# torus_checks.py  numpy 2.3.1  python 3.13.5

=== [G] Theorem 1.2(i),(ii), pull-back formula, Remark 3.1 flux (quadrature) ===
  c=+0.70: max|det Df - 1| = 5.8e-11, max|f^-1 f - id| = 1.1e-16, max Z^2-equivariance defect = 2.2e-16
  c=-2.30: max|det Df - 1| = 1.7e-10, max|f^-1 f - id| = 1.1e-16, max Z^2-equivariance defect = 4.4e-16
  c=+5.00: max|det Df - 1| = 1.1e-10, max|f^-1 f - id| = 1.1e-16, max Z^2-equivariance defect = 8.9e-16
  eps=+0.30 c=+1.10: B=int b = 0.1650000000 (eps c/2 = 0.1650000000); max|b_FD - eps c cos^2| = 2.0e-11; sup|F| = 1.88495559 (2 pi|eps| = 1.88495559); flux = 0.1650000000
  eps=-0.80 c=+2.50: B=int b = -1.0000000000 (eps c/2 = -1.0000000000); max|b_FD - eps c cos^2| = 1.2e-10; sup|F| = 5.02654825 (2 pi|eps| = 5.02654825); flux = -1.0000000000

=== [L1] eq. (1), tau, Lemma 2.1 identities as matrices (random smooth connection, 2 variables) ===
  ||nabla_x + nabla_x^H|| = 0.00e+00 (skew-adjointness on truncated space)
  max|D(d+d^H) - D(eq.1)| = 0.00e+00
  tau: max|tau^2 - 1| = 0.0e+00, max|tau D + D tau| = 0.0e+00, tau unitary: 0.0e+00
  tau on (1,dx,dy,vol) equals the paper's formulas: True
  Lemma 2.1: max|U_odd D U_ev^-1 - (2dbar (+) 2del)| = 4.0e-15; U_ev, U_odd unitary: True, True
  (dbar)^H = -del on truncated space: 0.0e+00
  (D^2)_(Omega^0 -> Omega^2) = F_xy wedge on interior modes: max err = 3.5e-15

=== [K] Theorem 1.2(iii),(iv): kernel dimensions on T^2 (full 2D Fourier box |k_x|,|k_y|<=K) ===
  eps      c         eps*c/(4pi)   K   dim ker D_E (+,-)   4 smallest|lam| for E          dim ker D_f*E (+,-)  4 smallest|lam| for f*E
  +0.0500   +1.00000     +0.003979   8   4 (2,2)   [4.7e-15 9.5e-15 2.1e-14 2.7e-14 6.3e+00]   0 (0,0)   [2.50e-02 2.50e-02 2.50e-02 2.50e-02 6.26e+00]
  +0.0500   +1.00000     +0.003979  12   4 (2,2)   [2.9e-15 1.7e-14 3.8e-14 3.9e-14 6.3e+00]   0 (0,0)   [2.50e-02 2.50e-02 2.50e-02 2.50e-02 6.26e+00]
  +0.3000   +2.00000     +0.047746   8   4 (2,2)   [2.5e-15 4.6e-15 5.3e-15 3.0e-14 6.3e+00]   0 (0,0)   [2.99e-01 2.99e-01 2.99e-01 2.99e-01 5.99e+00]
  +0.3000   +2.00000     +0.047746  12   4 (2,2)   [5.9e-15 1.7e-14 3.2e-14 4.7e-14 6.3e+00]   0 (0,0)   [2.99e-01 2.99e-01 2.99e-01 2.99e-01 5.99e+00]
  -0.7000   +1.30000     -0.072415   8   4 (2,2)   [8.0e-16 6.8e-15 6.9e-15 2.3e-14 6.2e+00]   0 (0,0)   [4.49e-01 4.49e-01 4.49e-01 4.49e-01 5.86e+00]
