  P1 k=3 eps=0.0125: annulus a<=|z|<=b: max abs.err of (3),(4) vs FD = 3.2e-12
  P1 k=3 eps=0.0125: max rel.err of (3),(4) vs FD = 5.4e-55; d^(k+1)(phi-id)(0) = -47.7284956477 (formula -(k+1)!(2+eps c_delta) = -47.7284956477); d^k log|phi_z|(0) = -23.8642478238 (half of it: -23.8642478238)
  P2 k=1 eps=0.0125: annulus a<=|z|<=b: max abs.err of (3),(4) vs FD = 8.5e-12
  P2 k=1 eps=0.0125: max rel.err of (3),(4) vs FD = 1.3e-60; d^(k+1)(phi-id)(0) = -3.9739819024 (formula -(k+1)!(2+eps c_delta) = -3.9739819024); d^k log|phi_z|(0) = -1.9869909512 (half of it: -1.9869909512)
  P2 k=2 eps=0.0125: annulus a<=|z|<=b: max abs.err of (3),(4) vs FD = 5.5e-12
  P2 k=2 eps=0.0125: max rel.err of (3),(4) vs FD = 1.4e-54; d^(k+1)(phi-id)(0) = -11.9219457073 (formula -(k+1)!(2+eps c_delta) = -11.9219457073); d^k log|phi_z|(0) = -5.9609728537 (half of it: -5.9609728537)
  P2 k=3 eps=0.0125: annulus a<=|z|<=b: max abs.err of (3),(4) vs FD = 3.5e-12
  P2 k=3 eps=0.0125: max rel.err of (3),(4) vs FD = 5.4e-55; d^(k+1)(phi-id)(0) = -47.6877828293 (formula -(k+1)!(2+eps c_delta) = -47.6877828293); d^k log|phi_z|(0) = -23.8438914147 (half of it: -23.8438914147)
Part E: k = 0 -- spiral maps and the smoothed-cone example (finite differences, float64)
  spiral eps=0.2   kappa=0: sup|phi^*g - g| = 0.4813 ; max|Jacobian - 1| = 3.4e-09 ; |d_z phi(0) - 1| = 0.958851 (phi = e^i z on |z| <= e^(-1/eps)/2: ratio phi(z)/z at |z|=1e-3 e^(-1/eps): 1.6e-16)
  spiral eps=0.2   kappa=1: sup|phi^*g - g| = 1.9219 ; max|Jacobian - 1| = 3.4e-09 ; |d_z phi(0) - 1| = 0.958851 (phi = e^i z on |z| <= e^(-1/eps)/2: ratio phi(z)/z at |z|=1e-3 e^(-1/eps): 1.6e-16)
  spiral eps=0.1   kappa=0: sup|phi^*g - g| = 0.2144 ; max|Jacobian - 1| = 4.3e-09 ; |d_z phi(0) - 1| = 0.958851 (phi = e^i z on |z| <= e^(-1/eps)/2: ratio phi(z)/z at |z|=1e-3 e^(-1/eps): 0.0e+00)
  spiral eps=0.1   kappa=1: sup|phi^*g - g| = 0.8576 ; max|Jacobian - 1| = 4.3e-09 ; |d_z phi(0) - 1| = 0.958851 (phi = e^i z on |z| <= e^(-1/eps)/2: ratio phi(z)/z at |z|=1e-3 e^(-1/eps): 0.0e+00)
  spiral eps=0.05  kappa=0: sup|phi^*g - g| = 0.1030 ; max|Jacobian - 1| = 3.1e-09 ; |d_z phi(0) - 1| = 0.958851 (phi = e^i z on |z| <= e^(-1/eps)/2: ratio phi(z)/z at |z|=1e-3 e^(-1/eps): 0.0e+00)
  spiral eps=0.05  kappa=1: sup|phi^*g - g| = 0.4119 ; max|Jacobian - 1| = 3.1e-09 ; |d_z phi(0) - 1| = 0.958851 (phi = e^i z on |z| <= e^(-1/eps)/2: ratio phi(z)/z at |z|=1e-3 e^(-1/eps): 0.0e+00)