  -0.7000   +1.30000     -0.072415  12   4 (2,2)   [1.4e-14 2.2e-14 2.6e-14 3.0e-14 6.2e+00]   0 (0,0)   [4.49e-01 4.49e-01 4.49e-01 4.49e-01 5.86e+00]
  +1.0000   +0.50000     +0.039789   8   4 (2,2)   [9.1e-16 3.1e-15 4.5e-15 6.4e-15 6.1e+00]   0 (0,0)   [2.44e-01 2.44e-01 2.44e-01 2.44e-01 6.09e+00]
  +1.0000   +0.50000     +0.039789  12   4 (2,2)   [2.8e-15 5.0e-15 2.3e-14 5.0e-14 6.1e+00]   0 (0,0)   [2.44e-01 2.44e-01 2.44e-01 2.44e-01 6.09e+00]
  +1.0000   -3.00000     -0.238732   8   4 (2,2)   [9.1e-16 3.1e-15 4.5e-15 6.4e-15 6.1e+00]   0 (0,0)   [1.45e+00 1.45e+00 1.45e+00 1.45e+00 4.87e+00]
  +1.0000   -3.00000     -0.238732  12   4 (2,2)   [2.8e-15 5.0e-15 2.3e-14 5.0e-14 6.1e+00]   0 (0,0)   [1.45e+00 1.45e+00 1.45e+00 1.45e+00 4.87e+00]
  +2.5000   +5.02655     +1.000000   8   4 (2,2)   [2.5e-16 1.5e-14 2.0e-14 2.1e-14 5.5e+00]   0 (0,0)   [5.56e-07 5.56e-07 5.56e-07 5.56e-07 5.52e+00]
  +2.5000   +5.02655     +1.000000  12   4 (2,2)   [2.2e-15 5.1e-15 7.3e-15 4.8e-14 5.5e+00]   4 (2,2)   [2.28e-12 2.29e-12 2.33e-12 2.34e-12 5.52e+00]
  +1.0000  +12.56637     +1.000000   8   4 (2,2)   [9.1e-16 3.1e-15 4.5e-15 6.4e-15 6.1e+00]   0 (0,0)   [1.14e-06 1.14e-06 1.14e-06 1.14e-06 6.13e+00]
  +1.0000  +12.56637     +1.000000  12   4 (2,2)   [2.8e-15 5.0e-15 2.3e-14 5.0e-14 6.1e+00]   4 (2,2)   [7.06e-12 7.11e-12 7.12e-12 7.16e-12 6.13e+00]
  -1.0000  +25.13274     -2.000000   8   4 (2,2)   [3.9e-15 5.0e-15 8.1e-15 1.3e-14 6.1e+00]   0 (0,0)   [2.09e-04 2.09e-04 2.09e-04 2.09e-04 6.13e+00]
  -1.0000  +25.13274     -2.000000  12   4 (2,2)   [1.4e-14 1.9e-14 3.2e-14 3.9e-14 6.1e+00]   4 (2,2)   [8.63e-09 8.63e-09 8.63e-09 8.63e-09 6.13e+00]
  +1.0000  +12.58637     +1.001592   8   4 (2,2)   [9.1e-16 3.1e-15 4.5e-15 6.4e-15 6.1e+00]   0 (0,0)   [9.75e-03 9.75e-03 9.75e-03 9.75e-03 6.13e+00]
  +1.0000  +12.58637     +1.001592  12   4 (2,2)   [2.8e-15 5.0e-15 2.3e-14 5.0e-14 6.1e+00]   0 (0,0)   [9.75e-03 9.75e-03 9.75e-03 9.75e-03 6.13e+00]
  +0.5000  +25.12274     +0.999602   8   4 (2,2)   [3.1e-15 8.9e-15 9.3e-15 1.8e-14 6.2e+00]   0 (0,0)   [2.49e-03 2.49e-03 2.49e-03 2.49e-03 6.24e+00]
  +0.5000  +25.12274     +0.999602  12   4 (2,2)   [2.0e-14 4.0e-14 4.3e-14 7.3e-14 6.2e+00]   0 (0,0)   [2.48e-03 2.48e-03 2.48e-03 2.48e-03 6.24e+00]
  +3.0000   +4.18879     +1.000000   8   4 (2,2)   [4.8e-15 7.5e-15 1.3e-14 1.5e-14 5.3e+00]   0 (0,0)   [3.52e-07 3.52e-07 3.52e-07 3.52e-07 5.27e+00]
  +3.0000   +4.18879     +1.000000  12   4 (2,2)   [1.4e-14 2.3e-14 4.7e-14 7.9e-14 5.3e+00]   4 (2,2)   [9.50e-13 9.53e-13 9.66e-13 9.78e-13 5.27e+00]
  +3.0000   +4.19179     +1.000716   8   4 (2,2)   [4.8e-15 7.5e-15 1.3e-14 1.5e-14 5.3e+00]   0 (0,0)   [3.62e-03 3.62e-03 3.62e-03 3.62e-03 5.27e+00]
  +3.0000   +4.19179     +1.000716  12   4 (2,2)   [1.4e-14 2.3e-14 4.7e-14 7.9e-14 5.3e+00]   0 (0,0)   [3.63e-03 3.63e-03 3.63e-03 3.63e-03 5.27e+00]
  +0.0010   +1.00000     +0.000080   8   4 (2,2)   [6.0e-15 6.0e-15 2.3e-14 3.0e-14 6.3e+00]   0 (0,0)   [5.00e-04 5.00e-04 5.00e-04 5.00e-04 6.28e+00]
  +0.0010   +1.00000     +0.000080  12   4 (2,2)   [6.7e-15 1.9e-14 2.6e-14 2.8e-14 6.3e+00]   0 (0,0)   [5.00e-04 5.00e-04 5.00e-04 5.00e-04 6.28e+00]
  +0.0001   +7.00000     +0.000056   8   4 (2,2)   [4.7e-15 8.9e-15 1.9e-14 5.0e-14 6.3e+00]   0 (0,0)   [3.50e-04 3.50e-04 3.50e-04 3.50e-04 6.28e+00]
  +0.0001   +7.00000     +0.000056  12   4 (2,2)   [4.5e-15 9.4e-15 1.1e-14 1.5e-14 6.3e+00]   0 (0,0)   [3.50e-04 3.50e-04 3.50e-04 3.50e-04 6.28e+00]

=== [C] Lemma 2.2 / Cor 2.3 for connections depending on x and y (random trig. polys, prescribed means) ===
  (A,B)=(+0.0000,+0.0000)  in (2piZ)^2: True  dim ker D = 4 (+2,-2)  smallest|lam|: [5.51e-16 3.35e-15 6.22e-15 1.93e-14 5.95e+00]
  (A,B)=(+6.2832,+0.0000)  in (2piZ)^2: True  dim ker D = 4 (+2,-2)  smallest|lam|: [3.56e-15 6.65e-15 3.24e-14 4.00e-14 5.83e+00]
  (A,B)=(+0.0000,-6.2832)  in (2piZ)^2: True  dim ker D = 4 (+2,-2)  smallest|lam|: [1.15e-15 7.23e-15 1.29e-14 1.49e-14 5.92e+00]
  (A,B)=(+6.2832,-6.2832)  in (2piZ)^2: True  dim ker D = 4 (+2,-2)  smallest|lam|: [1.21e-14 1.30e-14 1.57e-14 1.71e-14 6.07e+00]
  (A,B)=(+0.3000,+0.0000)  in (2piZ)^2: False  dim ker D = 0 (+0,-0)  smallest|lam|: [2.95e-01 2.95e-01 2.95e-01 2.95e-01 5.68e+00]
  (A,B)=(+0.0000,+0.0010)  in (2piZ)^2: False  dim ker D = 0 (+0,-0)  smallest|lam|: [9.81e-04 9.81e-04 9.81e-04 9.81e-04 5.94e+00]
  (A,B)=(+3.1416,+3.1416)  in (2piZ)^2: False  dim ker D = 0 (+0,-0)  smallest|lam|: [4.15e+00 4.15e+00 4.15e+00 4.15e+00 4.29e+00]
  (A,B)=(+6.3332,+0.0000)  in (2piZ)^2: False  dim ker D = 0 (+0,-0)  smallest|lam|: [4.93e-02 4.93e-02 4.93e-02 4.93e-02 5.83e+00]

=== [X] Theorem 1.2(iii): explicit kernel forms s_+(1+i vol), s_+(dx+i dy), s_-(1-i vol), s_-(dx-i dy) ===
  eps=+0.40: max|D omega| = s+(1+i vol): 1.5e-13, s+(dx+i dy): 1.5e-13, s-(1-i vol): 1.3e-13, s-(dx-i dy): 1.3e-13