  cone eps=0.2  : sup over 1e-3 eta <= |z| <= 1e6 of |g_eps - g_0| = 0.5318 (2.66 eps) ; u_eps(0) = -1.25000 (-1/(1-eps) = -1.25000) ; d_z phi(0) = 0.28650 (e^-1 = 0.36788)
  cone eps=0.1  : sup over 1e-3 eta <= |z| <= 1e6 of |g_eps - g_0| = 0.2218 (2.22 eps) ; u_eps(0) = -1.11111 (-1/(1-eps) = -1.11111) ; d_z phi(0) = 0.32919 (e^-1 = 0.36788)
  cone eps=0.05 : sup over 1e-3 eta <= |z| <= 1e6 of |g_eps - g_0| = 0.1021 (2.04 eps) ; u_eps(0) = -1.05263 (-1/(1-eps) = -1.05263) ; d_z phi(0) = 0.34902 (e^-1 = 0.36788)
Part D: K(g_eps) = e^{2F} Lap F, F = V o phi^{-1} (Newton inversion, 5-point Laplacian)
  parameter set P1 (radii of the finder's run: a=0.2 b=0.9 a_w=0.1 b_w=0.3 [0.35,0.9], A=16)
    k=1 kappa=0 eps=0.02    delta=1.93e-22 prec=120 | inner |z|<=0.98a_w: min K = 2.9546 (at |z|/delta = 5.08e+20, min K/K_h = 1.4917; min over |z| <= 1000 delta: 6.219e+17) | outer: min K = -0.0077 (at |z| = 0.689, min K/K_h = -0.0057) | max|K-K_h| beyond b: 7.5e-08 | Q(b_beta^2) = -2.8e-17 | 9.1s
    k=1 kappa=0 eps=0.0125  delta=1.80e-35 prec=134 | inner |z|<=0.98a_w: min K = 2.6428 (at |z|/delta = 5.43e+33, min K/K_h = 1.3342; min over |z| <= 1000 delta: 4.646e+30) | outer: min K = 0.4981 (at |z| = 0.689, min K/K_h = 0.3670) | max|K-K_h| beyond b: 7.5e-08 | Q(b_beta^2) = -2.8e-17 | 10.5s
    k=1 kappa=0 eps=0.008   delta=5.17e-55 prec=174 | inner |z|<=0.98a_w: min K = 2.4261 (at |z|/delta = 1.9e+53, min K/K_h = 1.2248; min over |z| <= 1000 delta: 1.111e+50) | outer: min K = 0.8010 (at |z| = 0.701, min K/K_h = 0.5931) | max|K-K_h| beyond b: 7.5e-08 | Q(b_beta^2) = -2.8e-17 | 13.2s
    k=1 kappa=0 eps=0.005   delta=1.38e-87 prec=238 | inner |z|<=0.98a_w: min K = 2.2685 (at |z|/delta = 7.08e+85, min K/K_h = 1.1452; min over |z| <= 1000 delta: 2.711e+82) | outer: min K = 0.9574 (at |z| = 0.821, min K/K_h = 0.7450) | max|K-K_h| beyond b: 7.5e-08 | Q(b_beta^2) = -2.8e-17 | 20.9s
    k=1 kappa=1 eps=0.02    delta=1.93e-22 prec=120 | inner |z|<=0.98a_w: min K = 1.1437 (at |z|/delta = 5.08e+20, min K/K_h = 1.1437; min over |z| <= 1000 delta: 1.555e+17) | outer: min K = 0.5063 (at |z| = 0.689, min K/K_h = 0.5063) | max|K-K_h| beyond b: 4.1e-08 | Q(b_beta^2) = -2.8e-17 | 9.4s
    k=1 kappa=1 eps=0.0125  delta=1.80e-35 prec=134 | inner |z|<=0.98a_w: min K = 1.1006 (at |z|/delta = 5.43e+33, min K/K_h = 1.1006; min over |z| <= 1000 delta: 1.162e+30) | outer: min K = 0.6894 (at |z| = 0.689, min K/K_h = 0.6894) | max|K-K_h| beyond b: 4.1e-08 | Q(b_beta^2) = -2.8e-17 | 10.1s