  eps=-1.30: max|D omega| = s+(1+i vol): 2.2e-13, s+(dx+i dy): 2.2e-13, s-(1-i vol): 2.7e-13, s-(dx-i dy): 2.7e-13
  eps=+2.70: max|D omega| = s+(1+i vol): 2.1e-13, s+(dx+i dy): 2.1e-13, s-(1-i vol): 2.0e-13, s-(dx-i dy): 2.0e-13

=== [M] full 2D box vs x-mode blocks: kernel only in the k_x = 0 block; lowest |lam| per block ===
   E: k_x=-3: 1.860e+01; k_x=-2: 1.238e+01; k_x=-1: 6.185e+00; k_x=+0: 2.875e-14; k_x=+1: 6.185e+00; k_x=+2: 1.238e+01; k_x=+3: 1.860e+01
  fE: k_x=-3: 1.860e+01; k_x=-2: 1.239e+01; k_x=-1: 6.199e+00; k_x=+0: 4.328e-01; k_x=+1: 6.199e+00; k_x=+2: 1.239e+01; k_x=+3: 1.860e+01

=== [P] Proposition 4.1: products T^2 x T^1 and T^2 x T^2 (block (k_x,k_z,k_w)=0, full exterior algebra) ===
  n=3 eps=+0.30 c=+1.70  E: dim ker D =  8; smallest|lam| = [4.84519413e-15 1.30079824e-14 1.73188564e-14] next after kernel = 6.288e+00; b^cap = [np.int64(0), np.int64(2), np.int64(2), np.int64(0)]; b^pi = [np.int64(2), np.int64(4), np.int64(4), np.int64(2)]; (b_ev, b_odd) = (np.int64(4), np.int64(4))
  n=3 eps=+0.30 c=+1.70 fE: dim ker D =  0; smallest|lam| = [0.25441583 0.25441583 0.25441583] next after kernel = 2.544e-01
  n=3 eps=-1.00 c=+2.00  E: dim ker D =  8; smallest|lam| = [2.08503052e-17 2.80653317e-16 3.92386586e-15] next after kernel = 6.336e+00; b^cap = [np.int64(0), np.int64(2), np.int64(2), np.int64(0)]; b^pi = [np.int64(2), np.int64(4), np.int64(4), np.int64(2)]; (b_ev, b_odd) = (np.int64(4), np.int64(4))
  n=3 eps=-1.00 c=+2.00 fE: dim ker D =  0; smallest|lam| = [0.97248119 0.97248119 0.97248119] next after kernel = 9.725e-01
  n=4 eps=+0.30 c=+1.70  E: dim ker D = 16; smallest|lam| = [4.18331107e-15 6.26555598e-15 8.31174054e-15] next after kernel = 6.288e+00; ker D^+ = 8, ker D^- = 8; b^cap = [np.int64(0), np.int64(2), np.int64(4), np.int64(2), np.int64(0)]; b^pi = [np.int64(2), np.int64(6), np.int64(8), np.int64(6), np.int64(2)]; (b_ev, b_odd) = (np.int64(8), np.int64(8))
  n=4 eps=+0.30 c=+1.70 fE: dim ker D =  0; smallest|lam| = [0.25441583 0.25441583 0.25441583] next after kernel = 2.544e-01
  n=4 eps=-1.00 c=+2.00  E: dim ker D = 16; smallest|lam| = [3.43843845e-16 6.61002795e-16 1.08636785e-15] next after kernel = 6.336e+00; ker D^+ = 8, ker D^- = 8; b^cap = [np.int64(0), np.int64(2), np.int64(4), np.int64(2), np.int64(0)]; b^pi = [np.int64(2), np.int64(6), np.int64(8), np.int64(6), np.int64(2)]; (b_ev, b_odd) = (np.int64(8), np.int64(8))