    k=1 kappa=1 eps=0.008   delta=5.17e-55 prec=174 | inner |z|<=0.98a_w: min K = 1.0688 (at |z|/delta = 1.9e+53, min K/K_h = 1.0688; min over |z| <= 1000 delta: 2.777e+49) | outer: min K = 0.8004 (at |z| = 0.689, min K/K_h = 0.8004) | max|K-K_h| beyond b: 4.1e-08 | Q(b_beta^2) = -2.8e-17 | 14.0s
    k=1 kappa=1 eps=0.005   delta=1.38e-87 prec=238 | inner |z|<=0.98a_w: min K = 1.0449 (at |z|/delta = 7.08e+85, min K/K_h = 1.0449; min over |z| <= 1000 delta: 6.777e+81) | outer: min K = 0.8749 (at |z| = 0.689, min K/K_h = 0.8749) | max|K-K_h| beyond b: 4.1e-08 | Q(b_beta^2) = -2.8e-17 | 29.4s
    k=2 kappa=0 eps=0.02    delta=1.93e-22 prec=120 | inner |z|<=0.98a_w: min K = 1.5211 (at |z|/delta = 5.08e+20, min K/K_h = 0.7679; min over |z| <= 1000 delta: 1.54) | outer: min K = 0.5730 (at |z| = 0.821, min K/K_h = 0.4798) | max|K-K_h| beyond b: 7.5e-08 | 7.8s
    k=2 kappa=0 eps=0.0125  delta=1.80e-35 prec=134 | inner |z|<=0.98a_w: min K = 1.6930 (at |z|/delta = 5.43e+33, min K/K_h = 0.8547; min over |z| <= 1000 delta: 1.713) | outer: min K = 0.8061 (at |z| = 0.821, min K/K_h = 0.6750) | max|K-K_h| beyond b: 7.5e-08 | 7.5s
    k=2 kappa=0 eps=0.008   delta=5.17e-55 prec=174 | inner |z|<=0.98a_w: min K = 1.7965 (at |z|/delta = 1.9e+53, min K/K_h = 0.9069; min over |z| <= 1000 delta: 1.816) | outer: min K = 0.9460 (at |z| = 0.821, min K/K_h = 0.7921) | max|K-K_h| beyond b: 7.5e-08 | 12.0s
    k=2 kappa=0 eps=0.005   delta=1.38e-87 prec=238 | inner |z|<=0.98a_w: min K = 1.8656 (at |z|/delta = 7.08e+85, min K/K_h = 0.9418; min over |z| <= 1000 delta: 1.885) | outer: min K = 1.0391 (at |z| = 0.821, min K/K_h = 0.8701) | max|K-K_h| beyond b: 7.5e-08 | 21.1s
    k=2 kappa=1 eps=0.02    delta=1.93e-22 prec=120 | inner |z|<=0.98a_w: min K = 0.8845 (at |z|/delta = 5.08e+20, min K/K_h = 0.8845; min over |z| <= 1000 delta: 0.885) | outer: min K = 0.7331 (at |z| = 0.821, min K/K_h = 0.7331) | max|K-K_h| beyond b: 4.1e-08 | 7.7s
    k=2 kappa=1 eps=0.0125  delta=1.80e-35 prec=134 | inner |z|<=0.98a_w: min K = 0.9277 (at |z|/delta = 5.43e+33, min K/K_h = 0.9277; min over |z| <= 1000 delta: 0.9281) | outer: min K = 0.8333 (at |z| = 0.821, min K/K_h = 0.8333) | max|K-K_h| beyond b: 4.1e-08 | 7.6s
    k=2 kappa=1 eps=0.008   delta=5.17e-55 prec=174 | inner |z|<=0.98a_w: min K = 0.9537 (at |z|/delta = 1.9e+53, min K/K_h = 0.9537; min over |z| <= 1000 delta: 0.954) | outer: min K = 0.8933 (at |z| = 0.821, min K/K_h = 0.8933) | max|K-K_h| beyond b: 4.1e-08 | 11.2s