  n=4 eps=-1.00 c=+2.00 fE: dim ker D =  0; smallest|lam| = [0.97248119 0.97248119 0.97248119] next after kernel = 9.725e-01
  T^4, eps=0.3, c=1.7: min |lam| over the 26 blocks (k_x,k_z,k_w) in {-1,0,1}^3 minus 0 = 6.2689  (>= 2pi - r = 5.6915)

=== [R] Proposition 4.2: Euclidean rank-2 bundle d + eps cos(2 pi y) dx (x) J (complex and real kernels) ===
  eps=+0.40 c= +1.3000  E: complex dim ker = 8; real form of D: max|Im| = 7.7e-16, real dim ker = 8; smallest |lam| = [2.22046071e-14], next = 6.258e+00
  eps=+0.40 c= +1.3000 fE: complex dim ker = 0; real form of D: max|Im| = 7.7e-16, real dim ker = 0; smallest |lam| = [0.25894226], next = 2.589e-01
  eps=-0.90 c= +2.2000  E: complex dim ker = 8; real form of D: max|Im| = 7.7e-16, real dim ker = 8; smallest |lam| = [4.13672139e-15], next = 6.160e+00
  eps=-0.90 c= +2.2000 fE: complex dim ker = 0; real form of D: max|Im| = 7.7e-16, real dim ker = 0; smallest |lam| = [0.96788064], next = 9.679e-01
  eps=+0.50 c=+25.1327  E: complex dim ker = 8; real form of D: max|Im| = 7.7e-16, real dim ker = 8; smallest |lam| = [8.87227605e-15], next = 6.244e+00
  eps=+0.50 c=+25.1327 fE: complex dim ker = 0; real form of D: max|Im| = 7.7e-16, real dim ker = 0; smallest |lam| = [8.65553921e-07], next = 8.656e-07

=== [D] Proposition 4.3: spin Dirac operator (trivial spin structure), two Clifford representations ===
  paper    Clifford relations (True, True, True, True, True); eps=+0.35 c=+1.900: E: ker 2 (next 6.26e+00, herm.defect 0e+00); fE: ker 0 (next 3.31e-01, herm.defect 0e+00)
  paper    Clifford relations (True, True, True, True, True); eps=-1.20 c=+0.800: E: ker 2 (next 6.07e+00, herm.defect 0e+00); fE: ker 0 (next 4.63e-01, herm.defect 0e+00)
  paper    Clifford relations (True, True, True, True, True); eps=+1.00 c=+12.566: E: ker 2 (next 6.13e+00, herm.defect 0e+00); fE: ker 2 (next 6.13e+00, herm.defect 0e+00)
  i*Pauli  Clifford relations (True, True, True, True, True); eps=+0.35 c=+1.900: E: ker 2 (next 6.26e+00, herm.defect 0e+00); fE: ker 0 (next 3.31e-01, herm.defect 0e+00)
  i*Pauli  Clifford relations (True, True, True, True, True); eps=-1.20 c=+0.800: E: ker 2 (next 6.07e+00, herm.defect 0e+00); fE: ker 0 (next 4.63e-01, herm.defect 0e+00)
  i*Pauli  Clifford relations (True, True, True, True, True); eps=+1.00 c=+12.566: E: ker 2 (next 6.13e+00, herm.defect 0e+00); fE: ker 2 (next 6.13e+00, herm.defect 0e+00)