    k=2 kappa=1 eps=0.005   delta=1.38e-87 prec=238 | inner |z|<=0.98a_w: min K = 0.9710 (at |z|/delta = 7.08e+85, min K/K_h = 0.9710; min over |z| <= 1000 delta: 0.9713) | outer: min K = 0.9333 (at |z| = 0.821, min K/K_h = 0.9333) | max|K-K_h| beyond b: 4.1e-08 | 19.3s
    k=3 kappa=0 eps=0.02    delta=1.93e-22 prec=120 | inner |z|<=0.98a_w: min K = 1.8865 (at |z|/delta = 5.08e+20, min K/K_h = 0.9523; min over |z| <= 1000 delta: 2) | outer: min K = 0.7522 (at |z| = 0.821, min K/K_h = 0.6298) | max|K-K_h| beyond b: 7.5e-08 | 5.0s
    k=3 kappa=0 eps=0.0125  delta=1.80e-35 prec=134 | inner |z|<=0.98a_w: min K = 1.9219 (at |z|/delta = 5.43e+33, min K/K_h = 0.9702; min over |z| <= 1000 delta: 2) | outer: min K = 0.9181 (at |z| = 0.821, min K/K_h = 0.7687) | max|K-K_h| beyond b: 7.5e-08 | 5.8s
    k=3 kappa=0 eps=0.008   delta=5.17e-55 prec=174 | inner |z|<=0.98a_w: min K = 1.9431 (at |z|/delta = 1.9e+53, min K/K_h = 0.9809; min over |z| <= 1000 delta: 2) | outer: min K = 1.0135 (at |z| = 0.833, min K/K_h = 0.8520) | max|K-K_h| beyond b: 7.5e-08 | 8.3s
    k=3 kappa=0 eps=0.005   delta=1.38e-87 prec=238 | inner |z|<=0.98a_w: min K = 1.9573 (at |z|/delta = 7.08e+85, min K/K_h = 0.9881; min over |z| <= 1000 delta: 2) | outer: min K = 1.0724 (at |z| = 0.930, min K/K_h = 0.9075) | max|K-K_h| beyond b: 7.5e-08 | 12.7s
    k=3 kappa=1 eps=0.02    delta=1.93e-22 prec=120 | inner |z|<=0.98a_w: min K = 0.9762 (at |z|/delta = 5.08e+20, min K/K_h = 0.9762; min over |z| <= 1000 delta: 1) | outer: min K = 0.8096 (at |z| = 0.821, min K/K_h = 0.8096) | max|K-K_h| beyond b: 4.1e-08 | 4.8s
    k=3 kappa=1 eps=0.0125  delta=1.80e-35 prec=134 | inner |z|<=0.98a_w: min K = 0.9851 (at |z|/delta = 5.43e+33, min K/K_h = 0.9851; min over |z| <= 1000 delta: 1) | outer: min K = 0.8810 (at |z| = 0.821, min K/K_h = 0.8810) | max|K-K_h| beyond b: 4.1e-08 | 5.3s
    k=3 kappa=1 eps=0.008   delta=5.17e-55 prec=174 | inner |z|<=0.98a_w: min K = 0.9905 (at |z|/delta = 1.9e+53, min K/K_h = 0.9905; min over |z| <= 1000 delta: 1) | outer: min K = 0.9239 (at |z| = 0.821, min K/K_h = 0.9239) | max|K-K_h| beyond b: 4.1e-08 | 7.7s
    k=3 kappa=1 eps=0.005   delta=1.38e-87 prec=238 | inner |z|<=0.98a_w: min K = 0.9941 (at |z|/delta = 7.08e+85, min K/K_h = 0.9941; min over |z| <= 1000 delta: 1) | outer: min K = 0.9524 (at |z| = 0.821, min K/K_h = 0.9524) | max|K-K_h| beyond b: 4.1e-08 | 12.5s
  parameter set P2 (different radii: a=0.3 b=0.8 a_w=0.15 b_w=0.25 [0.4,0.75], A=12)
    k=1 kappa=0 eps=0.02    delta=1.93e-22 prec=120 | inner |z|<=0.98a_w: min K = 2.2765 (at |z|/delta = 7.62e+20, min K/K_h = 1.1633; min over |z| <= 1000 delta: 3.455e+17) | outer: min K = -0.1437 (at |z| = 0.612, min K/K_h = -0.0987) | max|K-K_h| beyond b: 4.7e-08 | Q(b_beta^2) = 0.0e+00 | 7.4s
    k=1 kappa=0 eps=0.0125  delta=1.80e-35 prec=134 | inner |z|<=0.98a_w: min K = 2.1601 (at |z|/delta = 8.14e+33, min K/K_h = 1.1036; min over |z| <= 1000 delta: 2.491e+30) | outer: min K = 0.4499 (at |z| = 0.612, min K/K_h = 0.3090) | max|K-K_h| beyond b: 4.7e-08 | Q(b_beta^2) = 0.0e+00 | 8.0s
    k=1 kappa=0 eps=0.008   delta=5.17e-55 prec=174 | inner |z|<=0.98a_w: min K = 2.0883 (at |z|/delta = 2.85e+53, min K/K_h = 1.0668; min over |z| <= 1000 delta: 5.83e+49) | outer: min K = 0.8095 (at |z| = 0.612, min K/K_h = 0.5561) | max|K-K_h| beyond b: 4.7e-08 | Q(b_beta^2) = 0.0e+00 | 11.1s
    k=1 kappa=0 eps=0.005   delta=1.38e-87 prec=238 | inner |z|<=0.98a_w: min K = 2.0397 (at |z|/delta = 1.06e+86, min K/K_h = 1.0420; min over |z| <= 1000 delta: 1.402e+82) | outer: min K = 1.0118 (at |z| = 0.731, min K/K_h = 0.7219) | max|K-K_h| beyond b: 4.7e-08 | Q(b_beta^2) = 0.0e+00 | 16.9s
    k=1 kappa=1 eps=0.02    delta=1.93e-22 prec=120 | inner |z|<=0.98a_w: min K = 1.0242 (at |z|/delta = 7.62e+20, min K/K_h = 1.0242; min over |z| <= 1000 delta: 8.637e+16) | outer: min K = 0.4587 (at |z| = 0.612, min K/K_h = 0.4587) | max|K-K_h| beyond b: 2.8e-08 | Q(b_beta^2) = 0.0e+00 | 7.1s
    k=1 kappa=1 eps=0.0125  delta=1.80e-35 prec=134 | inner |z|<=0.98a_w: min K = 1.0151 (at |z|/delta = 8.14e+33, min K/K_h = 1.0151; min over |z| <= 1000 delta: 6.227e+29) | outer: min K = 0.6596 (at |z| = 0.612, min K/K_h = 0.6596) | max|K-K_h| beyond b: 2.8e-08 | Q(b_beta^2) = 0.0e+00 | 7.3s
    k=1 kappa=1 eps=0.008   delta=5.17e-55 prec=174 | inner |z|<=0.98a_w: min K = 1.0096 (at |z|/delta = 2.85e+53, min K/K_h = 1.0096; min over |z| <= 1000 delta: 1.457e+49) | outer: min K = 0.7814 (at |z| = 0.612, min K/K_h = 0.7814) | max|K-K_h| beyond b: 2.8e-08 | Q(b_beta^2) = 0.0e+00 | 10.5s
    k=1 kappa=1 eps=0.005   delta=1.38e-87 prec=238 | inner |z|<=0.98a_w: min K = 1.0060 (at |z|/delta = 1.06e+86, min K/K_h = 1.0060; min over |z| <= 1000 delta: 3.506e+81) | outer: min K = 0.8630 (at |z| = 0.612, min K/K_h = 0.8630) | max|K-K_h| beyond b: 2.8e-08 | Q(b_beta^2) = 0.0e+00 | 16.2s