=== [B] Proposition 4.4 on T^2 (b^cap, b^pi, parity) and Delta_k counts in [0,1] ===
  eps=+0.30 c=+1.20  E: dim ker=4 b^cap=[np.int64(0), np.int64(2), np.int64(0)] b^pi=[np.int64(2), np.int64(2), np.int64(2)] (b_ev,b_odd)=(2,2); #eig(Delta_k) in [0,1] = [1, 2, 1]; lowest eigs Delta_0: [ 0.045  39.3443 39.3443], Delta_1: [1.1512e-11 1.4713e-11 3.9300e+01], Delta_2: [ 0.045  39.3443 39.3443]
  eps=+0.30 c=+1.20 fE: dim ker=0; #eig(Delta_k) in [0,1] = [1, 2, 1]; lowest eigs Delta_0: [ 0.0774 37.2938 39.3761], Delta_1: [3.2252e-02 3.2252e-02 3.7310e+01], Delta_2: [ 0.0774 37.2938 39.3761]
  eps=+1.00 c=+1.00  E: dim ker=4 b^cap=[np.int64(0), np.int64(2), np.int64(0)] b^pi=[np.int64(2), np.int64(2), np.int64(2)] (b_ev,b_odd)=(2,2); #eig(Delta_k) in [0,1] = [1, 2, 1]; lowest eigs Delta_0: [ 0.4992 38.0757 38.0757], Delta_1: [-1.1286e-11 -3.2144e-12  3.7614e+01], Delta_2: [ 0.4992 38.0757 38.0757]
  eps=+1.00 c=+1.00 fE: dim ker=0; #eig(Delta_k) in [0,1] = [1, 2, 1]; lowest eigs Delta_0: [ 0.7492 33.9401 38.2821], Delta_1: [ 0.2374  0.2374 34.1533], Delta_2: [ 0.7492 33.9401 38.2821]
  eps=-0.60 c=+2.40  E: dim ker=4 b^cap=[np.int64(0), np.int64(2), np.int64(0)] b^pi=[np.int64(2), np.int64(2), np.int64(2)] (b_ev,b_odd)=(2,2); #eig(Delta_k) in [0,1] = [1, 2, 1]; lowest eigs Delta_0: [ 0.1799 38.9518 38.9518], Delta_1: [-4.0542e-12  9.3659e-12  3.8777e+01], Delta_2: [ 0.1799 38.9518 38.9518]
  eps=-0.60 c=+2.40 fE: dim ker=0; #eig(Delta_k) in [0,1] = [1, 2, 1]; lowest eigs Delta_0: [ 0.6983 31.1286 39.433 ], Delta_1: [ 0.5085  0.5085 31.2131], Delta_2: [ 0.6983 31.1286 39.433 ]
  eps=+1.00 c=+0.50  E: dim ker=4 b^cap=[np.int64(0), np.int64(2), np.int64(0)] b^pi=[np.int64(2), np.int64(2), np.int64(2)] (b_ev,b_odd)=(2,2); #eig(Delta_k) in [0,1] = [1, 2, 1]; lowest eigs Delta_0: [ 0.4992 38.0757 38.0757], Delta_1: [-1.1286e-11 -3.2144e-12  3.7614e+01], Delta_2: [ 0.4992 38.0757 38.0757]
  eps=+1.00 c=+0.50 fE: dim ker=0; #eig(Delta_k) in [0,1] = [1, 2, 1]; lowest eigs Delta_0: [ 0.5617 36.8892 38.1275], Delta_1: [ 0.0594  0.0594 37.0846], Delta_2: [ 0.5617 36.8892 38.1275]
  eps=+2.00 c=+1.00  E: dim ker=4 b^cap=[np.int64(0), np.int64(2), np.int64(0)] b^pi=[np.int64(2), np.int64(2), np.int64(2)] (b_ev,b_odd)=(2,2); #eig(Delta_k) in [0,1] = [0, 2, 0]; lowest eigs Delta_0: [ 1.9873 34.7237 34.7237], Delta_1: [-7.8312e-12 -1.8344e-12  3.3160e+01], Delta_2: [ 1.9873 34.7237 34.7237]
  eps=+2.00 c=+1.00 fE: dim ker=0; #eig(Delta_k) in [0,1] = [0, 2, 0]; lowest eigs Delta_0: [ 2.987  29.8689 35.2372], Delta_1: [ 0.8049  0.8049 30.9597], Delta_2: [ 2.987  29.8689 35.2372]

=== [S] Proposition 5.1: small eigenvalues (2D box K=10 for counts; 1D y-reduced SVD, |k_y|<=200, for sigma) ===
  eps      c        r      d=dist(eps c/2,2piZ)  #eig in[-r,r] E / fE   max|lam|<=r (E)  small eigs of D_f*E (2D)                         sigma_+ (1D)   sigma_- (1D)   e^{-|eps|/pi} d <= sigma <= d   gap: min|lam|>r  (E, fE)  vs 2pi-r
  +0.10   +1.00  0.1414  0.050000             4 / 4          6.5e-14      [-0.04998733 -0.04998733 +0.04998733 +0.04998733]  0.04998733     0.04998733     [0.048434, 0.050000] OK   6.2816, 6.2337  6.1418
  +0.30   +2.00  0.6708  0.300000             4 / 4          2.0e-14      [-0.29931099 -0.29931099 +0.29931099 +0.29931099]  0.29931099     0.29931099     [0.272677, 0.300000] OK   6.2689, 5.9884  5.6124
  -0.50   +1.50  0.9014  0.375000             4 / 4          3.2e-14      [-0.37260273 -0.37260273 +0.37260273 +0.37260273]  0.37260273     0.37260273     [0.319824, 0.375000] OK   6.2440, 5.9229  5.3818
  +1.00   +0.50  1.1180  0.250000             4 / 4          4.2e-14      [-0.24374774 -0.24374774 +0.24374774 +0.24374774]  0.24374774     0.24374774     [0.181844, 0.250000] OK   6.1330, 6.0897  5.1652
  +0.20  +10.00  2.0100  1.000000             4 / 4          3.3e-14      [-0.99887365 -0.99887365 +0.99887365 +0.99887365]  0.99887365     0.99887365     [0.938322, 1.000000] OK   6.2768, 5.2861  4.2732
  +1.00   +2.90  3.0676  1.450000             4 / 4          4.2e-14      [-1.40480022 -1.40480022 +1.40480022 +1.40480022]  1.40480022     1.40480022     [1.054697, 1.450000] OK   6.1330, 4.9212  3.2156
  -0.90   -3.00  2.8460  1.350000             4 / 4          3.6e-14      [-1.31683820 -1.31683820 +1.31683820 +1.31683820]  1.31683820     1.31683820     [1.013719, 1.350000] OK   6.1603, 5.0014  3.4371
  +2.00   +1.00  2.8284  1.000000             4 / 4          2.8e-14      [-0.89716041 -0.89716041 +0.89716041 +0.89716041]  0.89716041     0.89716041     [0.529078, 1.000000] OK   5.7584, 5.5641  3.4548
  +0.05  +30.00  1.5008  0.750000             4 / 4          3.1e-14      [-0.74994964 -0.74994964 +0.74994964 +0.74994964]  0.74994964     0.74994964     [0.738158, 0.750000] OK   6.2828, 5.5334  4.7824

# total time 419.8 s