    k=2 kappa=0 eps=0.02    delta=1.93e-22 prec=120 | inner |z|<=0.98a_w: min K = 1.4961 (at |z|/delta = 7.62e+20, min K/K_h = 0.7643; min over |z| <= 1000 delta: 1.54) | outer: min K = 0.5554 (at |z| = 0.741, min K/K_h = 0.4300) | max|K-K_h| beyond b: 4.7e-08 | 3.9s
    k=2 kappa=0 eps=0.0125  delta=1.80e-35 prec=134 | inner |z|<=0.98a_w: min K = 1.6684 (at |z|/delta = 8.14e+33, min K/K_h = 0.8523; min over |z| <= 1000 delta: 1.713) | outer: min K = 0.8315 (at |z| = 0.741, min K/K_h = 0.6439) | max|K-K_h| beyond b: 4.7e-08 | 4.5s
    k=2 kappa=0 eps=0.008   delta=5.17e-55 prec=174 | inner |z|<=0.98a_w: min K = 1.7723 (at |z|/delta = 2.85e+53, min K/K_h = 0.9053; min over |z| <= 1000 delta: 1.816) | outer: min K = 0.9971 (at |z| = 0.741, min K/K_h = 0.7721) | max|K-K_h| beyond b: 4.7e-08 | 7.4s
    k=2 kappa=0 eps=0.005   delta=1.38e-87 prec=238 | inner |z|<=0.98a_w: min K = 1.8417 (at |z|/delta = 1.06e+86, min K/K_h = 0.9408; min over |z| <= 1000 delta: 1.885) | outer: min K = 1.1075 (at |z| = 0.741, min K/K_h = 0.8576) | max|K-K_h| beyond b: 4.7e-08 | 11.5s
    k=2 kappa=1 eps=0.02    delta=1.93e-22 prec=120 | inner |z|<=0.98a_w: min K = 0.8834 (at |z|/delta = 7.62e+20, min K/K_h = 0.8834; min over |z| <= 1000 delta: 0.885) | outer: min K = 0.7103 (at |z| = 0.741, min K/K_h = 0.7103) | max|K-K_h| beyond b: 2.8e-08 | 3.6s
    k=2 kappa=1 eps=0.0125  delta=1.80e-35 prec=134 | inner |z|<=0.98a_w: min K = 0.9269 (at |z|/delta = 8.14e+33, min K/K_h = 0.9269; min over |z| <= 1000 delta: 0.9281) | outer: min K = 0.8190 (at |z| = 0.741, min K/K_h = 0.8190) | max|K-K_h| beyond b: 2.8e-08 | 4.3s
    k=2 kappa=1 eps=0.008   delta=5.17e-55 prec=174 | inner |z|<=0.98a_w: min K = 0.9531 (at |z|/delta = 2.85e+53, min K/K_h = 0.9531; min over |z| <= 1000 delta: 0.954) | outer: min K = 0.8842 (at |z| = 0.741, min K/K_h = 0.8842) | max|K-K_h| beyond b: 2.8e-08 | 6.9s
    k=2 kappa=1 eps=0.005   delta=1.38e-87 prec=238 | inner |z|<=0.98a_w: min K = 0.9707 (at |z|/delta = 1.06e+86, min K/K_h = 0.9707; min over |z| <= 1000 delta: 0.9713) | outer: min K = 0.9276 (at |z| = 0.741, min K/K_h = 0.9276) | max|K-K_h| beyond b: 2.8e-08 | 11.4s
    k=3 kappa=0 eps=0.02    delta=1.93e-22 prec=120 | inner |z|<=0.98a_w: min K = 1.8149 (at |z|/delta = 7.62e+20, min K/K_h = 0.9271; min over |z| <= 1000 delta: 2) | outer: min K = 0.7995 (at |z| = 0.741, min K/K_h = 0.6191) | max|K-K_h| beyond b: 4.7e-08 | 3.5s
    k=3 kappa=0 eps=0.0125  delta=1.80e-35 prec=134 | inner |z|<=0.98a_w: min K = 1.8684 (at |z|/delta = 8.14e+33, min K/K_h = 0.9544; min over |z| <= 1000 delta: 2) | outer: min K = 0.9840 (at |z| = 0.741, min K/K_h = 0.7620) | max|K-K_h| beyond b: 4.7e-08 | 5.2s
    k=3 kappa=0 eps=0.008   delta=5.17e-55 prec=174 | inner |z|<=0.98a_w: min K = 1.9005 (at |z|/delta = 2.85e+53, min K/K_h = 0.9708; min over |z| <= 1000 delta: 2) | outer: min K = 1.0947 (at |z| = 0.741, min K/K_h = 0.8477) | max|K-K_h| beyond b: 4.7e-08 | 6.2s
    k=3 kappa=0 eps=0.005   delta=1.38e-87 prec=238 | inner |z|<=0.98a_w: min K = 1.9220 (at |z|/delta = 1.06e+86, min K/K_h = 0.9817; min over |z| <= 1000 delta: 2) | outer: min K = 1.1685 (at |z| = 0.741, min K/K_h = 0.9048) | max|K-K_h| beyond b: 4.7e-08 | 9.9s
    k=3 kappa=1 eps=0.02    delta=1.93e-22 prec=120 | inner |z|<=0.98a_w: min K = 0.9638 (at |z|/delta = 7.62e+20, min K/K_h = 0.9638; min over |z| <= 1000 delta: 1) | outer: min K = 0.8062 (at |z| = 0.741, min K/K_h = 0.8062) | max|K-K_h| beyond b: 2.8e-08 | 4.1s
    k=3 kappa=1 eps=0.0125  delta=1.80e-35 prec=134 | inner |z|<=0.98a_w: min K = 0.9774 (at |z|/delta = 8.14e+33, min K/K_h = 0.9774; min over |z| <= 1000 delta: 1) | outer: min K = 0.8789 (at |z| = 0.741, min K/K_h = 0.8789) | max|K-K_h| beyond b: 2.8e-08 | 4.1s
    k=3 kappa=1 eps=0.008   delta=5.17e-55 prec=174 | inner |z|<=0.98a_w: min K = 0.9855 (at |z|/delta = 2.85e+53, min K/K_h = 0.9855; min over |z| <= 1000 delta: 1) | outer: min K = 0.9225 (at |z| = 0.741, min K/K_h = 0.9225) | max|K-K_h| beyond b: 2.8e-08 | 6.1s
    k=3 kappa=1 eps=0.005   delta=1.38e-87 prec=238 | inner |z|<=0.98a_w: min K = 0.9909 (at |z|/delta = 1.06e+86, min K/K_h = 0.9909; min over |z| <= 1000 delta: 1) | outer: min K = 0.9516 (at |z| = 0.741, min K/K_h = 0.9516) | max|K-K_h| beyond b: 2.8e-08 | 10.3s
  48 configurations; K > 0 at every grid point of every configuration: False
  k=1 kappa=0 eps=0.02 (P1): at z = -2 delta, K(g_eps) = 3.553e+20 with the correction w_eps, -4.115e+20 without it (delta = 1.93e-22)
  k=1 kappa=0 eps=0.01 (P1): at z = -2 delta, K(g_eps) = 1.069e+42 with the correction w_eps, -1.067e+42 without it (delta = 3.72e-44)
  configurations with a negative grid value (eps above the smallness threshold of the proof for these cut-offs): [('P1', 1, 0, 0.02), ('P2', 1, 0, 0.02)]
done
